Difference Kinetic Equations in Many-Particle Physics

TL;DR

This paper derives quantum difference kinetic equations using plane wavelets, incorporating two-particle correlations, and shows their relation to classical Boltzmann equations in certain limits.

Contribution

It introduces a quantum derivation of difference kinetic equations with a complete set of plane wavelet functions and a positive definite distribution function.

Findings

Derivation of quantum difference kinetic equations with two-particle correlations

Complete orthonormal set of plane wavelet functions established

Reduction to classical Boltzmann equation in the appropriate limit

Abstract

Difference Kinetic Equations are derived quantum mechanically in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors is used as the second quantization basis allowing introducing the positively definite distribution function. It is obtained that inhomogeneous system is described by numbers of particles at quantized positions with quantized momenta. Difference Kinetic Equation for distribution function transforms into the classical Boltzmann Equation in the limit, where expectation value of particles number varies little.