Self-consistent Overhauser model for the pair distribution function of an electron gas at finite temperature

We present calculations of the spin-averaged pair distribution function g(r) in a homogeneous gas of electrons moving in dimensionality D=3 or D=2 at finite temperature. The model involves the solution of a two-electron scattering problem via an effective potential, which embodies many-body effects through a self-consistent Hartree approximation, leading to two-body wave functions to be averaged over a temperature-dependent distribution of relative momentum for electron pairs. We report illustrative numerical results for g(r) in an intermediate-coupling regime and interpret them in terms of changes of short-range order with increasing temperature.     

Self-consistent medium polarization in RPA

The standard random-phase approximation for finite systems is extended by including the effect of the exchange of the RPA phonons in the residual interaction selfconsistently. It is shown that this particle-hole interaction is strongly energy dependent due to the presence of poles corresponding to 2p2h (and more complex) excitations. The RPA eigenvalue problem with this energy-dependent residual interaction also provides solutions for these predominantly 2p2h-like states. In addition a modified normalization condition is obtained.This new scheme is applied to ⁵⁶Ni (⁵⁶Co) in a large (up to 7ħω) configuration space using a residual interaction of G-matrix type. It is shown that the lowest 2⁺ eigenvalue, which in the standard RPA becomes imaginary, is stabilized when the selfconsistent screening is taken into account. Another feature observed is the splitting of the M1 strength as an example of 1p1h and 2p2h mixing.     

Pair fluctuations in ultra-small Fermi systems within self-consistent RPA at finite temperature

A self-consistent version of the thermal random phase approximation (TSCRPA) is developed within the Matsubara Green’s function (GF) formalism. The TSCRPA is applied to the many level pairing model. The normal phase of the system is considered. The TSCRPA results are compared with the exact ones calculated for the Grand Canonical Ensemble. Advantages of the TSCRPA over the thermal mean field approximation (TMFA) and the standard thermal random phase approximation (TRPA) are demonstrated. Results for correlation functions, excitation energies, single particle level densities, etc., as a function of temperature are presented.     

Holographic model at finite temperature with R-charge density

We consider a holographic model of QCD at finite temperature with nonzero chemical potentials conjugate to R-charge densities. A critical surface of the confinement–deconfinement phase transition is shown for five-dimensional charged black hole solution given by Behrndt, Cvetič and Sabra. On a special section of the parameter space, we find a critical curve being similar to the one expected in QCD. We calculate meson spectra and decay constants in the confinement phase of this section to see their temperature and chemical potential dependences. We could assure generalized Gell-Mann–Oakes–Renner relation and the reduction of pion velocity near the critical point.     

Non-Hermitian Ising model at finite temperature

As a very simple model, the Ising model plays an important role in statistical physics. In the paper,with the help of quantum Liouvillian statistical theory, we study the one-dimensional nonHermitian Ising model at finite temperature and give its analytical solutions. We find that the nonHermitian Ising model shows quite different properties from those of its Hermitian counterpart. For example, the ‘pseudo-phase transition’ is explored between the ‘topological’ phase and the ‘nontopological’ pha...     

Non-local Thirring model at finite temperature

We extend a recently proposed non-local and non-covariant version of the Thirring model to the finite-temperature case. We obtain a completely bosonized expression for the partition function, describing the thermodynamics of the collective modes which are the underlying excitations of this system. From this result we derive closed formulae for the free-energy, specific-heat, two-point correlation functions and momentum distribution, as functionals of electron-electron coupling potentials. © 1998 Elsevier Science B.V.     

Self-consistent RPA based on a many-body vacuum

Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.     

RPA instabilities in finite nuclei at low density

Early development of the instabilities in a dilute nuclear source is investigated using a finite temperature quantal RPA approach for different systems. The growth rates of the unstable collective modes are determined by solving a dispersion relation, which is obtained by parametrizing the transition density in terms of its multipole moments. Under typical conditions of a dilute finite system at moderate temperatures the dispersion relation exhibits an ultraviolet cut-off. As a result, only a finite number of multipole modes becomes unstable, and the number of the unstable collective modes increases with the size of the source. Calculations indicate that for an expanding source, unstable modes show a transition from surface to volume character.     

