GKLS vector field dynamics for Gaussian states

Abstract

We construct the vector field associated with the GKLS generator for systems described by Gaussian states . This vector field is defined on the dual space of the algebra of operators, restricted to operators quadratic in position and momentum. It is shown that the GKLS dynamics accepts a decomposition principle, that is, this vector field can be decomposed into three parts: a conservative Hamiltonian component, a gradient-like component, and a Choi–Kraus or jump vector field. The last two terms are considered “perturbations” associated with dissipation. Examples are presented for a harmonic oscillator with different dissipation terms.