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Reduced and extended weak coupling limit

100%

Dereziński J., De Roeck W.

Banach Center Publications

2007

tom 78

nr 1

91-119

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].

Positive energy quantization of linear dynamics

100%

Dereziński J., Gérard C.

Banach Center Publications

2010

tom 89

nr 1

75-104

The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into three stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. Four kinds of systems are distinguished: neutral bosonic, neutral bosonic, charged bosonic and charged fermionic. The formalism that is described follows closely the usual constructions employed in quantum physics to introduce noninteracting quantum fields.

Ograniczanie wyników

2 Banach Center Publications

2 Dereziński J.

1 De Roeck W.

1 Gérard C.

1 2010

1 2007

Wyniki wyszukiwania

Reduced and extended weak coupling limit

Positive energy quantization of linear dynamics