Thermal effects in gravitational Hartree systems
Analysis of PDEs
2015-05-19 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1009.0128,
title = {Thermal effects in gravitational Hartree systems},
author = {Gonca L. Aki and Jean Dolbeault and Christof Sparber},
journal= {arXiv preprint arXiv:1009.0128},
year = {2015}
}