First-order Quantum Corrections Research Articles

Study of first-order quantum corrections of thermodynamics to a Dyonic black hole solution surrounded by a perfect fluid

In this work, we review the metric for a dyonic global monopole with a perfect fluid. To calculate the standard temperature of a Dyonic black hole surrounded by a perfect fluid, we analyze the graphical interpretation of the Hawking temperature concerning the horizon under the effects of the black hole's surrounding field and electric-magnetic charges. For this purpose, we follow the semi-classical method, the Wentzel-Kramers-Brillouin (WKB) approximation, and the Lagrangian equation in the presence of quantum gravity as seen in the generalized uncertainty principle (GUP). We calculate the improved temperature of a Dyonic black hole using a bosonic tunneling strategy based on the Hamilton-Jacobi technique. We observe that the physical state of the Dyonic black hole is surrounded by a perfect fluid under the effects of the black hole solution and the gravity parameter. Further, we examine the improved entropy to study the influences of quantum gravity and black hole geometry on entropy. We explore the graphical behavior of entropy based on the black hole's horizon structure and analyze the influence of perfect fluid parameters, electric charge, magnetic charge, and quantum gravity on entropy. Finally, we investigate the unstable and stable conditions of a black hole via graphical results.

Generalized covariant entropy bound in Einstein gravity with quadratic curvature corrections

We explore the generalized covariant entropy bound in the theory where Einstein gravity is perturbed by quadratic curvature terms, which can be viewed as the first-order quantum correction to Einstein gravity. By replacing the Bekenstein-Hawking entropy with the holographic entanglement entropy of this theory and introducing two reasonable physical assumptions, we demonstrate that the corresponding Generalized Covariant Entropy Bound is satisfied under a first-order approximation of the perturbation from the quadratic curvature terms. Our findings suggest that the entropy bound and the Generalized Second Law of black holes are satisfied in the Einstein gravity under the first-order perturbation from the quadratic curvature corrections, and they also imply that the generalized covariant entropy bound may still hold even after considering the quantum correction of gravity, but in this case, we may need to use holographic entanglement entropy as the formula for gravitational entropy.

Contribution of BSM Particles on Electric Dipole Moment of Charged Leptons in the Minimal Left-Right Symmetric Model

In this paper, the contribution of Beyond the Standard Model (BSM) particles on the Electric Dipole Moment (EDM) of charged lepton is calculated in a minimal Left-Right Symmetric Model. First-order quantum correction i.e., one loop correction, from relevant diagrams in the unitary gauge using Feynman parameterization is used because there is no tree-level contribution in Electric Dipole Moment due to non-renormalizability of the dipole term in the Lagrangian. This study mainly focuses on the BSM Higgs sector contribution to the EDM of charged leptons due to phenomenological interest. CP violation is directly connected to the EDM of fundamental particles. Matter-antimatter asymmetry is a mystery of the universe that demands CP symmetry to be violated. The standard model cannot explain the observed CP violation. Standard Model (SM) is so far the best description of nature. Despite having tremendous success, e.g., Electro-weak Symmetry Breaking and Higgs discovery, the Standard model is not complete. Moreover, experimentally, we observed small neutrino mass and neutrino mixing. The Seesaw Mechanism can explain neutrino mass smallness and mixing introducing a large Majorana mass. Left-right symmetric model is the most natural extension of SM which can accommodate the Seesaw mechanism. So EDM contributions from BSM particles in the Left-Right symmetric Model are a good probe of new physics beyond the SM. These contributions then can be used to do phenomenology and test the Model.

