Low density limit in the theory of open quantum systems

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

References

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          
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)