Modified logarithmic Sobolev inequalities for Abelian quantum double models
量子物理
2026-05-20 v1 数学物理
math.MP
概率论
摘要
We establish rapid mixing for Davies Markov semigroups associated with 2D Abelian quantum double models at any positive temperature. A condition of Dobrushin-Shlosman (DS) type holds at any temperature, and we show that the latter implies a modified logarithmic Sobolev inequality for the Davies Lindbladian. A key step in the argument is to verify a strong martingale condition for the local conditional expectations of the Davies semigroup in the regime of validity of the DS condition.
引用
@article{arxiv.2605.19640,
title = {Modified logarithmic Sobolev inequalities for Abelian quantum double models},
author = {Sebastian Stengele and Ángela Capel and Li Gao and Angelo Lucia and David Pérez-García and Antonio Pérez-Hernández and Cambyse Rouzé and Simone Warzel},
journal= {arXiv preprint arXiv:2605.19640},
year = {2026}
}
备注
22 pages, 2 figures