Boson Quadratic GKLS Generators

Alexander Evgen’evich Teretenkov

We review results on GKSL-type equations with multi-modal generators which are quadratic in bosonic or fermionic creation and annihilation operators. General forms of such equations are presented. The Gaussian solutions are obtained in terms of equations for the first and the second moments. Different approaches for their solutions are discussed.

Apolodor Aristotel Raduta

Jorge R. Bolaños-Servín, Franco Fagnola, Roberto B. Quezada

Generators of Gaussian QMS have a GKLS form with noise operators that are linear in creation and annihilation operators, and Hamiltonian which is quadratic. We characterize Gaussian QMS arising in the Weak Coupling Limit (WCL) of a system interacting with some reservoirs. It turns out that their generators, under some natural assumptions, have a GKLS representation with noise operators that are either annihilation or creation operators and Hamiltonian [Formula: see text] which is diagonalizable as a quadratic operator.

Philip L. Taylor, Olle Heinonen

Alexander Evgen’evich Teretenkov