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Seminar of the Department of Theoretical Physics, Steklov Mathematical Institute of RAS
January 29, 2014 14:00, Moscow, Steklov Mathematical Institute of RAS, Room 404 (8 Gubkina)

Low density limit in the theory of open quantum systems

A. N. Pechen

Steklov Mathematical Institute of the Russian Academy of Sciences

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Abstract: In this talk we will discuss some results for the model of a quantum particle (e.g., atom, molecule) interacting with dilute quantum gas. Interaction between the system and particles of the gas is considered to be strong and preserving number of particles of the gas. Low density limit is defined as the limit of various quantities characterizing the model when density of the gas n goes to zero and time t goes to infinity in such a way that nt=const. Reduced dynamics of the system density matrix in the low density limit was studied by R. Dumcke in 1984. Quantum stochastic differential equations for the total dynamics were derived in joint works of the speaker with L. Accardi and I.V. Volovich. In this talk we will discuss the total dynamics of the system and the gas in the low density limit and the appearance of free statistics in the low density limit of time-dependent non-chronological correlation functions of operators describing the model

  1. L. Accardi, A. Pechen, I. V. Volovich, “A stochastic golden rule and quantum Langevin equation for the low density limit”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 6:3 (2003), 431–453  crossref  mathscinet  zmath  isi  scopus
  2. A. N. Pechen, “The multi-time correlation functions, free white noise, and the generalized Poisson statistics in the low density limit”, J. Math. Phys., 47 (2006)  crossref  mathscinet  zmath  scopus

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