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We construct charged, static black holes in three-dimensional de Sitter (dS$_{3}$) space that exactly account for semi-classical backreaction effects due to quantum conformal matter. This is accomplished using braneworld holography, where an accelerating, electrically charged anti-de Sitter$_{4}$ black hole localizes on a Randall-Sundrum end-of-the-world brane. Absent of backreaction, the black hole disappears, leaving a chemical conical defect. The "quantum" black hole has a physical parameter space characterized by a shark-fin diagram, with extremal, Nariai, and ultracold limits. We give a detailed analysis of the horizon thermodynamics, where we find the heat capacity of charged and neutral dS$_{3}$ black holes features Schottky peaks. In particular, for a specific temperature range, charged quantum black holes behave as thermal systems with a finite number of energy levels available to their underlying microscopic degrees of freedom, beyond which many energy levels become available. Finally, we compute the probability of nucleating quantum dS black holes. Our work gives a first step to study quantum matter backreaction effects on dS black hole decay., Comment: 41 pages + appendices, 13 figures

Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is the granularity of spacetime, which suggests that free particles would deviate from classical geodesics by following a covariant Brownian motion. This notion is further supported by swerves models in causal set theory, a discrete approach to quantum gravity. At an effective level, such deviations are described by a stochastic correction to the geodesic equation. We show that the form of this correction is strictly restricted by covariance and the mass-shell condition. Under minimal coupling to curvature, the resulting covariant Brownian motion is unique. The process is equivalently described by a covariant diffusion equation for the distribution of massive particles in their relativistic phase space. When applied to dark matter particles, covariant Brownian motion results in spontaneous warming at late times, suppressing the matter power spectrum at small scales in a time-dependent manner. Using bounds on the diffusion rate from CMB and growth history measurements of $f\sigma_8$, we show that the model offers a resolution to the $S_8$ tension. Future studies on the model's behavior at non-linear cosmological scales will provide further constraints and, therefore, critical tests for the viability of stochastic dark matter., Comment: 66 pages, 13 figures, 2 tables

A way to reconcile general relativity and quantum field theory without quantising the geometry is to demand the metric evolve stochastically. In this article, we explore the consequences of such a proposal at early cosmological times. We find the stochastic evolution results in the spatial metric diffusing away from its deterministic value, generating phantom cold dark matter (CDM). It is produced primarily at the end of the inflationary phase of the Universe's evolution, with a statistical distribution that depends on the specifics of the early-times cosmological model. We find the energy density of this phantom cold dark matter is positive on average, a necessary condition to reproduce the cosmological phenomenology of CDM, although further work is required to calculate its mean density and spatial distribution. If the density is cosmologically significant, phantom dark matter acts on the geometry in a way that is indistinguishable from conventional CDM. As such, it has the potential to reproduce phenomenology such as structure formation, lensing, and galactic rotation curves. We conclude by discussing the possibility of testing hybrid theories of gravity by combining measurements of the Cosmic Microwave Background with tabletop experiments., Comment: 21 pages + appendix

We review constructions of three-dimensional `quantum' black holes. Such spacetimes arise via holographic braneworlds and are exact solutions to an induced higher-derivative theory of gravity consistently coupled to a large$-c$ quantum field theory with an ultraviolet cutoff, accounting for all orders of semi-classical backreaction. Notably, such quantum-corrected black holes are much larger than the Planck length. We describe the geometry and horizon thermodynamics of a host of asymptotically (anti-) de Sitter and flat quantum black holes. A summary of higher-dimensional extensions is given. We survey multiple applications of quantum black holes and braneworld holography., Comment: Invited review, 97 pages + appendices, multiple figures; v2: references added

We use braneworld holography to construct a three-dimensional quantum-corrected Kerr-de Sitter black hole, exactly accounting for semi-classical backreaction effects due to a holographic conformal field theory. By contrast, classically there are no de Sitter black holes in three-dimensions, only geometries with a single cosmological horizon. The quantum Kerr black hole shares many qualitative features with the classical four-dimensional Kerr-de Sitter solution. Of note, backreaction induces inner and outer black hole horizons which hide a ring singularity. Moreover, the quantum-corrected geometry has extremal, Nariai, and ultracold limits, which appear as fibered products of a circle and two-dimensional anti-de Sitter, de Sitter, and Minkowski space, respectively. The thermodynamics of the classical bulk black hole, described by the rotating four-dimensional anti-de Sitter C-metric, has an interpretation on the brane as thermodynamics of the quantum black hole, obeying a semi-classical first law where the Bekenstein-Hawking area entropy is replaced by the generalized entropy. For purposes of comparison, we derive the renormalized quantum stress-tensor due to a free conformally coupled scalar field in the classical Kerr-de Sitter conical geometry and perturbatively solve for its backreaction., Comment: 31 pages + appendices, 3 figures; v2: references added, JHEP version

