A linearized kinetic problem on the half-line with collision operator from a Bose condensate with excitations

TL;DR

This paper analyzes a linearized quantum Boltzmann equation on the half-line, establishing existence, uniqueness, and asymptotic behavior of solutions with a focus on energy and entropy flows in a Bose condensate context.

Contribution

It introduces a novel analysis of a Milne problem for a quantum Boltzmann equation with non-constant energy flow and cubic velocity-dependent collision frequency.

Findings

Proved existence and uniqueness of solutions.

Established asymptotic properties related to energy and entropy flows.

Identified differences from classical Boltzmann equations in flow behavior.

Abstract

The paper studies a Milne type problem for a linearized quantum Boltzmann equation. Existence and uniqueness of the solution, together with asymptotic properties are proven for a given energy flow. The energy flow is proportional to the asymptotic limit of the mass flow, and the collision frequency is aymptoticlaly cubic in velocity. The setting differs from the one for the classical Boltzmann and related equations, where the fluid-dynamic mass flow along half-line is constant. Here it is no more constant. Instead the study is based on the energy flow which is no more fluid-dynamic, and on the entropy flow which differs from the classical case.