# Reduced and extended weak coupling limit

Jan Dereziński; Wojciech De Roeck

Banach Center Publications (2007)

- Volume: 78, Issue: 1, page 91-119
- ISSN: 0137-6934

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topJan Dereziński, and Wojciech De Roeck. "Reduced and extended weak coupling limit." Banach Center Publications 78.1 (2007): 91-119. <http://eudml.org/doc/282317>.

@article{JanDereziński2007,

abstract = {The main aim of our lectures is to give a pedagogical introduction to various mathematical formalisms used to describe open quantum systems: completely positive semigroups, dilations of semigroups, quantum Langevin dynamics and the so-called Pauli-Fierz Hamiltonians. We explain two kinds of the weak coupling limit. Both of them show that Hamiltonian dynamics of a small quantum system interacting with a large resevoir can be approximated by simpler dynamics. The better known reduced weak coupling limit leads to completely positive dynamics. The main topic of our lecture notes, the extended weak coupling limit, also known as the stochastic limit, leads to quantum Langevin dynamics. Our lecture notes are based partly on the results of our recent articles [DD1, DD2].},

author = {Jan Dereziński, Wojciech De Roeck},

journal = {Banach Center Publications},

keywords = {completely positive map; completely positive semigroup; weak coupling limit; Pauli-Fierz operator; Reservoir; Langevin dynamics; open systems; reduced dynamics},

language = {eng},

number = {1},

pages = {91-119},

title = {Reduced and extended weak coupling limit},

url = {http://eudml.org/doc/282317},

volume = {78},

year = {2007},

}

TY - JOUR

AU - Jan Dereziński

AU - Wojciech De Roeck

TI - Reduced and extended weak coupling limit

JO - Banach Center Publications

PY - 2007

VL - 78

IS - 1

SP - 91

EP - 119

AB - The main aim of our lectures is to give a pedagogical introduction to various mathematical formalisms used to describe open quantum systems: completely positive semigroups, dilations of semigroups, quantum Langevin dynamics and the so-called Pauli-Fierz Hamiltonians. We explain two kinds of the weak coupling limit. Both of them show that Hamiltonian dynamics of a small quantum system interacting with a large resevoir can be approximated by simpler dynamics. The better known reduced weak coupling limit leads to completely positive dynamics. The main topic of our lecture notes, the extended weak coupling limit, also known as the stochastic limit, leads to quantum Langevin dynamics. Our lecture notes are based partly on the results of our recent articles [DD1, DD2].

LA - eng

KW - completely positive map; completely positive semigroup; weak coupling limit; Pauli-Fierz operator; Reservoir; Langevin dynamics; open systems; reduced dynamics

UR - http://eudml.org/doc/282317

ER -

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