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Exact magnetic properties of two-dimensional (2D) spin-1 Cooper pairs are investigated within the framework of quantum statistical mechanics. We derive an exact analytical expression of the magnetization of 2D spin-1 Cooper pairs, which involves a q-digamma function and a q-Pochhammer symbol in mathematics. The magnetization density m(T) is a function of temperature T, Landé factor g, number density σ, and magnetic field B. Firstly, we examine the evolution of the magnetization density m(T) with the Landé factor g. m(T) is negative when g g c . Here, g c = 1 is the critical value of the Landé factor g, at which m ( T ) = 0 . Secondly, we examine the evolution of the magnetization density m(T) with the temperature T. When g m(T). The low-temperature asymptotic line is m ( T ) = − 387.5 nC s−1 and the high-temperature asymptotic line is m ( T ) = 0 . Finally, we examine the evolution of the magnetization density m(T) with the number density σ. No matter how large the Landé factor g is, there is a lower cutoff σ c of the number density σ. The lower cutoff number density is about σ c = 10 12 cm−2. If σ < σ c , the Cooper pair system does not support a solution of the reduced chemical potential x. As the number density σ is increased, the Bose–Einstein condensation of 2D Cooper pairs is strengthened.

Bose–Einstein condensation of two-dimensional spin-1 Cooper pairs in a uniform magnetic field is investigated within the framework of quantum statistical mechanics. We derive an exact analytical solution of two-dimensional spin-1 Cooper pairs in a uniform magnetic field, which involves a q-digamma function in mathematics. In two dimensions, it is found that the critical temperature and condensate fraction are monotonically increasing functions of magnetic field B, Landé factor g, and number density σ. Our investigation in two dimensions provides an example of the magnetic-field-tuned insulator-superconductor quantum phase transition.

Accurate estimation of state of charge (SOC), state of health (SOH) and remaining useful life (RUL) of Lithium-ion batteries is of great importance. This paper proposes a estimation framework based on charging voltage segment and hybrid method combining with equivalent circuit model and data-driven algorithms to achieve the accurate estimation of SOC, SOH and RUL of the long life cycle of the battery. The charging voltage segment, with the merit of flexibility and available, which contains much information for battery degradation, is suitable for battery modeling and state estimation. The rising time of the optimal charging voltage segment which has the highest correlation with the present capacity is extracted as health feature (HF) to estimate the SOH with least squares support vector machine (LSSVM), and the identified resistance and capacitance parameters acquired by fitting the charging voltage segment with equivalent circuit model and estimated capacity acquired by LSSCM are used to estimate SOC with the unscented Kalman filter (UKF) algorithm in the discharge stage for this cycle; Gaussian process regression (GPR) is used to prediction the trend of HF, which are combined with established LSSVM model to estimate RUL. Experimental results show that the proposed method can estimate SOC, SOH and RUL jointly with high accuracy.

A frequency synthesizer with high reliability and low noise was designed and manufactured by 0. 13um SiGe BICMOS process. The frequency synthesizer circuit is capable of generating 7. 5GHz-15GHz RF output signals (the entire VCO output band);The normalized phase noise of the frequency synthesizer reaches-230 dBC / Hz, and the VCO phase noise of the frequency synthesizer reaches-119dBC/Hz@1MHz at the oscillation frequency of 13GHz.

Type Ia Supernovae (SNe Ia) are widely used as standard candles to probe the Universe. However, how these fierce explosions are produced itself is still a highly debated issue. There are mainly two popular models for SNe Ia, i.e. the double-degenerate scenario and the single-degenerate scenario. The double-degenerate scenario suggests that SNe Ia are produced by the coalescence of two degenerate white dwarfs, while the single-degenerate scenario suggests that the continuous accretion of a single degenerate white dwarf from its normal stellar companion will finally lead to a disastrous explosion when it is over-massive, resulting in an SN Ia. The rapid development of the gravitational wave astronomy sheds new light on the nature of SNe Ia. In this study, we calculate the gravitational wave emissions of double white dwarf coalescences and compare them with the sensitivities of several upcoming detectors. It is found that the gravitational wave emissions from double white dwarf mergers in the locale universe are strong enough to be detected by LISA. We argue that LISA-like gravitational wave detectors sensitive in the frequency range of 0.01 - 0.1 Hz will be a powerful tool to test the double-degenerate model of SNe Ia, and also to probe the Universe., Comment: 10 pages, 5 figures, accepted by RAA. Reference added in Section 6. References updated to match the accepted version on RAA

We establish a quantum field theory of phase transitions in gapless superconductor CeCoIn 5. It is found that uniform Cooper pair gases with pure gradient interactions with negative coefficient can undergo a Bardeen–Cooper–Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare Cooper pairs with opposite wave vectors are bound into Cooper molecules, and uncoupled bare Cooper pairs are transformed into a new kind of quasiparticle, i.e., the dressed particles. The Cooper molecule system is a condensate or a superfluid, and the dressed particle system is a normal fluid. The critical temperature is derived analytically. The critical temperature of the superconductor CeCoIn 5 is obtained to be T c = 2.289 K, which approaches the experimental data. The transition from the BCS condensation state to the normal state is a first-order phase transition.

