Repeated quantum interactions Quantum Langevin equation and the low density limit
Collection titlecahier de recherche CEREMADE- Paris-Dauphine
DeweyProbabilités et mathématiques appliquées
SujetPoisson processes; low density limit; quantum stochastique differentiel equation (or quantum Langevin equation); Repeated quantum interactions
MetadataShow full item record
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Item number of pages18
Abstract (EN)We consider a repeated quantum interaction model describing a small system HhS in interaction with each one of the identical copies of the chain N/N∗ /Cn+1, modeling a heat bath, one after another during the same short time intervals [0, h]. We suppose that the repeated quantum interaction Hamiltonian is split in two parts: a free part and an interaction part with time scale of order h . After giving the GNS representation, we establish the connection between the time scale h and the classical low density limit. We introduce a chemical potential μ related to the time h as follows: h2 = eβμ . We further prove that the solution of the associated discrete evolution equation converges strongly, when h tends to 0, to the unitary solution of a quantum Langevin equation directed by Poisson processes.
Showing items related by title, author, creator and subject.
Esteban, Maria J.; Lewin, Mathieu; Séré, Eric (2008) Article accepté pour publication ou publié
Dhahri, Ameur (2009) Article accepté pour publication ou publié
Fu, Ying; Rabitz, Herschel; Turinici, Gabriel (2016) Article accepté pour publication ou publié