Equilibration in long-range quantum spin systems from a BBGKY perspective

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dc.contributor.authorPaskauskas R.
dc.contributor.authorKastner M.
dc.date.accessioned2012-04-12T08:23:06Z
dc.date.available2012-04-12T08:23:06Z
dc.date.issued2012
dc.description.abstractThe time evolution of ℓ-spin reduced density operators is studied for a class of Heisenberg-type quantum spin models with long-range interactions. In the framework of the quantum Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, we introduce an unconventional representation, different from the usual cluster expansion, which casts the hierarchy into the form of a second-order recursion. This structure suggests a scaling of the expansion coefficients and the corresponding time scales in powers of N 1/2 with the system size N, implying a separation of time scales in the large-system limit. For special parameter values and initial conditions, we can show analytically that closing the BBGKY hierarchy by neglecting ℓ-spin correlations never leads to equilibration, but gives rise to quasi-periodic time evolution with at most ℓ/2 independent frequencies. Moreover, for the same special parameter values and in the large- N limit, we solve the complete recursion relation (the full BBGKY hierarchy), observing a superexponential decay to equilibrium in rescaled time τ = tN -1/2. © 2012 IOP Publishing Ltd.
dc.identifier.citationJournal of Statistical Mechanics: Theory and Experiment
dc.identifier.citation2012
dc.identifier.citation2
dc.identifier.issn17425468
dc.identifier.other10.1088/1742-5468/2012/02/P02005
dc.identifier.urihttp://hdl.handle.net/10019.1/20620
dc.subjectladders and planes (theory)
dc.subjectmetastable states
dc.subjectspin chains
dc.titleEquilibration in long-range quantum spin systems from a BBGKY perspective
dc.typeArticle
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