Eur. Phys. J. D (2014) 68: 110
https://doi.org/10.1140/epjd/e2014-40597-5

Regular Article

Dissipative dynamics of a spin in a spin environment with non-uniform coupling

¹ School of Physics and Electronic Science, Changsha University of Science and Technology, Changsha 410004, P.R. China
² Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China

^a e-mail: guoyu1980@outlook.com

Received: 30 September 2013
Received in final form: 11 December 2013
Published online: 7 May 2014

Abstract

We investigate the reduced dynamics of a central spin coupled to a spin environment with non-uniform coupling. Through using the method of time-dependent density-matrix renormalization group (t-DMRG), we nonperturbatively show the dissipative dynamics of the central spin beyond the case of uniform coupling between the central spin and the environment spins. It is shown that only when the system-environment coupling is weak enough, the central spin system shows Markovian effect and will finally reach the steady state; otherwise, the reduced dynamics is non-Markovian and exhibits a quasi-periodic oscillation. The frequency spectrum and the correlation between the central spin system and the environment are also studied to elucidate the dissipative dynamics of the central spin system for different coupling strengths.