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arXiv:quant-ph/0401051 · Physical Review B

Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques

Heinz‐Peter Breuer, Daniel Klaus Burgarth, Francesco Petruccione

Published Jul 30, 2004• 256 citations
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Abstract

The reduced dynamics of a central spin coupled to a bath of $N$ spin-$\frac{1}{2}$ particles arranged in a spin star configuration is investigated. The exact time evolution of the reduced density operator is derived, and an analytical solution is obtained in the limit $N\ensuremath{\rightarrow}\ensuremath{\infty}$ of an infinite number of bath spins, where the model shows complete relaxation and partial decoherence. It is demonstrated that the dynamics of the central spin cannot be treated within the Born-Markov approximation. The Nakajima-Zwanzig and the time-convolutionless projection operator technique are applied to the spin star system. The performance of the corresponding perturbation expansions of the non-Markovian equations of motion is examined through a comparison with the exact solution.

DOI
10.1103/physrevb.70.045323

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