We investigate the Bose-Einstein condensation of photons and photon pairs in a two-dimension optical microcavity. We find that in the paraxial approximation, the mixed gas of photons and photon pairs is formally equivalent to a two dimension system of massive bosons with non-vanishing chemical potential, which implies the existence of two possible condensate phase. We also discuss the quantum phase transition of the system and obtain the critical point analytically. Moreover, we find that the quantum phase transition of the system can be interpreted as second harmonic generation.

Artificial graphene structures embedded in semiconductors could open novel routes for studies of electron interactions in low-dimensional systems. We propose a way to manipulate the transport properties of massless Dirac fermions in an artificial graphene-based tunnel junction. Velocity-modulation control of electron wave propagation in the different regions can be regarded as velocity barriers. Transmission probability of electron is affected profoundly by this velocity barrier. We find that there is no confinement for Dirac electron as the velocity ratio ξ is less than 1, but when the velocity ratio is larger than 1 the confined state appears in the continuum band. These localized Dirac electrons may lead to the decreasing of transmission probability.

Violations of Bell inequality, Cauchy—Schwarz inequality and entanglement in a two-mode three-level atomic system are investigated. It is shown that there are some states, which are entangled but do not violate Bell inequality in this system. Moreover, the relations of violations of Bell inequality, Cauchy—Schwarz inequality, and entanglement are discussed in detail.

We develop a numerical model to investigate the localization of surface exciton polaritons in the presence of random roughness and spatial dispersion. The localization criteria are examined. The localization effects are embodied in the large enhancement and rapid decay of the field intensity on the surface. The calculation shows that there is a transition from the localized state to the extended state. It has been found that the localization occurs in a limited frequency range above the resonant frequency of transverse excitons.

We have proposed an exact analytical solution to the problem of Bose–Einstein condensation (BEC) of harmonically trapped, one-dimensional, and ideal atoms. It is found that the number of atoms in vapor is characterized by an analytical function, which involves a q -digamma function in mathematics. We employ the q -digamma function to calculate the spatial density n(z;T, N) of ideal Bose atoms in a one-dimensional harmonic trap. The first main finding in this paper is that when Bose atoms are in the normal state, the density profile exhibits Friedel oscillations. The second main finding is that when Bose atoms are in the BEC state, the density profile exhibits a sharp peak with extremely narrow width. The third main finding is that the central peak of the spatial density is a monotonically increasing function of the number of atoms N but is a monotonically decreasing function of temperature T.

This paper presents a study of the cyclotron resonance of the interface polarons in a semi-infinite polar crystal. In the resonant magnetic field region the Landau-level corrections due to the resonant coupling of the electron with the bulk longitudinal-optical (LO) phonon and the surface optical (SO) phonon are calculated. At resonance the -th Landau level splits into a triplet. The cyclotron-resonance mass of the electron is evaluated for an arbitrary magnetic-field strength. For the interface system the magneto-optical anomalies display three branches of the cyclotron-resonance mass spectra. The numerical results show that in the interface system the polaron effect is weakened with respect to the ideal two-dimensional system. It is found that in the very weak magnetic fields the polaron effect is contributed mainly by the SO phonons, whereas in the large magnetic fields the LO-phonon contribution to the polaron effect becomes predominant.

We employ the q-digamma function to calculate the internal energy E, the entropy S, the Helmholtz free energy F, and the heat capacity at constant number of ideal Bose atoms in a one-dimensional harmonic trap. The first main finding in this paper is that in a one-dimensional harmonic trap and when the temperature approaches zero, the entropy of a finite number of ideal Bose atoms is nonzero but the entropy of an infinite number of ideal Bose atoms is zero. The second main finding is that the heat capacity at constant number has a classic limit as . In the thermodynamic limit, we find that at critical temperature the heat capacity at constant number is discontinuous. Hence, at there is a jump in the heat capacity and this jump is calculated. Consequently, the transition between normal and condensed states is a second-order phase transition.

Within the framework of quantum statistical mechanics, we have proposed an analytical solution to the problem of Bose–Einstein condensation (BEC) in harmonically trapped, one-dimensional and ideal atoms. It is found that the number of atoms of vapor is characterized by an analytical function, which involves a q -digamma function in mathematics. The results of the numerical calculation of the analytical solution agree completely with the previous experimental results in the BEC of harmonically trapped, one-dimensional and ideal atoms. The analytical expressions of the critical temperature and the condensate fraction are derived in the thermodynamic limit.

