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Title: On the inclusion of collisional correlations in quantum dynamics

We present a formalism to describe collisional correlations responsible for thermalization effects in finite quantum systems. The approach consists in a stochastic extension of time dependent mean field theory. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals allowing a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of time dependent mean-fields. This theory was formulated long ago in terms of density matrices but never applied in practical cases because of its complexity. We propose here a reformulation of the theory in terms of wave functions and use a simplified 1D model of cluster and molecules allowing to test the theory in a schematic but realistic manner. We illustrate the performance in terms of several observables, in particular global moments of the density matrix and single particle entropy built on occupation numbers. The occupation numbers remain fixed in time dependent mean-field propagation and change when evaluating the correlations, then taking fractional values. They converge asymptotically towards Fermi distributions which is a clear indication of thermalization.
Authors:
 [1] ;  [2] ;  [1] ;  [3]
  1. Laboratoire de Physique Théorique, Université Paul Sabatier, CNRS, F-31062 Toulouse Cédex (France)
  2. Institut für Theoretische Physik, Universität Erlangen, D-91058 Erlangen (Germany)
  3. (United States)
Publication Date:
OSTI Identifier:
22451152
Resource Type:
Journal Article
Resource Relation:
Journal Name: Annals of Physics; Journal Volume: 355; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; ENTROPY; MEAN-FIELD THEORY; PERTURBATION THEORY; QUANTUM SYSTEMS; STOCHASTIC PROCESSES; THERMALIZATION; TIME DEPENDENCE