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In \href{https://link.aps.org/doi/10.1103/PhysRevD.92.103004}{Phys. Rev. D 92 (2015) 103004}, simple analytical solutions of the Friedman equations were obtained for a universe having stiff matter component in the early universe together with a dark matter, and a dark energy component. In this analysis, the universe is considered to be made of a dark fluid which behaves as a stiff matter in the early phase of the universe (when the internal energy dominates). It is also more logical to consider quantum gravitational effects in the early phase of the cosmological evolution. In this analysis, following \href{https://link.aps.org/doi/10.1103/PhysRevD.65.043508}{Phys. Rev. D 65 (2002) 043508}, we consider renormalization group improved modified Friedmann equations where the Newton's gravitational constant ($G$) and the cosmological constant ($\Lambda$) flows with the momentum scale $k$ of the universe. It is observed that for a universe undergoing a stiff matter era, radiation era, and matter era, inflation is absent in the early time regime of the universe when the flow of the Newton's gravitational constant and cosmological constant is under consideration. Using the identification of the momentum scale with the scale factor of the universe, we then explore the era $t>t_{\text{Pl}}$ which indicates a primarily matter dominated era with accelerated expansion due to the presence of dark energy. Finally, considering the total equation of state as a combination of linear equation of state along with a polytropic equation of state, we observe that after the Planck-time the universe can undergo an inflationary phase and we find out that the inflation is enhanced by quantum gravitational effects arising due to the consideration of renormalization group approach to quantum gravity., Comment: 17 pages LATEX, comments are welcome. OTM

We investigate relativistic effects on the performance of a quantum battery in an open quantum framework. We consider an Unruh-DeWitt detector driven by a coherent classical pulse as a quantum battery that is interacting with a massless scalar field through a quadratic coupling. The battery follows a trajectory composed of uniform acceleration along one direction, combined with constant four-velocity components in the orthogonal plane to the acceleration. Accelerated motion degrades the performance of the quantum battery rapidly in the absence of the orthogonal velocity component. We show that the quadratic scalar field coupling enhances coherence and stability in the presence of orthogonal velocity. We observe that decoherence is mitigated significantly, resulting in remarkable improvement in the battery capacity and efficiency compared to the case of the usual linear field coupling. This opens up the possibility of nonlinear environmental coupling enabling stored energy to be retained over longer durations, leading to more efficient operation of quantum devices., Comment: 15 pages LaTeX; Comments are welcome

The effect of noise induced by gravitons on a Bose-Einstein condensate has been explored in (Phys. Rev. D 110 (2024) 026014; https://link.aps.org/doi/10.1103/PhysRevD.110.026014). In the previous paper, we investigated the effects of graviton while detecting a gravitational wave using a Bose-Einstein condensate. In this work we shall explicitly calculate the decoherence due to the noise of gravitons between two momentum states of the Bose-Einstein condensate. This decoherence happens due to Bremsstrahlung from the Bose-Einstein condensates due to the effect of the noise induced by gravitons. It is also observed that the two states become entangled because of the existence of a surrounding graviton field which degrades over time via means of this gravitational Bremsstrahlung. Using this property of the Bose-Einstein condensate in a quantum gravity background, we propose an experimental test via the use of atom lasers (generated from the condensate) which would, in principle, help to detect gravitons in future generations of very advanced ultra-cold temperature experiments., Comment: 18 pages LATEX. Comments are welcome. Om Thakur Ma

We investigate the thermodynamics of a Schwarzschild black hole, surrounded by the quintessence energy-matter in the linear and quadratic generalized uncertainty principle framework. Considering the variance in the position to be of the order of the event horizon radius and equating the variance in the momentum to the Hawking temperature of the black hole, we substitute these variances in the deformed algebra. From there we obtained the generalized uncertainty principle-modified black hole temperature and eventually the specific heat of the black hole. Then we calculate the critical as well as the remnant mass and obtain the entropy relation. We observe that the entropy relation includes the usual leading order ``\textit{area divided by four}" term, sub-leading logarithmic term, and higher order inverse of the area corrections. Finally, calculating the energy output as a function of time, we obtain the evaporation time of the black hole. The results show the dependence of the quintessence parameter on the thermodynamic quantities in the framework of linear and quadratic generalized uncertainty principle., Comment: 17 pages LATEX; Comments are welcome

In this work, we have studied various mixed state information theoretic quantities for an excited state of Lifshitz spacetime in $3+1$-dimensions. This geometry is the gravity dual to a class of $2+1$-dimensional quantum field theories having Lifshitz symmetry. We have holographically calculated mutual information, entanglement wedge cross section, entanglement negativity and mutual complexity for strip like subsystems at the boundary. For this we have used the results of holographic entanglement entropy and complexity present in the literature. We first calculate all of these mentioned quantities for the pure state of Lifshitz spacetime. Then we have moved on to calculate all these quantities for excited state of the Lifshitz spacetime. The gravity dual of excited state of Lifshitz systems in field theory can be obtained by applying constant perturbations along the boundary direction. Further, we would like to mention that for the simplicity of calculation we are only considering results up to the first order in perturbation. The change in the obtained holographic information theoretic quantities are then related to entanglement entropy, entanglement pressure, entanglement chemical potential and charge using the stress tensor complex. These relations are analogous to the first law of entanglement thermodynamics given earlier in the literature. All the calculations are carried out for both values of dynamical scaling exponent ($z$) present in the Lifshitz field theory., Comment: v1: 51 pages LaTex, multiple figures, v2: matches with the published version

