Nonlocal Kinetic Theory (original) (raw)

Nonlocal corrections to the Boltzmann equation for dense Fermi systems

Physics Letters A, 1998

A kinetic equation which combines the quasiparticle drift of Landau's equation with a dissipation governed by a nonlocal and noninstant scattering integral in the spirit of Snider's equation for gases is derived. Consequent balance equations for the density, momentum and energy include quasiparticle contributions and the second order quantum virial corrections. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. An implementation to heavy ion collisions is discussed.

Correlational latent heat by nonlocal quantum kinetic theory

Physical review, 2018

The kinetic equation of nonlocal and non-instantaneous character unifies the achievements of the transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. Large cancellations in the off-shell motion appear which are hidden usually in non-Markovian behaviors. The remaining corrections are expressed in terms of shifts in space and time that characterize the non-locality of the scattering process. In this way quantum transport is possible to recast into a quasi-classical picture. The balance equations for the density, momentum, energy and entropy include besides quasiparticle also the correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy. For Maxwellian particles with time-dependent s-wave scattering, the correlated parts of the observables are calculated and a sign change of the latent heat is reported at a universal ratio of scattering length to the thermal De Broglie wavelength. This is interpreted as a change from correlational heating to cooling.

Kinetic equation for strongly interacting dense Fermi systems

Annales De Physique, 2001

We review the non-relativistic Green's-function approach to the kinetic equations for Fermi liquids far from equilibrium. The emphasis is on the consistent treatment of the off-shell motion between collisions and on the non-instant and non-local picture of binary collisions.

Retarded versus Time-Nonlocal Quantum Kinetic Equations

Annals of Physics, 2001

The finite duration of the collisions in Fermionic systems as expressed by the retardation time in non-Markovian Levinson-type kinetic equations is discussed in the quasiclassical limit. We separate individual contributions included in the memory effect resulting in (i) off-shell tails of the Wigner distribution, (ii) renormalization of scattering rates and (iii) of the single-particle energy, (iv) collision delay and (v) related non-local corrections to the scattering integral. In this way we transform the Levinson equation into the Landau-Silin equation extended by the non-local corrections known from the theory of dense gases. The derived nonlocal kinetic equation unifies the Landau theory of quasiparticle transport with the classical kinetic theory of dense gases. The space-time symmetry is discussed versus particle-hole symmetry and a solution is proposed which transforms these two exclusive pictures into each other. * Equations derived from the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of reduced densities.

Fluctuations due to the nonlocal character of collisions

New Journal of Physics - NEW J PHYS, 2007

It is shown that the collision integral describing the nonlocal character of collisions leads to the same mean-field fluctuations in the one-particle distribution as proposed by Boltzmann Langevin pictures. It is argued that this appropriate collision integral contains the fluctuation dissipation theorems in equilibrium itself and therefore there is no need to assume additionally stochasticity. This leads to tremendous simplifications in numerical simulation schemes.

Nonlocal dynamical correlations of strongly interacting electron systems

Physical Review B, 1998

We introduce an extension of the dynamical mean field approximation (DMFA) which retains the causal properties and generality of the DMFA, but allows for systematic inclusion of non-local corrections. Our technique maps the problem to a self-consistently embedded cluster. The DMFA (exact result) is recovered as the cluster size goes to one (infinity). As a demonstration, we study the Falicov-Kimball model using a variety of cluster sizes. We show that the sum rules are preserved, the spectra are positive definite, and the non-local correlations suppress the CDW transition temperature.

Transient oscillations in a macroscopic effective theory of the Boltzmann equation

Physical Review D, 2016

A new transient effective theory of the relativistic Boltzmann equation is derived for locally momentum-anisotropic systems. In the expansion of the distribution function around a local "quasiequilibrium" state a non-hydrodynamic dynamical degree of freedom is introduced at leading order that breaks local momentum isotropy. By replacing the deviation of the distribution function from this quasi-equilibrium state in terms of moments of the leading-order distribution and applying a systematic power counting scheme that orders the non-hydrodynamic modes by their microscopic time scales, a closed set of equations for the dynamical degrees of freedom is obtained. Truncating this set at the level of the slowest non-hydroynamic mode we find that it exhibits transient oscillatory behavior-a phenomenon previously found only in strongly coupled theories, where it appears to be generic. In weakly coupled systems described by the Boltzmann equation, these transient oscillations depend on the breaking of local momentum isotropy being treated non-perturbatively at leading order in the expansion of the distribution function.

Long and short time quantum dynamics: II. Kinetic regime

Physica E-low-dimensional Systems & Nanostructures, 2005

Non-equilibrium Green's functions reduce to quantum kinetic equations in the kinetic regime, that is, if the quasiclassical, quasi-particle picture is valid. The classical tool yielding the kinetic equations, the Kadanoff-Baym Ansatz, has been improved and generalized to a whole Ansatz family including the so-called extended quasi-particle approximation. Each Ansatz produces a quantum kinetic theory: a quasi-particle kinetic equation and a functional of the quasi-particle distribution returning the average values of observables. In the extended quasi-particle model, the theory is physically consistent: causal, gauge invariant and conserving. This model leads to kinetic equations for dense Fermi liquids which combine the Landau quasi-particle drift with non-local scattering integrals in the spirit of the Enskog equation.

Nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas

Physical Review A, 2014

The average-density approximation is used to construct a nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas. This functional is then used to formulate a Thomas-Fermi von Weizsäcker-like theory for the description of the ground state properties of the system. The quality of the kinetic energy functional is tested by performing a fully self-consistent calculation for an ideal, harmonically confined, two-dimensional system. Good agreement with exact results are found, with the number and kinetic energy densities exhibiting oscillatory structure associated with the nonlocality of the energy functional. Most importantly, this functional shows a marked improvement over the two-dimensional Thomas-Fermi von Weizsäcker theory, particularly in the vicinity of the classically forbidden region.