Reduced and extended weak coupling limit

Volume 78 / 2007

Jan Derezi/nski, Wojciech De Roeck Banach Center Publications 78 (2007), 91-119 MSC: 81Q99, 47N50. DOI: 10.4064/bc78-0-7


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].


  • Jan Derezi/nskiDepartment of Mathematical Methods in Physics
    Warsaw University
    Hoża 74
    00-682 Warszawa, Poland
  • Wojciech De RoeckInstituut voor Theoretische Fysica
    K.U. Leuven, Belgium

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