Equilibration in long-range quantum spin systems from a BBGKY perspective
Date
2012
Authors
Paskauskas R.
Kastner M.
Journal Title
Journal ISSN
Volume Title
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Abstract
The 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.
Description
Keywords
ladders and planes (theory), metastable states, spin chains
Citation
Journal of Statistical Mechanics: Theory and Experiment
2012
2
2012
2