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Time behavior of the correlation functions in a simple dissipative quantum model
Authors:C. Aslangul  N. Pottier  D. Saint-James
Affiliation:(1) Groupe de Physique des Solides de l'école Normale Supérieure (Laboratoire associé au C.N.R.S.), Université Paris VII, 2 place Jussieu, 75251 Paris Cedex 05, France;(2) Laboratoire de Physique Statistique, Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, France
Abstract:
The force and velocity correlation functions for a particle interacting with a bath are calculated within a model allowing for finite memory effects. The relevance of a Brownian picture is delineated in view of the respective behavior of these functions and appears fully inadequate below some cross-over temperature; then, the interplay between quantum and thermal fluctuations yields some long time tails on the same time scale for both correlation functions. The real space transient diffusion coefficient is found to exceed its asymptotic Einstein value for most times in that regime. The limiting case of an infinitely short memory time is also investigated and is seen to produce weak divergences on a time scale which is small as compared to the other characteristic times.
Keywords:Quantum noise  correlation functions  long time tails  Brownian motion
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