Arbitrary spin in a spin bath: Exact dynamics and approximation techniques

Vitalii Semin, Ilya Sinayskiy, and Francesco Petruccione
Phys. Rev. A 89, 012107 – Published 13 January 2014

Abstract

A model of an arbitrary spin coupled to a bath of spins 12 in a star configuration is considered. The exact reduced dynamics of the central spin is found for the case of noncorrelated initial conditions of the system and the bath. The exact solution is used to test two approximation techniques, namely, the Nakajima-Zwanzig projection operator technique and the time-convolutionless projection operator technique corresponding to the second order of the coupling constant. Two types of projection operators are used for deriving the master equations, and the results are compared with the exact solution for a central spin equal to one. It is shown that the approximate master equations reproduce the exact dynamics on time scales 1/(AN), where A is the coupling constant and N is the number of spins in the bath.

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  • Received 7 August 2013

DOI:https://doi.org/10.1103/PhysRevA.89.012107

©2014 American Physical Society

Authors & Affiliations

Vitalii Semin*

  • Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban, 4001, South Africa

Ilya Sinayskiy and Francesco Petruccione

  • Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban, 4001, South Africa and National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, South Africa

  • *semin@ukzn.ac.za
  • sinayskiy@ukzn.ac.za
  • petruccione@ukzn.ac.za

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Issue

Vol. 89, Iss. 1 — January 2014

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