We study the quantum backflow problem of a relativistic charged Dirac fermion constrained to move on a ring of radius $R$. Using the relativistic current operator we compute the probability flux through a generic time interval to show emergence of quantum backflow. We also discuss the limiting case when the particle moves along a line., Comment: 11 pages, 4 figures. Added a detailed discussion of the continuity equation and of the radial and azimuthal components of the probability current

We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow in each case and how they differ from each other. We also propose a probability associated with the occurence of angular momentum backflow and investigate whether or not the probability depends on a physical parameter, namely the magnetic field., Comment: 10 pages, 5 figures. Accepted for publication in Physical Review A

In this paper, we present the one-loop radiative corrections to the electroweak precision observable $\Delta \rho$ coming from the $I_W=1$ multiplet excited leptons. We have calculated the couplings of the exotic lepton triplet to the vector bosons and ordinary leptons using effective Lagrangian approach. These couplings are then used to estimate the excited lepton triplet contribution to the $\Delta \rho$ parameter. The mass degenerate excited lepton contribution to $\Delta \rho $ is small and can be neglected. However, if the excited leptons are non-degenerate, their contribution can be large which can result in more stringent constraints on the excited fermion parameter space compared to the constraints from present experimental searches and perturbative unitarity condition.

We present the derivation of the Casimir-Polder interactions mediated by a massive photon between two neutral systems described in terms of their atomic polarizability tensors. We find a compact expression for the leading term at large distances between the two systems. Our result reduces, in the mass-less photon limit, to the standard Casimir-Polder. We discuss implications of our findings with respect to recent scenarios of physics beyond the standard model such as universal extra dimensions, Randall-Sundrum and scale-invariant models. For each model we compute the correction to the Casimir-Polder interaction in terms of the free parameters., Comment: 12 pages, 2 figures

We use the extension problem proposed by Caffarelli and Silvestre to study the quantization of a scalar nonlocal quantum field theory built out of the fractional Laplacian. We show that the quantum behavior of such a nonlocal field theory in $d$-dimensions can be described in terms of a local action in $d+1$ dimensions which can be quantized using the canonical operator formalism though giving up local commutativity. In particular, we discuss how to obtain the two-point correlation functions and the vacuum energy density of the nonlocal fractional theory as a brane limit of the bulk correlators. We show explicitly how the quantized extension problem reproduces exactly the same particle content of other approaches based on the spectral representation of the fractional propagator. We also briefly discuss the inverse fractional Laplacian and possible applications of this approach in general relativity and cosmology., Comment: 28 pages, no figures

In this paper we present exact solutions of the Dirac equation on the non-commutative plane in the presence of crossed electric and magnetic fields. In the standard commutative plane such a system is known to exhibit contraction of Landau levels when the electric field approaches a critical value. In the present case we find exact solutions in terms of the non-commutative parameters $\eta$ (momentum non-commutativity) and $\theta$ (coordinate non-commutativity) and provide an explicit expression for the Landau levels. We show that non-commutativity preserves the collapse of the spectrum. We provide a dual description of the system: (i) one in which at a given electric field the magnetic field is varied and the other (ii) in which at a given magnetic field the electric field is varied. In the former case we find that momentum non-commutativity ($\eta$) splits the critical magnetic field into two critical fields while coordinates non-commutativity ($\theta$) gives rise to two additional critical points not at all present in the commutative scenario., Comment: 6 pages, 4 figures, Accepted for publication by EuroPhysics Letters (EPL)

The Dirac oscillator in a homogenous magnetic field exhibits a chirality phase transition at a particular (critical) value of the magnetic field. Recently, this system has also been shown to be exactly solvable in the context of noncommutative quantum mechanics featuring the interesting phenomenon of re-entrant phase transitions. In this work we provide a detailed study of the thermodynamics of such quantum phase transitions (both in the standard and in the noncommutative case) within the Maxwell-Boltzmann statistics pointing out that the magnetization has discontinuities at critical values of the magnetic field even at finite temperatures., Comment: 10 pages, 8 figures

It is shown that bound state solutions of the one dimensional Bogoliubov-de Gennes (BdG) equation may exist when the Fermi velocity becomes dependent on the space coordinate. The existence of bound states in continuum (BIC) like solutions has also been confirmed both in the normal phase as well as in the super-conducting phase. We also show that a combination of Fermi velocity and gap parameter step-like profiles provides scattering solutions with normal reflection and transmission., Comment: 9 pages, 7 figures. Accepted for publication by Physics Letters A

