On the reduced dynamics of a subset of interacting bosonic particles

Year: 2018

Authors: Gessner M., Buchleitner A.

Autors Affiliation: [Gessner, Manuel; Buchleitner, Andreas] Albert Ludwigs Univ Freiburg, Phys Inst, Hermann Herder Str 3, D-79104 Freiburg 3, Germany.
[Gessner, Manuel] CNR, INO, QSTAR, Largo Enrico Fermi 2, I-50125 Florence, Italy and LENS, Largo Enrico Fermi 2, I-50125 Florence, Italy.
[Gessner, Manuel] Ist Nazl Ric Metrol, Str Cacce 91, I-10135 Turin, Italy.
[Buchleitner, Andreas] Univ Oxford, Keble Coll, Oxford OX1 3PG, England

Abstract: The quantum dynamics of a subset of interacting bosons in a sub-space of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an N-particle system produces a hierarchical expansion for the subdynamics of M <= N particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross-Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction induced decoherence in form of a nonlinear Lindblad-type master equation. (C) 2018 Elsevier Inc. All rights reserved. Journal/Review: ANNALS OF PHYSICS

Volume: 390      Pages from: 192  to: 213

KeyWords: identical particles; Reduced density matrix; Bosons; Open quantum systems; BBGKY hierarchy
DOI: 10.1016/j.aop.2018.01.013

Citations: 2
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