On coupling kinetic and Schrodinger equations

TL;DR

This paper studies a coupled system of a quantum Boltzmann equation and a nonlinear Schrödinger equation, establishing existence, uniqueness, convergence to equilibrium, and scattering results for the Bose-Einstein Condensate and thermal cloud dynamics.

Contribution

It introduces a novel coupled model combining kinetic and quantum wave equations, with rigorous analysis of its well-posedness and long-term behavior.

Findings

Proved existence and uniqueness of solutions.

Established convergence to equilibrium for the thermal cloud.

Developed scattering theory for the condensate wave function.

Abstract

We consider in this paper a system coupling a linear quantum Boltzmann equation and a defocusing cubic nonlinear Schrodinger equation. The Schrodinger equation reflects the dynamics of the wave function of the Bose-Einstein Condensate and the kinetic part of the system describes the evolution of the density function of the thermal cloud. An existence and uniqueness result for the system is supplied. We also prove the convergence to equilibrium of the density function of the thermal cloud and a scattering theory for the wave function of the condensate.