Subdynamics of relevant observables: a field theoretical approach

Details Subdynamics of relevant observables: a field theoretical approach Subdynamics of relevant observables: a field theoretical approach

2002-04-16

arxiv.org/abs/quant-ph/0204091v1

Int.J.Mod.Phys. A17 (2002) 435-463

Physics

Quantum Physics

28 pages, latex, no figures

Scientific paper

10.1142/S0217751X02005918

An approach to the description of subdynamics inside non-relativistic quantum field theory is presented, in which the notions of relevant observable, time scale and complete positivity of the time evolution are stressed. A scattering theory derivation of the subdynamics of a microsystem interacting through collisions with a macrosystem is given, leading to a master-equation expressed in terms of the operator-valued dynamic structure factor, a two-point correlation function which compactly takes the statistical mechanics properties of the macrosystem into account. For the case of a free quantum gas the dynamic structure factor can be exactly calculated and in the long wavelength limit a Fokker-Planck equation for the description of quantum dissipation and in particular quantum Brownian motion is obtained, where peculiar corrections due to quantum statistics can be put into evidence.

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