New methods and structures in the theory of the multi-mode Dicke laser model

Abstract

We base a treatment of the dissipative, multi-mode version of Dicke laser model on the theory of completely positive dynamical semigroups and quantum Markov processes. This leads to new results at both the mathematical and physical levels. On the physical side, it provides a generalization of the Hepp–Lieb model that admits both chaotic and polychromatic laser radiation. On the mathematical side, it extends the theory of dynamical semigroups to a regime where the generators are perturbed by unbounded derivations.