Spectral Properties of Circulant Quantum Markov Semigroups

We study the spectral properties of the generators of circulant quantum Markov semigroups. We can find an explicit expression for eigenvalues and eigenvectors of the infinitesimal generator and, in particular, we prove that the spectral gap is strictly positive. By proper techniques, we can reduce the problem on non-commutative algebras to the analogous one for a classical process with a circulant generator.