Ergodic Theory of Inhomogeneous Quantum Processes

TL;DR

This paper establishes a rigorous framework for analyzing ergodicity and mixing in inhomogeneous quantum processes, extending classical theories and connecting with quantum many-body systems.

Contribution

It introduces a quantum Markov-Dobrushin approach to quantify mixing and provides new conditions for convergence and stability in time-inhomogeneous quantum dynamics.

Findings

Sharpened conditions for convergence rates

Exponential stability of quantum dynamics

Unified framework for inhomogeneous quantum systems

Abstract

This work develops a rigorous framework for analysing ergodicity and mixing in time-inhomogeneous quantum dynamics. It considers quantum evolutions generated by sequences of quantum channels and examines in detail the relationship between the forward and backward dynamics, showing that they are generically nonequivalent in a structurally meaningful way. A central contribution is the adoption of a quantum Markov-Dobrushin approach to quantify mixing, which yields sharpened conditions for convergence rates and for establishing exponential stability of the induced dynamics. The resulting formalism not only extends classical and stationary quantum theories, but also naturally accommodates non-translationally invariant matrix product states, thereby providing a unified interface with experimentally relevant quantum many-body systems.