Bolaños-Servin, Jorge R.; Carbone, Raffaella Spectral properties of circulant quantum Markov semigroups. (English) Zbl 1309.81122 Open Syst. Inf. Dyn. 21, No. 4, Article ID 1450007, 18 p. (2014). Summary: 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. Cited in 7 Documents MSC: 81S25 Quantum stochastic calculus PDFBibTeX XMLCite \textit{J. R. Bolaños-Servin} and \textit{R. Carbone}, Open Syst. Inf. Dyn. 21, No. 4, Article ID 1450007, 18 p. (2014; Zbl 1309.81122) Full Text: DOI References: [1] doi:10.1142/S1230161213500091 · Zbl 1271.81089 · doi:10.1142/S1230161213500091 [2] doi:10.1142/S0219025700000030 · Zbl 1040.47503 · doi:10.1142/S0219025700000030 [3] doi:10.1142/S0219025713500161 · Zbl 1302.46051 · doi:10.1142/S0219025713500161 [4] doi:10.1007/BF02676724 · Zbl 1015.47026 · doi:10.1007/BF02676724 [5] doi:10.1063/1.2890700 · Zbl 1153.81331 · doi:10.1063/1.2890700 [6] doi:10.1142/S0219025704001633 · Zbl 1059.46051 · doi:10.1142/S0219025704001633 [7] doi:10.1103/PhysRevA.76.032308 · doi:10.1103/PhysRevA.76.032308 [8] doi:10.1142/S1230161210000163 · Zbl 1213.81160 · doi:10.1142/S1230161210000163 [9] doi:10.1214/aoap/1034968224 · Zbl 0867.60043 · doi:10.1214/aoap/1034968224 [10] doi:10.1006/jfan.1998.3342 · Zbl 0923.46066 · doi:10.1006/jfan.1998.3342 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.