Uniform and Completely Nonequilibrium Invariant States for Weak Coupling Limit Type Quantum Markov Semigroups Associated with Eulerian Cycles

Abstract

We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.