In this paper, we study the head-on collision between two electron acoustic solitary waves (EASWs) in magnetized quantum electron–positron–ion plasma. Using the extended Poincare–Lighthill–Kuo perturbation method, we obtain the Korteweg–de Vries equations, the phase shifts and the trajectories after the head-on collision of the two EASWs. It is found that the phase shifts are significantly affected by the values of the quantum parameter H, the ion to electron number density ratio δ, the electron cyclotron to electron plasma frequency ratio α and the obliqueness θ (propagation angle).

The nonlinear properties of magnetoacoustic solitary waves (MASWs) are investigated in magnetized pair ion–electron (PIE) plasmas. The three-fluid collisionless electromagnetic model is considered and the reductive perturbation method is employed to derive the Korteweg–de Vries equation for MASWs in PIE plasmas. It is found that the system under consideration admits compressive solitary structures. The effects of magnetic field intensity, plasma number density and negative ions concentration on MASWs are studied. This study may have relevance to nonlinear wave formation and the propagation of pair ion plasmas containing impurities.

The photon polaron in a two-dimensional optical micro-cavity is investigated within the framework of quantum statistical mechanics. Our experimental set-up is based on a planar Fabry-Perot cavity filled with a nonlinear non-polar crystal. The Fabry-Perot cavity provides a chemical potential and an effective mass for a photon, making the system formally equivalent to a two-dimensional gas of number-conserving, massive bosons. A photon polaron is a photon dressed with a cloud of virtual transverse optical phonons, namely, the dressed photon. One of the most important properties of the photon polaron is an increased inert mass. Because of the effect of photon polarons, we find that the photon-photon interaction is enhanced greatly. The photon polaron is a quantum effect of cavity nonlinear optics but its increased inert mass is a classical property.

We develop a quantum hydrodynamic fluid model including spin-orbit coupling effects for electrons in quantum plasmas. An effective field being analogous to the magnetic field of the magnetic moment is found. In the strong-radiation case, this effective field has a more important influence on the motion of plasmas than the usual Bohm potential correction. We find a resonance-like mechanism by which the transverse electromagnetic (TEM) wave and the Langmuir wave both propagating in plasmas with the same frequency can cause a stationary alignment of spins. This alignment will become a traveling wave when the frequency increases. Then it will vanish when the reciprocal of the difference between the frequencies of TEM and Langmuir waves reaches a value shorter than the characteristic spin relaxation time.

We investigate the energy-level shift of a hydrogen atom in a two-dimensional optical microcavity, where there exists a Bose—Einstein condensation of photons. It is found that below the critical temperature Tc, the energy-level shift of the bound electron is dependent on temperature, and it is a monotonically increasing function of the absolute temperature T. Especially, at the absolute zero temperature, the energy-level shift entirely comes from the Lamb shift, and the atom can be treated approximately, that is, in vacuum.

In this paper, we investigate the transport features and the Fano factor of Dirac electrons on the surface of a three-dimensional topological insulator with a magnetic modulation. We consider a hard wall bounding condition on the edge of the topological insulator, which implies that a surface state of the topological insulator is insulating. We find that a valley of conductivity at the Dirac point is associated with a Fano factor peak, and more interestingly, this topological metal changes from insulating to metallic by controlling the effective exchange field.

We find that uniform Bose atomic gases with weak attraction can undergo a Bardeen—Cooper—Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particles, i.e. the dressed atoms. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.

In the present paper, a charged oscillator in a harmonic potential well interacting with a Kerr-nonlinear blackbody is investigated. A quantum Langevin equation is derived. It is shown that below a transition temperature Tc, the memory function is a decreasing function of the Kerr-nonlinear coefficient. In the large-cutoff limit, the free-energy shift is a complicated function of temperature which is no longer a simply T2-dependent function. The energy level shift of an oscillator in a normal blackbody is negative, while in our Kerr-nonlinear blackbody, only near zero temperature is the corresponding energy level shift negative. As the temperature increases to the transition temperature Tc, the corresponding energy level shift becomes a large positive value. Above Tc, our results are the same as those found in a normal blackbody.

We investigate the dynamic Stark shift and atomic depopulation rate induced by real photons in a Kerr nonlinear blackbody. We found that the dynamic Stark shift and atomic depopulation rate are equally modified by a nonlinear contribution factor and a linear contribution factor under a transition temperature Tc. The nonlinear contribution factor depends on the Kerr nonlinear coefficient as well as the absolute temperature. Below Tc, the absolute values of the dynamic Stark shift and depopulation rate of a single atomic state (not the ground state) are correspondingly larger than those in a normal blackbody whose interior is filled with a nonabsorbing linear medium. Above Tc, the dynamic Stark shift and atomic depopulation rate are correspondingly equal to those in a normal blackbody with a nonabsorbing linear medium in its interior.