Contractivity properties of a quantum diffusion semigroup
Abstract
We consider a quantum generalization of the classical heat equation, and study contractivity properties of its associated semigroup. We prove a Nash inequality and a logarithmic Sobolev inequality. The former leads to an ultracontractivity result. This in turn implies that the largest eigenvalue and the purity of a state with positive Wigner function, evolving under the action of the semigroup, decrease at least inverse polynomially in time, while its entropy increases at least logarithmically in time.
Cite
@article{arxiv.1607.04242,
title = {Contractivity properties of a quantum diffusion semigroup},
author = {Nilanjana Datta and Yan Pautrat and Cambyse Rouze},
journal= {arXiv preprint arXiv:1607.04242},
year = {2017}
}
Comments
The results of this paper were presented at the "48th Symposium on Mathematical Physics; Gorini-Kossakowski-Lindblad-Sudarshan Master Equation - 40 Years After", held in Torun, Poland (June 10-12, 2016). v2: minor typos and proof of Theorem 7 corrected. v3, v4: minor typos corrected and overall presentation improved. v5: Published version. v6: metadata modified