First-order quantum correction of thermodynamics in a charged accelerating AdS black hole with gauge potential

In this paper, we study the tunneling radiation from a charged-accelerating AdS black hole with gauge potential under the impact of quantum gravity. Using the semi-classical phenomenon known as the Hamilton–Jacobi ansatz, it is studied that tunneling radiation occurs via the horizon of a black hole and also employs the Lagrangian equation using the generalized uncertainty principle. Furthermore, we investigate the impact of charge, gauge potential, and first order correction parameters on the temperature as well as the stable and unstable states of the black hole. We also compute thermodynamic properties such as entropy, internal energy, Helmholtz free energy, enthalpy, specific heat, and Gibbs free energy under the impact of the correction parameter for the black hole. We calculate the logarithmic modification terms for entropy around the equilibrium state to analyze the impacts of logarithmic correction. In the presence of the correction terms, we also check the validity of the thermodynamics. It examines the graphical representation of the influence of logarithmic correction on the thermodynamic properties of black hole stability as well as charged, accelerating, and gauge potential parameters.

First-order quantum corrections of tunneling radiation in modified Schwarzschild–Rindler black hole

First-order quantum corrections of tunneling radiation in modified Schwarzschild–Rindler black hole

Thermal rate of transmission through a barrier: Exact expansion of up to and including terms of order ℏ4

Nine decades after Wigner's formulation of quantum rate theory, his celebrated result was recently generalized to the asymmetric barrier using an exact first-order expansion of the transmission probability in terms of ${\ensuremath{\hbar}}^{2}$. This paper extends the first-order quantum correction to second-order correction of order ${\ensuremath{\hbar}}^{4}$ for the thermally averaged transmission probability through an arbitrary barrier. The derivation employs a systematic expansion of the projection operator onto products and the thermal distribution which involves a Taylor expansion of the potential about the barrier up to eighth order. The resulting exact analytical expression is calibrated with numerical calculations of several model potentials and shows excellent agreement when the ${\ensuremath{\hbar}}^{4}$ term is included. In comparison, the semiclassical transition state theory cannot reproduce the correct ${\ensuremath{\hbar}}^{4}$ terms when the anharmonicity is treated on the level of VPT-4 (vibrational perturbation theory---fourth order) and will potentially need a VPT-6 expansion. Further analysis of the quartic barrier reveals suppressed transmission due to the dominant role of quantum reflection above the barrier. These results not only provide a conceptual framework but can also be applied to heavy atom tunneling and machine learning.

First-order quantum correction in coherent state expectation value of loop-quantum-gravity Hamiltonian

Given the non-graph-changing Hamiltonian $\widehat{H[N]}$ in Loop Quantum Gravity (LQG), $\langle\widehat{H[N]}\rangle$, the coherent state expectation value of $\widehat{H[N]}$, admits an semiclassical expansion in $\ell^2_{\rm p}$. In this paper, as presenting the detailed derivations of our previous work arXiv:2012.14242, we explicitly compute the expansion of $\langle\widehat{H[N]}\rangle$ to the linear order in $\ell^2_{\rm p}$ on the cubic graph with respect to the coherent state peaked at the homogeneous and isotropic data of cosmology. In our computation, a powerful algorithm is developed, supported by rigorous proofs and several theorems, to overcome the complexity in the computation of $\langle \widehat{H[N]} \rangle$. Particularly, some key innovations in our algorithm substantially reduce the complexity in computing the Lorentzian part of $\langle\widehat{H[N]}\rangle$. Additionally, some quantum correction effects resulting from $\langle\widehat{H[N]}\rangle$ in cosmology are discussed at the end of this paper.

Quantum corrected thermodynamics of nonlinearly charged BTZ black holes in massive gravity’s rainbow

In this paper, we consider three-dimensional massive gravity’s rainbow and obtain black hole solutions in three different cases of Born–Infeld, logarithmic, and exponential theories of nonlinear electrodynamics. We discuss the horizon structure and geometrical properties. Then, we study thermodynamics of these models by considering the first-order quantum correction effects, which appear as a logarithmic term in the black hole entropy. We discuss such effects on the black hole stability and phase transitions. We find that due to the quantum corrections, the second-order phase transition happens in Born–Infeld and logarithmic models. We obtain the modified first law of black hole thermodynamics in the presence of logarithmic corrections.

