We classify generators of quantum Markov semigroups on (h), with h finite-dimensional and with a faithful normal invariant state ρ satisfying the standard quantum detailed balance condition with an anti-unitary time reversal θ commuting with ρ, namely $tr\left({\rho }^{1/2}x{\rho }_t^{1/2}\left(y\right)\right)=tr({\rho }^{1/2}\theta y*\theta {\rho }_t^{1/2}(\theta x*\theta ))$ for all x,y ∈ and t ≥ 0. Our results also show that it is possible to find a standard form for the operators in the Lindblad representation of the generators extending the standard form of generators of quantum Markov semigroups satisfying the usual...

We review recent results on interface states in quantum statistical mechanics.