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within the Anti-Snyder modified uncertainty relation characterized by a momentum cut-off ($p\leq p_{\text{max}}=1/ \sqrt{\beta}$). In ordinary quantum mechanics ($\beta\to 0$) this system is known to have a single left-right chiral quantum phase transition (QPT). We show that a finite momentum cut-off modifies the spectrum introducing additional quantum phase transitions. It is also shown that the presence of momentum cut-off modifies the degeneracy of the states., Comment: 10 pages, 2 Figures. Accepted for publication by the Physical Review D

We obtain exact solutions of the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field within a minimal length ($\Delta x_0=\hbar \sqrt{\beta}$), or generalised uncertainty principle (GUP) scenario. This system in ordinary quantum mechanics has a single left-right chiral quantum phase transition (QPT). We show that a non zero minimal length turns on a infinite number of quantum phase transitions which accumulate towards the known QPT when $\beta \to 0$. It is also shown that the presence of the minimal length modifies the degeneracy of the states and that in this case there exist a new class of states which do not survive in the ordinary quantum mechanics limit $\beta \to 0$., Comment: 7 pages, 1 figure

We study the (2+1) dimensional Dirac oscillator in a homogeneous magnetic field in the non-commutative plane. It is shown that the effect of non-commutativity is twofold: $i$) momentum non commuting coordinates simply shift the critical value ($B_{\text{cr}}$) of the magnetic field at which the well known left-right chiral quantum phase transition takes place (in the commuting phase); $ii$) non-commutativity in the space coordinates induces a new critical value of the magnetic field, $B_{\text{cr}}^*$, where there is a second quantum phase transition (right-left), --this critical point disappears in the commutative limit--. The change in chirality associated with the magnitude of the magnetic field is examined in detail for both critical points. The phase transitions are described in terms of the magnetisation of the system. Possible applications to the physics of silicene and graphene are briefly discussed., Comment: 26 pages, two figures. Editorial improvements, few references added. Version accepted by Physical Review A

We consider $(2+1)$ dimensional massless Dirac equation in the presence of complex vector potentials. It is shown that such vector potentials (leading to complex magnetic fields) can produce bound states and the Dirac Hamiltonians are $\eta$-pseudo Hermitian. Some examples have been explicitly worked out., Comment: 8 pages, NO figures

In this paper we present the un-Casimir effect, namely the study of the Casimir energy in the presence of an unparticle component in addition to the electromagnetic field contribution. The distinctive feature of the un-Casimir effect is a fractalization of metallic plates. This result emerges through a new dependence of the Casimir energy on the plate separation that scales with a continuous power controlled by the unparticle dimension. As long as the perfect conductor approximation is valid, we find bounds on the unparticle scale that are independent of the effective coupling constant between the scale invariant sector and ordinary matter. We find regions of the parameter space such that for plate distances around $5\mu$m and larger the un-Casimir bound wins over the other bounds., Comment: 13 pages, 3 figures; v2: improved discussion, additional references, v3: title slightly changed, version matching that in press on Physics Letters B

We study the (2+1) dimensional Dirac equation in an homogeneous magnetic field (relativistic Landau problem) within a minimal length, or generalized uncertainty principle -GUP-, scenario. We derive exact solutions for a given explicit representation of the GUP and provide expressions of the wave functions in the momentum representation. We find that in the minimal length case the degeneracy of the states is modified and that there are states that do not exist in the ordinary quantum mechanics limit (\beta -->0). We also discuss the mass-less case which may find application in describing the behavior of charged fermions in new materials like Graphene., Comment: 9 pages, to appear in Physical Review D

We study generalized Dirac oscillators with complex interactions in $(1+1)$ dimensions. It is shown that for the choice of interactions considered here, the Dirac Hamiltonians are $\eta$ pseudo Hermitian with respect to certain metric operators $\eta$. Exact solutions of the generalized Dirac Oscillator for some choices of the interactions have also been obtained. It is also shown that generalized Dirac oscillators can be identified with Anti Jaynes Cummings type model and by spin flip it can also be identified with Jaynes Cummings type model., Comment: To appear in Annals of Physics (Elsevier)

We examine the one dimensional Dirac equation with modulated or position dependent velocity. In particular, it is shown that using suitable velocity profiles it is possible to create bound state in continuum (BIC) like, as well as, discrete energy bound state solutions., Comment: 9 pages, two figures. Version to match the one to appear in Physics Letters A

We study the corrections to the Casimir effect in the classical geometry of two parallel metallic plates, separated by a distance $a$, due to the presence of a minimal length ($\hbar\sqrt{(\beta)}$) arising from quantum mechanical models based on a Generalized Uncertainty Principle (GUP). The approach for the quantization of the electromagnetic field is based on projecting onto the maximally localized states of a few specific GUP models and was previously developed to study the Casimir-Polder effect. For each model we compute the lowest order correction in the minimal length to the Casimir energy and find that it scales with the fifth power of the distance between the plates $a^{-5}$ as opposed to the well known QED result which scales as $a^{-3}$ and, contrary to previous claims, we find that it is always attractive. The various GUP models can be in principle differentiated by the strength of the correction to the Casimir energy as every model is characterized by a specific multiplicative numerical constant., Comment: 19 pages, 1 figure