In this paper we consider a single particle, spin-momentum entangled state and measure the effect of relativistic boost on quantum coherence. The effect of the relativistic boost on single-particle generalized Gaussian wave packets is studied. The coherence of the wave function as measured by the boosted observer is studied as a function of the momentum and the boost parameter. Using various formulations of coherence, it is shown that in general the coherence decays with the increase in momentum of the state, as well as the boost applied to it. A more prominent loss of coherence due to relativistic boost is observed for a single particle electron than that of a neutron. The analysis is carried out with generalized Gaussian wave packet of the form $\mathcal{N} p^n \exp(-\frac{p^2}{\sigma^2})$ with $n$ being the ``generalization parameter" and $\mathcal{N}$ denoting the appropriate normalization constant. We also obtain a range for parameter $n$ appearing in the wave packet. The upper bound is found to have a dependence on the mass of the particle and the width of the Gaussian wave packet. We have obtained the Frobenius-norm measure of coherence, $l_1$ and $l_2$ norm measure of coherence, and relative entropy of coherence for a (1+1) and (3+1)-dimensional analysis. Corresponding to each of the cases, we observe that the $l_1$ norm measure of coherence is equal to the Frobenius norm measure of coherence. We have analyzed the scenario for which such a beautiful coincidence can occur. Finally, we have plotted different measures of coherence for the electron as well as the neutron for different values of the width of the wave-function $\sigma$, boost parameter $\beta$, and generalization parameter $n$., Comment: 16 pages LATEX

In this work, we consider a general gravitational wave detector of gravitational wave interacting with an incoming gravitational wave carrying plus polarization only placed inside a harmonic trap. This model can be well acquainted with the description of a resonant detector of gravitational wave as well. The well known detector-gravitational wave interaction scenario uses the method of a semi classical approach where the detector is treated quantum mechanically but the gravitational wave is considered at a classical level. In our analysis, we use a discrete mode decomposition of the gravitational wave perturbation which results in a Hamiltonian involving the position and momentum operators corresponding to the gravitational wave and the harmonic oscillator. We have then calculated the transition probability for the harmonic oscillator-gravitational wave tensor product state for going from an initial state to some unknown final state. Using the energy flux relation of the gravitational waves, we observe that if we consider the total energy as a combination of the number of gravitons in the initial state of the detector then the transition probability for the resonant absorption case scenario takes the analytical form which is exactly similar to the semi-classical absorption case. In case of the emission scenario, we observe a spontaneous emission of a single graviton which was completely absent in the semi-classical analouge of this model. This therefore gives a direct signature of linearized quantum gravity., Comment: 8 pages LATEX; Comments are welcome. Om Thakur Ma

In an earlier analysis \href{https://link.aps.org/doi/10.1103/PhysRevD.105.085007}{Phys. Rev. D 105 (2022) 085007}, we have explored the event of acceleration radiation for an atom freely falling into the event horizon of a quantum-corrected Schwarzschild black hole. We want to explore the acceleration-radiation when the atom is freely falling into the event horizon of a charged quantum-corrected black hole. We consider the quantum effects of the electromagnetic field along with the gravitational field in an asymptotic safety regime. Introducing the quantum improved Reisner-Nordstr\"{o}m metric, we have calculated the excitation probability of a two-level atom freely falling into the event horizon of quantum improved charged black hole. Recently, in the case of the braneworld black hole (where the tidal charge has the same dimension as the square of the charge of a Reissner-Nordstr\"{o}m black hole in natural units), we have observed from the form of the transition probability that the temperature will have no contribution in the first order of the tidal charge. We observe that for a quantum corrected Reissner-Nordstr\"{o}m black hole, there is a second-order contribution in the charge parameter in the temperature that can be read off from the transition probability. Next, we calculate the HBAR entropy in this thought experiment and show that this entropy has a leading order Bekenstein-Hawking entropy term along with some higher order correction terms involving logarithmic as well as fractional terms of the black hole area due to infalling photons. We have finally investigated the validity of Wien's displacement law and compared the critical value of the field wavelength with the general Schwarzschild black hole and its corresponding quantum-corrected case., Comment: 12 pages LATEX, comments are welcome

We consider a Bose-Einstein condensate interacting with a gravitational wave for the case when the gravitational fluctuations are quantized in order to incorporate quantum gravity effects into the theory. We observe that the solution of the time-dependent part of the pseudo-Goldstone boson has infusions from the noise induced by gravitons and the corresponding differential equation of motion is Langevin-like. Using this result, we obtain the quantum gravity modified Fisher information which has been termed as the quantum gravitational Fisher information (QGFI). The inverse square root of the stochastic average of the QGFI gives the minimum uncertainty in the measurement of the gravitational wave amplitude. The minimum uncertainty does not go to infinity as the measurement time approaches zero in a quantum gravity setup rather it has a measurable finite value for gravitons with high squeezing. Finally, we observe the effect of decoherence due to interacting phonon modes in the QGFI and observe a less obvious decoherence effect for higher squeezing of the initial graviton., Comment: 8 pages LATEX. This is a letter version of arXiv:2403.18460 [hep-th]. OTM

The effect of noise induced by gravitons has been investigated using a Bose-Einstein condensate. The gravitational wave perturbation is then considerd as a sum of discrete Fourier modes in the momentum space. Coming to an operatorial representation and quantizing the phase space variables via appropriately introduced canonincal commutation relations between the canonically conjugate variables corresponding to the graviton and bosonic part of the total system, one obtains a proper quantum gravity setup. Then we obtain the Bogoliubov coefficients from the solution of the time-dependent part of the pseudo-Goldstone boson and construct the covariance metric for the bosons initially being in a squeezed state. Using the stochastic average of the Fisher information, we obtain a lower bound on the amplitude parameter of the gravitational wave. As the entire calculation is done at zero temperature, the bosonic system, by construction, will behave as a Bose-Einstein condensate. For a Bose-Einstein condensate with a single mode, we observe that the lower bound of the expectation value of the square of the uncertainty in the amplitude measurement does not become infinite when the total observational term approaches zero. In order to sum over all possible momentum modes, we next consider a noise term with a suitable Gaussian weight factor which decays over time. We then obtain the lower bound on the final expectation value of the square of the variance in the amplitude parameter. Because of the noise induced by the graviton, there is a minimum value of the measurement time below which it is impossible to detect any gravitational wave using a Bose-Einstein condensate. Finally, we consider interaction between the phonon modes of the Bose-Einstein condensate which results in the decoherence. We observe that the decoherence effect becomes significant for gravitons with minimal squeezing., Comment: 26 pages LATEX. Om Thakur Ma

This paper investigates the dynamics of current and efficiency in a bosonic system consisting of a central system interacting with two reservoirs at different temperatures. We derive a master equation describing the time evolution of the density matrix of the system, accounting for the interactions and energy transfer between the components. We quantify the current, representing the flow of bosons through the system and analyse its dependence on the system's parameters and temperatures of the thermal reservoirs. In the steady state regime, we derived an expression for the efficiency of the energy transfer process. Our analysis show that quantum effects, such as the dependence on temperature and the quantum correction factor, can significantly impact energy transfer efficiency. In particular, we observe that at high temperatures, the efficiency of the quantum system is greater than the Carnot efficiency. The insights gained from this analysis may have implications in various fields, including quantum computing and energy harvesting, where optimising energy utilisation is crucial.

