×

zbMATH — the first resource for mathematics

Low density limit: Without rotating wave approximation. (English) Zbl 0885.46058
Summary: In the present paper, we investigate the low density limit of a quantum “System + Reservoir” model in which the temperature is finite and the Hamiltonian of the system has a discrete spectrum. It is proved that the matrix elements of the time evolution operator, with a time rescaling and some proper choice of collective vector, tends to matrix elements of a solution of a quantum stochastic differential equation driven by a quantum Poisson process.

MSC:
46N50 Applications of functional analysis in quantum physics
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Accardi, L.; Lu, Y.-G., Commun. math. phys., 141, 9, (1991)
[2] Accardi, L.; Lu, Y.-G., Nagoya math., 126, 25, (1992)
[3] Accardi, L.; Lu, Y.-G., J. phys. A: math. gen., 24, 3483, (1991)
[4] Frigerio, A., Lecture notes in math., 1303, 107, (1988)
[5] Frigerio, A.; Maassen, H., Prob. th. rel. fie., 83, 489, (1989)
[6] Hudson, R.L.; Parthasarathy, K.R., Commun. math. phys., 93, 301, (1984)
[7] Lu, Y.-G., J. math. phys., 33, 9, 3060, (1992)
[8] Palmer, P.F., The rigorous theory of infinite quantum mechanical system. master equations and the dynamics of open systems, ()
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.