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

Heinz-Peter Breuer, Daniel Burgarth, Francesco Petruccione

Research output: Contribution to journalArticlepeer-review

219 Citations (Scopus)


The reduced dynamics of a central spin coupled to a bath of N spin-12 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→∞ 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.
Original languageEnglish
Article number045323
Pages (from-to)045323-1-045323-10
Number of pages10
JournalPhysical Review B: Condensed Matter and Materials Physics
Issue number4
Publication statusPublished - 15 Jul 2004
Externally publishedYes


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