In this work, we extend the study in \href{https://link.springer.com/article/10.1007/JHEP11(2022)013}{JHEP11(2022)013} incorporating the AdS/CFT duality to establish a relationship between the local temperatures (Tolman temperatures) of a large (AdS) spherical and a (AdS) planar Schwarzschild black hole near the AdS boundary considering Gauss-Bonnet curvature correction in the gravitational action. We have shown that the higher curvature corrections appear in the local temperature relationship due to the inclusion of Gauss-Bonnet term in the bulk. By transforming the metric into Fefferman-Graham form, we have calculated the energy density of the conformal fluid at the boundary. The obtained result contains finite coupling corrections which are holographically induced by the Gauss-Bonnet curvature correction in the bulk theory. Following the well known approach of fluid/gravity duality, the energy density of the conformal fluid at the boundary is then compared with the black body radiation energy density. This comparison shows that the energy density is proportional to the temperature of the conformal fluid. The temperature of the conformal fluid is then shown to be related to the Tolman temperature of the black hole which then eventually helps us to establish both the Hawking temperature and Tolman temperature relationship between large spherically symmetric and planar Schwarzschild black holes in Gauss-Bonnet gravity near the AdS boundary., Comment: v1: 17 pages LaTex, v2: 23 pages & multiple new figures, to appear in Classical and Quantum Gravity

In this study, we revisit the Fulling-Davies-Unruh effect in the context of two-level single and entangled atomic systems that are static in a thermal bath. We consider the interaction between the systems and a massless scalar field, covering the scenarios of free space as well as within a cavity. Through the calculation of atomic transition rates and comparing with the results of [\textcolor{blue}{\textit{Phys. Rev. D 108 (2023) 085018}}], it is found that in free space there is an equivalence between the upward and downward transition rates of a uniformly accelerated atom with respect to an observer with that of a single atom which is static with respect to the observer and immersed in a thermal bath, as long as the temperature of the thermal bath matches the Unruh temperature. This equivalence between the upward and downward transition rates breaks down in the presence of a cavity. For two-atom systems, considering the initial state to be in a general pure entangled form, we find that in this case the equivalence between the upward and downward transition rates of the accelerated and static thermal bath scenarios holds only under specific limiting conditions in free space, but breaks down completely in a cavity setup. Though the ratio of the upward and downward transition rates in the thermal bath matches exactly with those of the accelerated systems in free space as well as inside the cavity., Comment: 36 pages LaTeX, Comments are welcome

The behaviour of a chaotic system and its effect on existing quantum correlation has been holographically studied in presence of non-conformality. Keeping in mind the gauge/gravity duality framework, the non-conformality in the dual field theory has been introduced by considering a Liouville type dilaton potential for the gravitational theory. The resulting black brane solution is associated with a parameter $\eta$ which represents the deviation from conformality. The parameters of chaos, namely, the Lyapunov exponent and butterfly velocity are computed by following the well-known shock wave analysis. The obtained results reveal that presence of non-conformality leads to suppression of the chaotic nature of a system. Further, for a particular value of the non-conformal parameter $\eta$, the system achieves Lyapunov stability resulting from the vanishing of both the Lyapunov exponent and as well as butterfly velocity. Interestingly, this particular value of $\eta$ matches with the previously given upper bound of $\eta$ known as Gubser bound in the literature. The effects of chaos and non-conformality on the existing correlation of a thermofield doublet state have been quantified by holographically computing the thermo mutual information in both the presence and absence of the shock wave. Furthermore, the entanglement velocity is also computed and the effect of non-conformality on it has been observed. Finally, the obtained results for the Lyapunov exponent and the butterfly velocity have also been computed from the pole-skipping analysis. The results from the two approaches agree with each other., Comment: v1: 28 pages, 12 figures; v2: Some text along with some new equations have added, v3: matches with the version to appear in Phys. Rev. D

The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in \href{https://link.aps.org/doi/10.1103/PhysRevD.107.066024}{Phys. Rev. D 107 (2023) 066024}. There the authors have calculated the quantum gravity modified Newton's law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum., Comment: 11 pages LATEX

The concept of horizon brightened acceleration radiation (HBAR) has brought to us a distinct mechanism of particle production in curved spacetime. In this manuscript we examine the HBAR phenomena for a braneworld black hole (BBH) which emerges as an effective theory in our $(3+1)$ dimensional universe due to the higher dimensional gravitational effects. Despite being somewhat similar to the Reissner-Nordstr$\ddot{\rm o}$m solution in general relativity, the BBH is unique with respect to its charge term which is rather the tidal charge. In this background, we study the transition probability of the atom due to the atom-field interaction and the associated HBAR entropy. Both the quantities acquire modifications over the standard Schwarzschild results and turn out to be the function of the tidal charge. This modifications appear solely due to the bulk gravitational effects as induced on the 3-brane. Studying the Wien's displacement, we observe an important feature that the wavelengths of HBAR corresponding to the Schwarzschild and the BBH, deviate from each other depending on their masses. This deviation is found to be more pronounced for the mass values slightly greater or comparable to the Planck mass., Comment: 13 pages, 2 figures

