Adiabatic Lindbladian Evolution with Small Dissipators
Abstract
We consider a timedependent small quantum system weakly coupled to an environment, whose effective dynamics we address by means of a Lindblad equation. We assume the Hamiltonian part of the Lindbladian is slowly varying in time and the dissipator part has small amplitude. We study the properties of the evolved state of the small system as the adiabatic parameter and coupling constant both go to zero, in various asymptotic regimes. In particular, we analyse the deviations of the transition probabilities of the small system between the instantaneous eigenspaces of the Hamiltonian with respect to their values in the purely Hamiltonian adiabatic setup, as a function of both parameters.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 April 2022
 DOI:
 10.1007/s00220021043065
 arXiv:
 arXiv:2106.15749
 Bibcode:
 2022CMaPh.391..223J
 Keywords:

 Mathematical Physics;
 Quantum Physics;
 81Q05;
 81Q93;
 81Q12
 EPrint:
 Some arguments slightly extended, comments and references added, typos corrected. To appear in Commun. Math. Phys