Gaussian Quantum Markov Semigroups on a One-Mode Fock Space: Irreducibility and Normal Invariant States
Julián Agredo, Franco Fagnola, Damiano Poletti
Abstract
We consider the most general Gaussian quantum Markov semigroup on a one-mode Fock space, discuss its construction from the generalized GKSL representation of the generator. We prove the known explicit formula on Weyl operators, characterize irreducibility and its equivalence to a Hörmander type condition on commutators and establish necessary and sufficient conditions for existence and uniqueness of normal invariant states. We illustrate these results by applications to the open quantum oscillator and the quantum Fokker-Planck model.
Topics & Concepts
Fock spaceIrreducibilityMathematicsPure mathematicsSemigroupQuantumGaussianInvariant (physics)UniquenessMathematical physicsQuantum mechanicsMathematical analysisPhysicsQuantum Information and CryptographyQuantum optics and atomic interactionsCold Atom Physics and Bose-Einstein Condensates