This work explores the behaviour of a noncommutative harmonic oscillator in a time-dependent background, as previously investigated in [1]. Specifically, we examine the system when expressed in terms of commutative variables, utilizing a generalized form of the standard Bopp-shift relations recently introduced in [2]. We solved the time dependent system and obtained the analytical form of the eigenfunction using the method of Lewis invariants, which is associated with the Ermakov-Pinney equation, a non-linear differential equation. We then obtain exact analytical solution set for the Ermakov-Pinney equation. With these solutions in place, we move on to compute the dynamics of the energy expectation value analytically and explore their graphical representations for various solution sets of the Ermakov-Pinney equation, associated with a particular choice of quantum number. Finally, we determined the generalized form of the uncertainty equality relations among the operators for both commutative and noncommutative cases. Expectedly, our study is consistent with the findings in [1], specifically in a particular limit where the coordinate mapping relations reduce to the standard Bopp-shift relations., Comment: 19 pages Latex, To appear in International Journal of Theoretical Physics

Motivated by the recent development in quantum cosmology, we revisit the anisotropic Kantowski-Sachs model in the light of a Lorentzian path integral formalism. Studies so far have considered the Euclidean method where the choice of the lapse integration contour is constrained by certain physical considerations rather than mathematical justification. In this paper, we have studied the Hartle-Hawking no-boundary proposal along with the use of Picard-Lefschetz theory in performing the lapse integration. In an isotropic limit, we show our results agree with the studies made in FLRW cosmology. We also observe that in the large scale structure the no-boundary proposal tends towards a conical singularity at the beginning of time. We have also performed a massless scalar perturbation analysis with no back reaction. This reveals that if there were any perturbation present at the beginning of the universe then that would flare up at the final boundary., Comment: 9 pages, 4 figures

In this work, we consider a resonant bar detector of gravitational wave in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis [http://dx.doi.org/10.1088/1361-6382/abac45, Class. Quantum Grav. 37 (2020) 195006]. We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis., Comment: 19 pages LATEX. Comments are welcome

We investigate entanglement degradation in the vicinity of a quantum corrected black hole. We consider a biprtite system (Alice-Rob) with Alice freely falling (radially) into the event horizon of a quantum corrected black hole and Rob being in the vicinity of the event horizon of the black hole. We consider a maximally entangled state (in the Fock basis) and start with the basic assumption that Rob is an uniformly accelerated observer. We then give a pedagogical analysis of the relation involving the Minkowski vaccum state and Rindler number states. Following the analogy given in https://link.aps.org/doi/10.1103/PhysRevD.82.064006 {Phys. Rev. D 82 (2010) 064006}, we establish the relation between the Hartle-Hawking vacuum state and Boulware and Anti-Bouware number states from the Minkowski-Rindler relation. We then write down the quantum corrected black hole metric by making use of the near horizon approximation in an appropriate form. Next, we obtain the analytical forms of logarithmic negativity and mutual information and plot as a function of Rob's distance from the $r=0$ point. We observe that the entanglement degradation slows down due to the incorporation of quantum gravity corrections in the Schwarzschild black hole. This observation may lead to identification of quantum gravity signatures in future generation of advanced observational scenarios. We can also interpret this effect as a noisy quantum channel with an operator sum representation of a completely positive and trace preserving (CPTP) map. We then finally obtain the entanglement fidelity using this operator sum representation., Comment: Comments are welcome

Two different entanglement measures for mixed states, namely, the entanglement of purification and entanglement negativity has been holographically computed for the dipole deformed supersymmetric Yang-Mills (SYM) theory by considering its gravity dual. The dipole deformation induces non-locality in the SYM theory which is characterized by a length-scale $a=\lambda^{\frac{1}{2}}\tilde{L}$. Considering a strip like subsystem of length $\frac{l}{a}$ (in dimensionless form), we first analytically calculate the holographic entanglement entropy for and compare the obtained results with that of obtained numerically.~The analytical calculations have been carried out by considering $au_t \leq 1$,~$1\leq au_t < au_b$ and $au_t\sim au_b$, where $au_b$ is the UV cut-off. The choice of these regions enable us to identify the expansion parameters needed to carry out binomial expansions. The entanglement measures expectedly displays a smooth behaviour with respect to the subsystem size as the geometry has a smooth transition between the mentioned regions. Using these results, the holographic mutual information is then computed for two disjoint subsystems $A$ and $B$. Based upon the $E_{P}=E_{W}$ duality, the entanglement of purification ($E_{P}$) is then computed and the effects of dipole deformation in this context have been studied. Finally, we proceed to compute entanglement negativity for this theory and compare the obtained result with that of the standard SYM theory in order to get a better understanding about the effects of the non-locality., Comment: 23 pages Latex,7 figures

In this work, we consider a gravitational wave interacting with a quantum harmonic oscillator in the transverse-traceless gauge. We take the gravitational wave to be carrying the signatures of both plus and cross polarization at first. We then try to obtain a suitable form of the Lewis invariant using the most general form possible while considering only quadratic order contributions from both position and momentum variables. In order to progress further, we then drop the cross terms obtaining a separable Hamiltonian in terms of the first and the second spatial coordinates. We then obtain two Lewis invariants corresponding to each separable parts of the entire Hamiltonian of the system. Using both Lewis invariants, one can obtain two Ermakov-Pinney equations, from which we finally obtain the corresponding Lewis phase and eventually the Berry phase for the entire system. Finally, we obtain some explicit expressions of the Berry phase for a plane polarized gravitational wave with different choices of the harmonic oscillator frequency., Comment: About to appear in Physica Scripta (16 pages LATEX)

In this work, we study time-like and null geodesics in a charged black hole background immersed in perfect fluid dark matter (PFDM). Using the condition for circular geodesics, we evaluate the energy ($E$) and angular momentum ($L$) in terms of the radius ($r_c$) of the circular orbits. The existence and finite-ness of $E$ and $L$ constrain the possible range of PFDM parameter ($\chi$) and the radius of the circular orbit ($r_c$). We then use the Lyapunov exponent ($\lambda$) to study the stability of the geodesics. Then we analyze the critical exponent ($\gamma$) useful for determining the possibility of detection of gravitational wave signals. After that, we study the perturbation due to a massless scalar field in such a background and calculate the quasinrmal mode (QNM) frequencies and their dependence on PFDM parameter $\chi$ and black hole charge $Q$. Also, we compare the obtained QNM frequencies both in the exact case and in the eikonal limit. We also calculate the quality factor of the oscillating system and study its dependence on $\chi$ and $Q$. Finally, we evaluate the black hole shadow radius $R_s$ and graphically observe the effect of $\chi$ and $Q$ on it., Comment: 29 pages, 18 Figures; Comments are welcome

