Return to equilibrium in the XY model
type: Item
instance of: scholarly article
title: Return to equilibrium in the XY model
zbMATH Open document ID: 0632.46071
DOI: 10.1007/BF01011909
author: Leigh Hume
author: Derek W. Robinson
published in: Journal of Statistical Physics
publication date: 1986-01-01T00:00:00Z
review text: We prove that the locally perturbed XY model returns to equilibrium under the unperturbed evolution but the unperturbed model does not necessarily approach equilibrium under the perturbed evolution. In fact this latter property is false for perturbation by a local magnetization. The failure is directly attributable to the formation of bound states. If the perturbation is quadratic these problems are reduced to spectral analysis of the one-particle Hamiltonian. We demonstrate that the perturbed Hamiltonian has a finite set of eigenvalues of finite multiplicity together with some absolutely continuous spectrum. Eigenvalues can occur in the continuum if, and only if, the perturbation dislocates the system. Singular continuous spectrum cannot occur.
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 81T05
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 4028189
zbMATH Keywords: quadratic perturbation
zbMATH Keywords: locally perturbed XY model returns to equilibrium
zbMATH Keywords: perturbation by a local magnetization
zbMATH Keywords: formation of bound states
MaRDI profile type: Publication
cites work: Relaxation of Local Thermal Deviations from Equilibrium
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description: scientific article; zbMATH DE number 4028189