Thermal effects in gravitational Hartree systems

TL;DR

This paper studies gravitational Hartree systems at finite temperature, establishing conditions for the existence of stationary states, and characterizing the transition between pure and mixed quantum states based on temperature thresholds.

Contribution

It introduces a framework for constructing thermal stationary states in gravitational Hartree models and identifies critical temperatures influencing state purity.

Findings

Existence of minimizers below a temperature threshold

Characterization of pure versus mixed states based on temperature

Dependence of critical temperature on entropy functional choice

Abstract

We consider the non-relativistic Hartree model in the gravitational case, i.e. with attractive Coulomb-Newton interaction. For a given mass, we construct stationary states with non-zero temperature by minimizing the corresponding free energy functional. It is proved that minimizers exist if and only if the temperature of the system is below a certain threshold(possibly infinite), which itself depends on the specific choice of the entropy functional. We also investigate whether the corresponding minimizers are mixed or pure quantum states and characterize a positive critical temperature above which mixed states appear.