We investigate the transition rates of uniformly accelerated two-level single and entangled atomic systems in empty space as well as inside a cavity. We take into account the interaction between the systems and a massless scalar field from the viewpoint of an instantaneously inertial observer and a coaccelerated observer, respectively. The upward transition occurs only due to the acceleration of the atom. For the two-atom system, we consider that the system is initially prepared in a generic pure entangled state. In the presence of a cavity, we observe that for both the single and the two-atom cases, the upward and downward transitions are occurred due to the acceleration of the atomic systems. The transition rate manifests subtle features depending upon the cavity and system parameters, as well as the initial entanglement. It is shown that no transition occurs for a maximally entangled super-radiant initial state, signifying that such entanglement in the accelerated two-atom system can be preserved for quantum information procesing applications. Our analysis comprehensively validates the equivalence between the effect of uniform acceleration for an inertial observer and the effect of a thermal bath for a coaccelerated observer, in free space as well as inside a cavity, if the temperature of the thermal bath is equal to the Unruh temperature., Comment: 42 pages LaTeX, Comments are welcome

In this paper we have considered a quantized and linearly polarized gravitational wave interacting with a gravitational wave detector (interferometer detector) in the generalized uncertainty principle (GUP) framework. Following the analysis in Phys. Rev. Lett. 127 (2021) 081602 (https://link.aps.org/doi/10.1103/PhysRevLett.127.081602), we consider a quantized gravitational wave interacting with a gravitational wave detector (LIGO/VIRGO etc.) using a path integral approach. Although the incoming gravitational wave was quantized, no Planck-scale quantization effects were considered for the detector in earlier literatures. In our work, we consider a modified Heisenberg uncertainty relation with a quadratic order correction in the momentum variable between the two phase space coordinates of the detector. Using a path integral approach, we have obtained a stochastic equation involving the separation between two point-like objects. It is observed that random fluctuations (noises) and the correction terms due to the generalized uncertainty relation plays a crucial role in dictating such trajectories. Finally, we observe that the solution to the stochastic equation leads to time dependent standard deviation due to the GUP insertion, and for a primordial gravitational wave (where the initial state is a squeezed state) both the noise effect and the GUP effects exponentially enhance which may be possible to detect in future generation of gravitational wave detectors. We have also given a plot of the dimensionless standard deviation with time depicting that the GUP effect will carry a distinct signature which may be detectable in the future space based gravitational wave observatories., Comment: 7 pages LATEX; Comments are welcome

In this work, we show that the two proposals associated to the mutual information of matter fields can be given for an eternal Schwarzschild black hole in de-Sitter spacetime. These proposals also depicts the status of associated entanglement wedges and their roleplay in obtaining the correct Page curve of radiation. The first proposal has been give for the before Page time scenario, which shows that the mutual information $I(R_{H}^{+}:R_{H}^{-})$ vanishes at a certain value of the observer's time $t_{b_{H}}=t_{H}$ (where $t_{H}\ll \beta_{H}$). We claim that this is the Hartman-Maldacena time at which the entanglement wedge associated to $R_{H}^{+}\cup R_{H}^{-}$ gets disconnected and the fine-grained radiation entropy has the form $S(R_{H})\sim \log(\beta_{H})$. The second proposal depicts the fact that just after the Page time, when the replica wormholes are the dominating saddle-points, the mutual information $I(B_{H}^{+}:B_{H}^{-})$ vanishes as soon as the time difference $t_{a_{H}}-t_{b_{H}}$ equals the scrambling time. Holographically, this reflects that the entanglement wedge associated to $B_{H}^{+}\cup B_{H}^{-}$ jumps to the disconnected phase at this particular time-scale. Furthermore, these two proposals lead us to the correct time-evolution of the fine-grained entropy of radiation as portrayed by the Page curve. We have also shown that similar observations can be obtained for the radiation associated to the cosmological horizon., Comment: v1:18 pages LaTex with multiple figures, v2: matches with the accepted version; To appear in Physical Review D

In this work, we calculate the Hawking temperature for a quantum corrected black hole geometry using the $reflection$ $from$ $the$ $horizon$ method. We observe that quantum gravity corrections indeed show up in the Hawking temperature formula of the quantum corrected black hole. It is important to notice that the quantum gravity corrections arise in the Hawking temperature formula only due to the underlying quantum gravity corrections to the lapse function of the black hole metric rather than the semi-classical methods used in the analysis. We also substantiate our result by computing the Hawking temperature using the tunneling approach., Comment: This manuscript is accepted for publication is Europhysics Letters

Entropic force has been drawing the attention of theoretical physicists following E. Verlinde's work in 2011 to derive Newton's second law and Einstein's field equations of general relativity. In this paper, we extend the idea of entropic force to the distribution of quantum particles. Starting from the definition of Shannon entropy for continuous variables, here we have derived quantum osmotic pressure as well as the consequent entropic forces for bosonic and fermionic particles. The entropic force is computed explicitly for a pair of bosons and fermions. The low temperature limit of this result show that the entropic force for bosons is similar to Hooke's law of elasticity revealing the importance of this idea in the formation of a Bose-Einstein condensate. For fermions, the low temperature limit boils down to the well known Neumann's radial force and also reveals the Pauli's exclusion principle. The classical limit of the entropic force between quantum particles is then discussed. As a further example, the entropic force for quantum particles in noncommutative space is also computed. The result reveals a violation of the Pauli exclusion principle for fermions in noncommutative space.

