Global and local relaxation of a spin chain under exact Schrödinger and master-equation dynamics.

Phys Rev E Stat Nonlin Soft Matter Phys

Institute of Theoretical Physics I, University of Stuttgart, Pfaffenwaldring 57, 70550 Stuttgart, Germany.

Published: August 2005

We solve the Schrödinger equation for an interacting spin chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin chain as well as of single spins is analyzed. We show that the total spin chain relaxes to a thermal equilibrium state independently of the internal interaction strength. In contrast, the asymptotic states of each individual spin are thermal for weak but nonthermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of 0.1 x deltaE , with deltaE denoting the Zeeman splitting. We compare these results with a master-equation treatment; when time averaged, both approaches lead to the same asymptotic state and finally with analytical results.

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http://dx.doi.org/10.1103/PhysRevE.72.026104DOI Listing

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