We study the one-dimensional Dirac equation in the framework of a position dependent mass under the action of a Woods-Saxon external potential. We find that constraining appropriately the mass function it is possible to obtain a solution of the problem in terms of the hypergeometric function. The mass function for which this turns out to be possible is continuous. In particular we study the scattering problem and derive exact expressions for the reflection and transmission coefficients which are compared to those of the constant mass case. For the very same mass function the bound state problem is also solved, providing a transcendental equation for the energy eigenvalues which is solved numerically., Comment: Version to match the one which has been accepted for publication by J. Phys. A: Math. Theor. Added one figure, several comments and few references. (24 pages and 7 figures)

The standard model of strong interactions invokes the quantum chromodynamics (QCD) of quarks and gluons interacting within a fluid. At sufficiently small length scales, the effective interactions between the color charged particles within the fluid are thought to be weak. Short distance asymptotic freedom provides the perturbation theory basis for comparisons between QCD theory and laboratory high energy scattering experiments. It is here shown that the asymptotically free vacuum has negative dissipation implicit in the color electrical conductivity. Negative dissipation implies an asymptotically free QCD negative temperature {\em excited state amplifier} unstable to decay. The qualitative experimental implications of this instability are explored., Comment: Manuscript accepted for publication by the International Journal of Modern Physics A

We study the formation and detection at the next linear e^+e^- collider of bound states of level-1 quark Kaluza-Klein excitations B_KK within a scenario of universal extra-dimensions (UED). The interactions of such Kaluza-Klein excitations are modeled by an alpha_s driven Coulomb potential. In order to obtain the threshold cross-section, we employ the Green function method which is known to properly describe the peaks below threshold and to yield a net increase in the continuum region (above threshold) relative to the naive Born cross-section. We study such effect at different values of the scale (R^-1) of the extra-dimensions with an explicit calculation of the mass spectrum as given by radiative corrections. The overall effect is roughly 2.7 at R^-1=300 GeV and goes down to 2.2 at R^-1=1000 GeV and a relatively large number of events is expected from N_events ~ 2.5*10^4 at R^-1=300 GeV down to N_events ~ 10^3 at R^-1=1000 GeV at the anticipated annual integrated luminosity of L_0= 100 fb^-1. We finally discuss some potentially observable signatures such as the multilepton channels 2j + 2l + missing energy, and 2j + 4l + missing energy for which we estimate statistical significance >~ 2 for R^-1 up to 600 ~ 700 GeV., Comment: Accepted for publication in Phys. Rev. D. Enhanced version. 13 pages, 5 figures, 2 tables

No consensus seems to exist as to what constitutes a measurement which is still considered somewhat mysterious in many respects in quantum mechanics. At successive stages mathematical theory of measure, metrology and measurement theory tried to systematize this field but significant questions remain open about the nature of measurement, about the characterization of the observer, about the reliability of measurement processes etc. The present paper attempts to talk about these questions through the information science. We start from the idea, rather common and intuitive, that the measurement process basically acquires information. Next we expand this idea through four formal definitions and infer some corollaries regarding the measurement process from those definitions. Relativity emerges as the basic property of measurement from the present logical framework and this rather surprising result collides with the feeling of physicists who take measurement as a myth. In the closing this paper shows how the measurement relativity wholly consists with some effects calculated in QM and in Einstein's theory., Comment: Prepared for : Quantum Theory: Reconsideration of Foundations - 4 (QTFR-4), Vaxjo, Sweden, 6-11 June 2007. To be published by the American Institute of Physics in the AIP Conference Proceedings series. Talk presented by Paolo Rocchi

Generalized uncertainty relations are known to provide a minimal length $\hbar\sqrt{\beta}$. The effect of such minimal length in the Casimir-Polder interactions between neutral atoms (molecules) is studied. The first order correction term in the minimal uncertainty parameter is derived and found to describe an attractive potential scaling as $r^{-9}$ as opposed to the well known $r^{-7}$ long range retarded potential., Comment: 1 Figure. Version published by Physical Review D. Few references added, typos corrected

An investigation of two-time correlation functions is reported within the framework of (i) Stochastic Quantum Mechanics and (ii) conventional Heisenberg-Schr\"odinger Quantum Mechanics. The spectral functions associated with the two-time electric dipole correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for stochastic and conventional quantum mechanics, differences arise in the two approaches for multiple time correlation functions., Comment: Version published by the Eur. Phys. J. B. Few references added. Minor typos corrected