Mass correction to chiral kinetic equations

We study fermion mass correction to chiral kinetic equations in electromagnetic fields. Different from the chiral limit where fermion number density is the only independent distribution, the number and spin densities are coupled to each other for massive fermion systems. To the first order in $\ensuremath{\hbar}$, we derived the quantum correction to the classical on-shell condition and the Boltzmann-type transport equations. To the linear order in the fermion mass, the mass correction does not change the structure of the chiral kinetic equations and behaves like additional collision terms. While the mass correction exists already at classical level in general electromagnetic fields, it is only a first-order quantum correction in the study of the chiral magnetic effect.

THERMAL AND TRANSPORT PROPERTIES OF A NONRELATIVISTIC QUANTUM GAS INTERACTING THROUGH A DELTA-SHELL POTENTIAL

This work extends the seminal work of Gottfried on the two-body quantum physics of particles interacting through a delta-shell potential to many-body physics by studying a system of nonrelativistic particles when the thermal De-Broglie wavelength of a particle is larger than the range of the potential and the density is such that average distance between particles is larger than the above range. The ability of the delta-shell potential to reproduce some basic properties of the deuteron are examined. Relations for moments of bound-states are derived. The virial expansion is used to calculate the first quantum correction to the ideal gas pressure in the form of the second virial coefficient. Additionally, all thermodynamical functions are calculated up to the first-order quantum corrections. For small departures from equilibrium, the net flows of mass, energy and momentum, characterized by the coefficients of diffusion, thermal conductivity and shear viscosity, respectively, are calculated. Properties of the gas are examined for various values of physical parameters including the case of infinite scattering length when the unitary limit is achieved.

Phase diagram and thermodynamic properties of H2

A statistical mechanical-based theory is used to develop the equation of state for the molecular fluid of H(2). We incorporate in this equation the long-range correlations through the double Yukawa potential, dimerization of the H(2) molecule by treating the fluid as a hard convex body fluid, and first-order quantum correction which is important at low temperatures. We use this to calculate the liquid-vapor equilibrium of H(2), including the temperature and pressure dependence of compressibility factor, entropy, specific heat, compressibility, and sound velocity.

Effective action for EPRL/FK spin foam models

We show that a natural modification of the EPRL/FK vertex amplitude gives a finite spin foam model whose effective action gives the Einstein-Hilbert action in the limit of large spins and arbitrarily fine spacetime triangulations. The first-order quantum corrections can be easily computed and we show how to calculate the higher-order corrections.

First-order quantum correction to the Larmor radiation from a moving charge in a spatially homogeneous time-dependent electric field

First-order quantum correction to the Larmor radiation is investigated on the basis of the scalar QED on a homogeneous background of a time-dependent electric field, which is a generalization of a recent work by Higuchi and Walker so as to be extended for an accelerated charged particle in a relativistic motion. We obtain a simple approximate formula for the quantum correction in the limit of the relativistic motion when the direction of the particle motion is parallel to that of the electric field.

FIRST-ORDER QUANTUM CORRECTION TO THE GROUND-STATE ENERGY DENSITY OF TWO-DIMENSIONAL HARD-SPHERE BOSE ATOMS

Divergence exponents of the first-order quantum correction of a two-dimensional hard-sphere Bose atoms are obtained by an effective field theory method. The first-order correction to the ground-state energy density with respect to the zeroth-order is given by [Formula: see text], where D is the spatial dimension, and γ is the gas parameter (γ = naD). As D →2, α = α′ = 1. We show that the first-order quantum correction of the energy density is not perturbative in low dimensions of D < 2.2 regardless of any gas parameter which is much less than unity.

The role of conformal symmetry in the Jackiw–Pi model

The Jackiw–Pi model in 2 + 1 dimensions is a non-relativistic conformal field theory of charged particles with point-like self-interaction. For specific values of the interaction strengths the classical theory possesses vortex and multi-vortex solutions, which are all degenerate in energy. We compute the full set of first-order perturbative quantum corrections. Only the coupling constant g 2 requires renormalization; the fields and electric charge e are not renormalized. It is shown that in general the conformal symmetries are broken by an anomalous contribution to the conservation law, proportional to the β-function. However, the β-function vanishes upon restricting the coupling constants to values g 2 = ± e 2 , which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.