We have extended our previous work [1] on rotating holographic superfluids to include Lifshitz scaling. Presence of this scaling breaks relativistic invariance of the boundary superfluid system and indicates the existence of a Lifshitz fixed point [2]. We have analytically shown that we still get same vortex solutions as discovered earlier in [1]. We have recovered previous results for the case of z = 1, which restores the relativistic invariance in the holographic superfluid system. However, for z $\neq$ 1 this study indicate surprising results regarding dissipation in such a holographic superfluid. We found that higher winding number vortices increase with higher values of imaginary chemical potential for values of z in the open interval (1, 2). This result is remarkable because it asserts that dissipation in the rotating holographic superfluid increases in the presence of Lifshitz scaling., Comment: 7 pages, 9 figures

In this work we investigate the phenomena of acceleration radiation for a two-level atom falling into the event horizon of a Kerr-Newman black hole. In https://link.aps.org/doi/10.1103/PhysRevD.104.065006 (Phys. Rev. D 104 (2021) 065006), it has been shown that conformal quantum mechanics has a connection to the generated Planck-like spectrum due to acceleration radiation. In this particular aspect, the near horizon approximation played a significant role. In https://link.aps.org/doi/10.1103/PhysRevD.106.025004 (Phys. Rev. D 106 (2022) 025004), we have used the beyond near horizon approximation to show that the excitation probability attains a Planck-like spectrum irrespective of the non-existence of an underlying conformal symmetry for a general class of static spherically symmetric black holes. In our analysis we have gone beyond the near horizon approximation for the rotating and charged case and even without the consideration of the conformal symmetry we observe a similar Planck-like spectrum. However, the coefficient of the spectrum is significantly different from the near horizon case. We have then considered a different scenario where a two-level atom emits multiple photons while freely falling into the event horizon of the Kerr-Newman black hole. It is observed that the Planck factor in the excitation probability is significantly small than that of the case of single-photon emission (for large number of simultaneously emitted photons from the two-level atom). Finally, we have computed the von-Neumann entropy which is also known as the horizon brightened acceleration radiation entropy or the HBAR entropy. We have carried out our analysis for a scalar field only to see the effect of the charge and rotation of the black hole in this particular scenario., Comment: 15 Pages LATEX

We study the Newtonian cosmology taking into account the leading classical and quantum corrections of order $\mathcal{O}(G^{2})$ in the Newtonian potential. We first derive the modified Friedmann equations starting from the non-relativistic conservation of kinetic energy and potential energy for an infinitesimal mass. We then consider the leading classical correction term and the quantum correction term in the Newtonian potential for deriving the Friedmann equation, however, the quantum correction term is too small and hence does not contribute in the physical results. We then investigate the difference in scale factor with the usual scale factor for various matter like radiation, dust and cosmological constant by considering the corrections in the Newtonian potential. We observe that the evolution of the universe is similar for radiation and dust cases at late times. The cosmological constant case shows a steep increase in the scale factor compared to the other cases. We also note that the universe may have a bounce in the case of radiation depending on the sign of the coefficient of the leading classical correction., Comment: 13 pages, 3 figures, Comments are welcome

In this paper, we have studied the thermodynamics of Gauss-Bonnet black holes in D-dimensional $AdS$ spacetime. Here, the cosmological constant ($\Lambda$), Newton's gravitational constant ($G$) and the Gauss-Bonnet parameter ($\alpha$) are varied in the bulk, and a mixed first law is rewritten considering central charge ($C$) (of dual boundary conformal theory) and its conjugate variable utilising the gauge-gravity duality. A novel universal nature of central charge near the critical point of black hole phase transition in Einstein's gravity has been observed in \cite{mann1}. We observe that this universal nature breaks when such phase transition is considered for black holes in the Gauss-Bonnet gravity. Apart from this, treating the Gauss-Bonnet parameter as a thermodynamic variable as suggested in \cite{kastori} in light of the consistency between first law and the Smarr relation leads to modified thermodynamic volume (conjugate to variable cosmological constant), adding to a new understanding of the Van der Waals gas like behaviour of the black holes in higher dimensional and higher curvature gravity theories. Our analysis considers a general $D$ dimensional background. We have then imposed a greater focus in the analysis of the phase structure of the five dimensional Gauss-Bonnet spacetime. Our analysis also shows that the general universal nature of the critical value of the central charge (which was present in four dimensional $AdS$ spacetime), breaks down in case of five dimensional $AdS$ spacetime even in the absence of Gauss-Bonnet gravity. This finding indicates the universal nature of the central charge may be a special feature of the four dimensional $AdS$ spacetime only., Comment: This manuscript is accepted for publication in Physical Review D

It has been recently shown in [Phys. Rev. Lett. 125 (2020) 041302] that microstate counting carried out for quantum states residing on the horizon of a black hole leads to a correction of the form $\exp(-A/4l_p^2)$ in the Bekenstein-Hawking form of the black hole entropy. In this paper, we develop a novel approach to obtain the possible form of the spacetime geometry from the entropy of the black hole for a given horizon radius. The uniqueness of this solution for a given energy-momentum tensor has also been discussed. Remarkably, the black hole geometry reconstructed has striking similarities to that of noncommutative-inspired Schwarzschild black holes [Phys. Lett. B 632 (2006) 547]. We also obtain the matter density functions using Einstein field equations for the geometries we reconstruct from the thermodynamics of black holes. These also have similarities to that of the matter density function of a noncommutative-inspired Schwarzschild black hole. The conformal structure of the metric is briefly discussed and the Penrose-Carter diagram is drawn. We then compute the Komar energy and the Smarr formula for the effective black hole geometry and compare it with that of the noncommutative-inspired Schwarzschild black hole. We also discuss some astrophysical implications of the solutions. Finally, we propose a set of quantum Einstein vacuum field equations, as a solution of which we obtain one of the spacetime solutions obtained in this work. We then show a direct connection between the quantum Einstein vacuum field equations and the first law of black hole thermodynamics., Comment: 16 pages LATEX

The Heisenberg uncertainty principle gets modified by the introduction of an observer independent minimal length. In this work we have considered the resonant gravitational wave detector in the modified uncertainty principle framework where we have used the position momentum uncertainty relation with a quadratic order correction only. We have then used the path integral approach to calculate an action for the bar detector in presence of a gravitational wave and then derived the Lagrangian of the system leading to the equation of motion for the configuration-space position coordinate in one dimension. We then find a perturbative solution for the coordinate of the detector for a circularly polarized gravitational wave leading to a classical solution of the same for given initial conditions. Using this classical form of the coordinate of the detector, we finally obtain the classical form of the on-shell action describing the harmonic oscillator-gravitational wave system. Finally, we have obtained the free particle propagator containing the quantum fluctuation term considering gravitational wave interaction., Comment: This manuscript has been accepted for publication in "Universe"; Special Edition: "Quantum Gravity Phenomenology"

