Generators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance

TL;DR

This paper characterizes the structure of generators for quantum Markov semigroups on B(h) that are symmetric with respect to a specific scalar product and satisfy quantum detailed balance conditions, advancing understanding of quantum symmetries.

Contribution

It provides a detailed description of generators of symmetric quantum Markov semigroups satisfying quantum detailed balance conditions, extending classical notions to the quantum setting.

Findings

Characterization of generators of symmetric quantum Markov semigroups.

Connection between symmetry, detailed balance, and antiunitary time reversal.

Framework for analyzing quantum detailed balance conditions.

Abstract

We find the structure of generators of norm continuous quantum Markov semigroups on B(h) that are symmetric with respect to the scalar product tr(\rho^{1/2}x\rho^{1/2}y) induced by a faithful normal invariant state invariant state \rho and satisfy two quantum generalisations of the classical detailed balance condition related with this non-commutative notion of symmetry: the so-called standard detailed balance condition and the standard detailed balance condition with an antiunitary time reversal.