Classical and Quantum Part of the Environment for Quantum Langevin Equations

Stéphane Attal (1) , Ivan Bardet (1)

1 EDPA - Équations aux dérivées partielles, analyse

Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is purely algebraic, in terms of the coefficients of the equation. In a second part, we consider general quantum Langevin equations and we prove that they can always be split into a maximal part driven by classical noises and a purely quantum one.

Mots clés: quantum and classical noises; quantum Langevin Equation

Domaines: Physique mathématique [math-ph]; Probabilités [math.PR]; Algèbres d'opérateurs [math.OA]; Physique Quantique [quant-ph]

Stéphane Attal, Ivan Bardet. Classical and Quantum Part of the Environment for Quantum Langevin Equations. 2016. ⟨hal-01378617⟩