caa a22 4500 475742052 CHVBK 20180406123502.0 cr unu---uuuuu 170329e20000501xx s 000 0 eng 10.1007/BF02676340 doi (NATIONALLICENCE)springer-10.1007/BF02676340 Shustikov S. Faculty of Physics, M. V. Lomonosov Moscow State University, USSR aut Regularity criterion for a mathematical model of the laser [Elektronische Daten] [S. Shustikov] There exists a deep relationship between the nonexplosion conditions for Markov evolution in classical and quantum probability theories. Both of these conditions are equivalent to the preservation of the unit operator (total probability) by a minimal Markov semigroup. In this work, we study the Heisenberg evolution describing an interaction between the chain ofN two-level atoms andn-mode external Bose field, which was considered recently by J. Alli and J. Sewell. The unbounded generator of the Markov evolution of observables acts in the von Neumann algebra. For the generator of a Markov semigroup, we prove a nonexplosion condition, which is the operator analog of a similar condition suggested by R. Z. Khas'minski and later by T. Taniguchi for classical stochastic processes. For the operator algebra situation, this condition ensures the uniqueness and conservativity of the quantum dynamical semigroup describing the Markov evolution of a quantum system. In the regular case, the nonexplosion condition establishes a one-to-one relation between the formal generator and the infinitesimal operator of the Markov semigroup. Kluwer Academic/Plenum Publishers, 2000 Markov evolution nationallicence quantum dynamical semigroup nationallicence nonexplosion condition nationallicence quantum interaction nationallicence two-level atom nationallicence infinitesimal operator nationallicence Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/5(2000-05-01), 665-671 0001-4346 67:5<665 2000 67 11006 https://doi.org/10.1007/BF02676340 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02676340 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Shustikov S. Faculty of Physics, M. V. Lomonosov Moscow State University, USSR aut NATIONALLICENCE 773 0- Mathematical Notes Kluwer Academic Publishers-Plenum Publishers 67/5(2000-05-01), 665-671 0001-4346 67:5<665 2000 67 11006 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer