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

Markus J. Henrich·Mathias Michel·Michael Hartmann·Guenther Mahler·Jochen Gemmer
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Abstract

We solve the Schroedinger 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 non-thermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of $0.1 \times ΔE$, with $ΔE$ 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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Markus J. Henrich, Mathias Michel, Michael Hartmann, Guenther Mahler, Jochen Gemmer. 2005-11-03. Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics. https://doi.org/10.1103/physreve.72.026104

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