We examine the virtual transition of an atom-mirror system with the simultaneous emission of two scalar photons, where the atom and the mirror admit a relative acceleration between them. For the single photon emission, literature (Phys. Rev. Lett. 121 (2018) 071301) dictates that the transition probabilities of two individual systems, such as an atom accelerating with respect to the mirror and its reverse, turn out to be equivalent under the exchange of the frequencies of atom and the field. Addressing the observational merit of such excitation process, a detectable probability ($P \sim 10^{-2}$) is also reported in the above literature. In the present manuscript our finding dictates that the simultaneous emission of dual photon instead of one, destroys the equivalence between the transition probabilities as reported in the above literature., Comment: 9 pages, 3 figures

At present the gravitational waves detectors achieve the sensitivity to detect the length variation ($\delta L$), $\mathcal{O} \approx 10^{-17}-10^{-21}$ meter. Recently a more stringent upperbound on the dimensionless parameter $\beta_0$, bearing the effect of generalized uncertainty principle has been given which corresponds to the intermediate length scale $l_{im}= \sqrt{\beta_0} l_{pl} \sim 10^{-23} m$. Hence it becomes quite obvious to search for the generalized uncertainty principle by observing the response of the vibrations of phonon modes in such resonant detectors in the near future. Therefore, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors in the generalized uncertainty principle framework. This presentation is based on the work published in \cite{sb2}., Comment: 4 pages, Contribution to the proceedings of XXIV DAE-BRNS High Energy Physics Symposium 2020

The exact renormalization group flow equations for gravity lead to quantum corrections of Newton's constant and cosmological constant. Using this we investigate the Bianchi-I cosmological model at late times. In particular, we obtain the scale factors in different directions, and observe that they eventually evolve into Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe for radiation. However, for stiff matter the universe shows a Kasner like behaviour. The presentation is based on our work published in \cite{Mandal:2019xlg}., Comment: 4 pages, Contribution to the proceedings of XXIV DAE-BRNS High Energy Physics Symposium 2020

In this work, we have analytically computed the holographic transport coefficients for (2 + 1)- dimensional strongly coupled field theories, placed in a spatially modulated chemical potential along the x-direction, in the presence of Born-Infeld electrodynamics. We have obtained these coefficients in terms of the black hole horizon data only. We have observed that the Born-Infeld parameter affects these coefficients in a non-trivial way. We have, then, used these results to further study a holographic model for ultra-clean graphene near Dirac point. This is a two current model with an inhomogeneous holographic lattice., Comment: 8 pages, no figures, matched with accepted version in the European Physical Journal C

In this work, we give two proposals regarding the status of connectivity of entanglement wedges and the associated saturation of mutual information. The first proposal has been given for the scenario before the Page time depicting the fact that at a particular value of the observer's time $t_b=t_R$ (where $t_R\ll\beta$), the mutual information $I(R_+:R_-)$ vanishes representing the disconnected phase of the radiation entanglement wedge. We argue that this time is the Hartman-Maldacena time at which the fine-grained entropy of radiation goes as $S(R)\sim \log(\beta)$, where $\beta$ is the inverse of Hawking temperature of the black hole. On the other hand, the second proposal probes the crucial role played by the mutual information of black hole subsystems in obtaining the correct Page curve of radiation., Comment: v1: 7 pages LaTex, 2 figures, v2: 9 pages LaTex, 2 figures. Accepted for publication in Physical Review D

We consider a spherically symmetric black hole metric in (3+1)-dimensions in presence of a positive cosmological constant $\Lambda$. We use a general approach as proposed in \cite{1} to transform the metric in co-moving coordinates. Then for a general metric we have evaluated the angular shadow size both in absence and presence of plasma. By using the aberration relation, we then find the corresponding shadow radius as viewed by a co-moving observer for Schwarzschild de-Sitter or Kottler spacetime. The effect of cosmological constant $\Lambda$ and plasma parameter $k$ on the angular size of black hole shadow has been observed in detail. Finally, by using the observed angular size of M87$^*$ and Sgr A$^*$ black hole, we constrain the value of the plasma parameter $k$ with a specific observational value of the cosmological constant $\Lambda$ (or the Hubble constant $H_0$)., Comment: V1, 21 Pages, 12 Figures; V2, 23 Pages, 18 Figures; Accepted in Classical and Quantum Gravity

Analytical investigation of the properties of $s$-wave holographic superconductors in the background of a massive gravity theory in the probe limit has been carried out employing the Sturm-Liouville eigenvalue method . We obtain the analytical expression for the relation between the critical temperature and the charge density. We also obtain the expression for the condensation operator and value of the critical exponent. Our findings show that as we increase the massive gravity couplings the critical temperature increases and the condensate decreases. More precisely we observe that the presence of massive graviton increases the critical temperature compared to the superconductors in Einstein gravity at some point if we keep on increasing the coupling constants. We also obtain the frequency dependence of conductivity by solving analytically the wave equation for electromagnetic perturbations. From the real part of the conductivity, we finally estimate the energy band gap., Comment: 17 pages

We introduce a new model of relativistic quantum analogue of the classical Otto engine in the presence of a perfectly reflecting boundary. A single qubit acts as the working substance interacting with a massless quantum scalar field, with the boundary obeying the Dirichlet condition. The quantum vacuum serves as a thermal bath through the Unruh effect. We observe that the response function of the qubit gets significantly modified by the presence of the reflecting boundary. From the structure of the correlation function, we find that three different cases emerge, namely, the intermediate boundary regime, the near boundary regime, and the far boundary regime. As expected, the correlation in the far boundary regime approaches that of the Unruh quantum Otto engine (UQOE) when the reflecting boundary goes to infinity. The effect of the reflecting boundary is manifested through the reduction of the critical excitation probability of the qubit and the work output of the engine. In spite of the reduced work output, the efficiency of the engine remains unaltered even in the presence of the boundary., Comment: Version accepted in JHEP