Static structure factor and quantum melting of vortex lattices in two-dimensional Bose-Einstein condensates

The first-order quantum corrections to the static structure factor of vortex lattices in a rapidly rotating quasi-two-dimensional Bose-Einstein condensate are calculated. Furthermore, we estimate the melting filling fraction by using a criterion similar to that used in thermal melting related to the Debye-Waller factor of the smallest reciprocal lattice vector.

Ferromagnetism in thet−t′Hubbard model: Interplay of lattice, band dispersion, and interaction effects studied within a Goldstone-mode preserving scheme

Ferromagnetism in the Hubbard model is investigated on sc, bcc, and fcc lattices using a systematic inverse-degeneracy ($1/{\cal N}$) expansion which incorporates self-energy and vertex corrections such that spin-rotation symmetry and the Goldstone mode are explicitly preserved. First-order quantum corrections to magnon energies are evaluated for several cases, providing a comprehensive picture of the interplay of lattice, band dispersion, and interaction effects on the stability of the ferromagnetic state with respect to both long- and short-wavelength fluctuations. Our results support the belief that ferromagnetism is a generic feature of the Hubbard model at intermediate and strong coupling provided the DOS is sufficiently asymmetric and strongly peaked near band edge, as for fcc lattice with finite $t'$. For short-wavelength modes, behavior of a characteristic energy scale $\omega^* \sim T_c$ (magnon-DOS-peak energy) is in excellent agreement with the $T_c$ vs. $n$ behavior within DMFT, both with respect to the stable range of densities ($0.20 < n < 0.85$) as well as the optimal density $n=0.65$. However, our finding of vanishing spin stiffness near optimal density highlights the role of long-wavelength fluctuations in further reducing the stable range of densities.

Equation of State of He-H2 and He-D2 Dense Fluid Mixtures at High Pressures and Temperatures

The fluid variational theory is used to calculate the Hugoniot equation of state (EOS) of He, D 2 , He + H 2 , and He + D 2 fluid mixtures with different He:H 2 and He:D 2 compositions at high pressures and temperatures. He, H 2 , and D 2 are the lightest elements. Therefore, the quantum effect is included via a first-order quantum correction in the framework of the Wigner-Kirk-wood expansion. An examination of the reliability of the above computations is performed by comparing experiments and calculations, in which the calculation procedure used for He and D 2 is adopted also for He + D 2 and He + H 2 , since no experimental data for the mixtures are available to conduct these comparisons. Good agreement in both comparisons is found. This result may be seen as an indirect verification of the calculation procedures used here, at least, in the pressure and temperature domains covered by the experimental data for He and D 2 used for comparisons, which is nearly up to 40 GPa and 10 5 K. Also, the equation of state of He + H 2 fluid mixtures with different compositions is predicted over a wide range of temperatures and pressures.

Semiclassical statistical mechanics of hard-body fluid mixtures

The thermodynamic properties of semiclassical hard-body fluid mixtures are studied. Explicit expressions are given for the free-energy, equation of state and virial coefficients of the classical hard convex-body fluid mixtures. The numerical results are discussed under different conditions. The agreement with the exact data is good in all cases. The first-order quantum corrections are also studied. The quantum effects depend on the condition, shape parameters L11* and L22*, and concentrations x1 and x2 in general and increase with an increase of packing fraction eta, in particular.

Second virial coefficients of water beyond the conventional first-order quantum correction

We present high quality theoretical calculations for the second virial coefficient of water at low temperatures, beyond the conventional first order quantum correction (FOQC). The calculations were performed with some of the best ab initio potentials available at present in conjunction with an effective potential semiclassical approach that has proved to be of similar accuracy to converged path integral Monte Carlo. These new results are compared with FOQC and with some recent experimental correlations. Although a much better agreement with experiment is achieved, some differences still remain at very low temperatures. Possible reasons for these discrepancies are discussed.