Kinetic Theories

M. Bönitz

Fedir T. Vasko, O. É. Raichev

Kenneth E. Hawker

Vir B. Bulchandani, Xiangyu Cao, Joel E. Moore

Abstract We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe–Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the kinetic theory depends smoothly on Planck’s constant, and explicitly characterise the leading quantum corrections to classical behaviour. The classical kinetic theory is compared with direct numerical simulations and shows excellent agreement. Finally, we connect the Bethe–Boltzmann approach with the classical inverse scattering method, by identifying conserved quasiparticles with the spectrum of the Lax matrix.

Anton Sergeevich Trushechkin

Katsuhiko Higuchi, Masahiko Higuchi

We derive the coupling-constant expression for the kinetic energy (KE) functional of the pair-density-functional theory. Such the expression can be effectively used in developing the approximate KE functional. Indeed, on the basis of this expression, we present an approximate form of the KE functional by means of the perturbation theory. Furthermore, as the first step of an alternative way of obtaining the approximate KE functional, we derive several relations and bounds for the KE functional by investigating how the KE functional changes with the nonuniform scaling, rotation, and translation of electron coordinates. Such relations and bounds can be utilized as restrictive conditions on the approximate form. Thus, the coupling-constant expression, relations and bounds obtained here provide useful tools for devising various types of the approximate KE functional that is indispensable for advancing the pair-density-functional theory.