Quantitative Hypocoercivity and Lifting of Classical and Quantum Dynamics

TL;DR

This paper provides a unified analysis of hypocoercivity in classical and quantum open systems, offering new estimates and a framework to accelerate convergence rates of Markov semigroups.

Contribution

It introduces a unified approach to hypocoercivity estimates and a lifting framework to enhance convergence rates in both classical and quantum dynamics.

Findings

Unified hypocoercivity estimates based on space-time Poincare inequality

A lifting framework for accelerating convergence in Markov semigroups

Bounds on convergence rates for classical and quantum systems

Abstract

We consider quantitative convergence analysis for hypocoercive dynamics such as Langevin and Lindblad equations describing classical and quantum open systems. Our goal is to provide an overview of recent results of hypocoercivity estimates based on space-time Poincare inequality, providing a unified treatment for classical and quantum dynamics. Furthermore, we also present a unified lifting framework for accelerating both classical and quantum Markov semigroups, which leads to upper and lower bounds of convergence rates.