Massive light-front Schwinger model at finite temperature

The determination of the partition function and thermodynamical quantities of the massive Schwinger model in light-front quantization is discussed. Discrete light cone quantization is used to derive a finite Hamiltonian matrix in Fock space representation. The thermodynamical and continuum limit are treated with care and systematical errors are estimated.     

Cellular model of INVAR at finite temperature

The cellular model,² derived from the Kachi and Asano model³ by taking into account the non-local interaction between cells of n ? 14 atoms, is treated at finite temperature. In the INVAR case, with the introduction of spin waves it allows a very good fit with the Crangle and Hallam data¹ for the magnetization and accounts for the evolution of the repartition of hyperfine fields.²     

Chiral Schwinger model with a Podolsky term at finite temperature

We study an exactly solvable two-dimensional model which mimics the basic features of the standard model. This model combines chiral coupling with an infrared behavior which resembles low energy QCD. This is done by adding a Podolsky higher-order derivative term in the gauge field to the Lagrangian of the usual chiral Schwinger model. We adopt a finite temperature regularization procedure in order to calculate the non-trivial fermionic Jacobian and obtain the photon and fermion propagators, first at zero temperature and then at finite temperature in the imaginary and real time formalisms. Both singular and non-singular cases, corresponding to the choice of the regularization parameter, are treated. In the nonsingular case there is a tachyonic mode as usual in a higher order derivative theory, however in the singular case there is no tachyonic excitation in the spectrum.     

Thermo field dynamics in the treatment of the nuclear pairing problem at finite temperature

The use of the thermo field dynamics, in dealing with the study of nuclear properties at finite temperature, is discussed for the case of a nuclear Hamiltonian which includes a single-particle term and a monopole pairing residual two-body interaction. The rules of the thermo field dynamics are applied to double the Hilbert space, thus accounting for the thermal occupation of single-particle states, and to construct dual spaces, both for single-particle (BCS) and collective (RPA) degrees of freedom. It is shown that the rules of the thermo field dynamics yield to a temperature dependence of the equations describing quasiparticle and phonon excitations which is similar to the one found in the more conventional finite temperature Wick's theorem approach, namely: by dealing with thermal averages.     

The second RPA description for the decay of the one-phonon nuclear collective states at finite temperature

The zero-temperature second RPA is generalized to finite temperatures through the use of the method of linearization of the equations of motion. After elimination of the quadruples, for low enough temperatures and within the subspace spanned by the doubles, a proper symmetrization yields an eigenvalue equation which exhibits formal properties like the simple RPA. From this second RPA eigenvalue equation, a closed formula for the spreading width of an isolated collective state is extracted. The second RPA can be recast in the form of a generalized collision term and be compared with the method of the Bethe-Salpeter equation for the two-body Green function. However, the second RPA method (and results) contrasts with the approach (and corresponding results) of the Boltzmann collision term, which is usually viewed as the appropriate agent for nuclear dissipation.     

A Bohr-Mottelson model of nuclei at finite temperature

Starting from Boltzmann-Langevin equation and performing a fluid dynamical reduction, a system of coupled Langevin equations is derived for a multipolar velocity field. This system is then applied to monopole andβ-,γ-quadrupole resonances, making a link between microscopic approaches and phenomenological macroscopic ones.     

Self-consistent RPA retarded polaron Green function for quantum kinetics

We compute numerically the time dependent retarded Green function of the polaron within the self-consistent RPA approximation. The results show an approximately Gaussian behaviour at t=0 changing at later times its concavity to an exponential decay, as it has been predicted in the approximate form of an inverse hyperbolic cosine function. The result contrasts with the non-selfconsistent RPA, where the exponential decay is only a transitory behaviour and the asymptotics is rather oscillatory. Our conclusions are significant in the context of the quantum kinetics with LO-phonons, where the transition from an intitially coherent scattering kinetics to a Markov kinetics with energy conservation is controlled by the time behaviour of the retarded Green function. Received: 18 September 1997 / Revised: 24 October 1997 / Accepted: 6 November 1997     

有限温度下一维Gaudin-Yang模型的热力学性质

本文通过数值求解有限温度下一维均匀费米Gaudin-Yang模型的热力学Bethe-ansatz方程, 研究了此模型的基本性质,得到了在给定的温度或给定的相互作用下, 化学势、相互作用、粒子密度和熵的相互变化图像. 对结果分析发现, 在给定温度和相互作用下, 熵随着化学势的变化有一个量子临界区域.