The near horizon aspects (and beyond) of a black hole metric, which belongs to a large class of static spherically symmetric black holes, are considered here. It has been realized recently that an atom falling into a black hole leads to the generation of acceleration radiation through virtual transitions. In recent studies, it has been argued that this acceleration radiation can be understood from the near horizon physics of the black hole. The near horizon approximation leads to conformal symmetry in the problem. We go beyond the near horizon approximation in our analysis. This breaks the conformal symmetry associated with the near horizon physics of the black hole geometry. We observe that even without the consideration of the conformal symmetry, the modified equivalence relation holds. Further, our analysis reveals that the probability of virtual transition retains its Planck like form with the amplitude getting modified due to the beyond near horizon approximation. For the next part of our analysis, we have observed the horizon brightened acceleration radiation entropy (HBAR) for a Garfinkle-Horowitz-Strominger (GHS) black hole. We observe that the HBAR entropy misses out on quantum gravity like corrections while considering the conformal case. However, such corrections emerge when the conformal symmetry gets broken in the beyond near horizon analysis., Comment: This revised version of the manuscript has been accepted for publication in Physical Review D

In this paper we have considered the thermodynamics of a Born-Infeld $AdS$ black hole using inputs from the dual boundary field theory. Here, we have varied the cosmological constant $\Lambda$ and the Newton's gravitational constant $G$ along with the Born-Infeld parameter $b$ in the bulk. A novel universal critical behaviour of the central charge (occurring in the boundary conformal field theory) in extended black hole thermodynamics for charged black holes has been recently observed \cite{mann1}, and we have extended this study to Born-Infeld $AdS$ black holes. The Born-Infeld parameter has the dimension of inverse length, therefore, when considered in the first law of thermodynamics of the bulk in the mixed form which includes the central charge of the boundary conformal field theory, it modifies the thermodynamic volume and the chemical potential (which are conjugate to pressure and central charge respectively). We observe that due to this inclusion of the Born-Infeld non-linearity in this analysis, the universal nature of the critical value of the central charge observed in \cite{mann1} breaks down. We also observe an interesting behaviour of the free energy of the black hole with Hawking temperature due to the variations in both the central charge and the Born-Infeld parameter. It is also observed in our analysis that for a sufficiently small value of the Born-Infeld parameter (small value of this parameter has more prominent non-linear effects), there exists a critical value of the temperature below which no black hole can exist., Comment: This revised version of the manuscript has been accepted for publication in Physical Review D

We have investigated the black hole thermodynamics and the phase transition for renormalized group improved asymptotically safe Schwarzschild black hole. This geometry takes into account the quantum gravitational correction in the running gravitational constant identifying $G(r) \equiv G(k=k(r))$. We studied various thermodynamic quantity like the Hawking temperature, specific heat and entropy for the general parameter $\gamma$ for quantum corrected Schwarzschild metric. We have noticed that the coefficient of the leading quantum correction, that is, the logarithmic correction gets affected by the presence of $\gamma$. We further study the local temperature, thermal stability of the black hole and the free energy considering a cavity enclosing the black hole. According to the local specific heat, there exists three black hole states, among them the large and tiny black hole are thermally stable states. We further investigate the on-shell free energy and find that no Hawking-Page phase transition occurs here unlike the ordinary Schwarzschild black hole. The black hole state always prevails for all temperatures. Also, we have found two critical points, $T_{c1}$ and $T_{c2}$, corresponding to the phase transition from one black hole state to another., Comment: 18 pages, 9 figures, comments are welcome

In this paper, we study various mixed state information theoretic quantities for a boosted black brane geometry. We have considered two setups, namely, a strip-like subsystem taken parallel and perpendicular to the direction of the boost. The quantities we calculate are the entanglement wedge cross-section, mutual information, entanglement negativity, and purification complexity. In the subsequent analysis, we have incorporated the thin-strip approximation and computed the leading order change (over pure AdS) in the concerned information theoretic quantities due to the boost parameter. We also show the relation of these quantities computed holographically to the energy and pressure of the boundary field theory. We then proceed to calculate the asymmetry ratios of these quantities, and observe that they are independent of the subsystem size. Finally, we proceed to study an interesting limit of the boosted black brane geometry, which is the so called AdS wave geometry. We once again compute all the mixed state information theoretic quantities for this geometry., Comment: v1:32 pages LaTex and 9 figures, v2:40 pages LaTex, v3: matches with the accepted version

In this work, we have investigated the phenomenon of acceleration radiation exhibited by an atom falling into a quantum corrected Schwarzschild black hole. We observe that the excitation-probability of the atom with simultaneous emission of a photon satisfies the equivalence principle when we compare it to the excitation probability of a mirror accelerating with respect to an atom. We also demonstrate the validity of the equivalence principle for a generic black hole geometry. Then we calculate the horizon brightened acceleration radiation (HBAR) entropy for this quantum corrected black hole geometry. We observed that the HBAR entropy has the form identical to that of Bekenstein-Hawking black hole entropy along with universal quantum gravity corrections., Comment: This revised version of the manuscript is accepted for publication in Physical Review D

In this article we have analytically deduced the frequency dependent expression of conductivity and the band gap energy in $AdS_{4}$ Schwarzschild background for p-wave holographic superconductors considering Einstein-Yang-Mills theory. We also used the self consistent approach to obtain the expressions of conductivity for different frequency ranges at low temperature. We then compared the imaginary part of conductivity at low frequency region. The band gap energy obtained from these two methods seem to agree very well., Comment: 19 pages single column, 5 figures

In this work we have considered a simple mechanical oscillator interacting with a single mode optical field inside a cavity in the generalized uncertainty principle framework (GUP). Our aim is to calculate the modified noise spectrum and observe the effects of the GUP. The commutation relation that we have considered has an extra linear order momentum term along with a quadratic order term. Confronting our theoretical results with the observational results, we observe that we get a much tighter bound on the GUP parameters from the noise spectrum using the values of the system parameters from different experiments., Comment: 16 pages LATEX