A model of an arbitrary spin coupled to a bath of spins 1/2 in a star
configuration is considered. The exact reduced dynamics of the central spin is
found for the case of non-correlated 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.
Описание
Arbitrary spin in a spin bath: Exact dynamics and approximation
techniques
%0 Generic
%1 semin2014arbitrary
%A Semin, V.
%A Sinayskiy, I.
%A Petruccione, F.
%D 2014
%K interesting
%R 10.1103/PhysRevA.89.012107
%T Arbitrary spin in a spin bath: Exact dynamics and approximation
techniques
%U http://arxiv.org/abs/1401.7575
%X A model of an arbitrary spin coupled to a bath of spins 1/2 in a star
configuration is considered. The exact reduced dynamics of the central spin is
found for the case of non-correlated 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.
@misc{semin2014arbitrary,
abstract = {A model of an arbitrary spin coupled to a bath of spins 1/2 in a star
configuration is considered. The exact reduced dynamics of the central spin is
found for the case of non-correlated 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 $1/(A\sqrt{N})$, where A is the coupling
constant and N is the number of spins in the bath.},
added-at = {2014-06-20T14:28:32.000+0200},
author = {Semin, V. and Sinayskiy, I. and Petruccione, F.},
biburl = {https://www.bibsonomy.org/bibtex/2e58926df1d3e73662c0418da9d39666d/scavgf},
description = {Arbitrary spin in a spin bath: Exact dynamics and approximation
techniques},
doi = {10.1103/PhysRevA.89.012107},
interhash = {c964934a2508b8b552e11d77b9fe729d},
intrahash = {e58926df1d3e73662c0418da9d39666d},
keywords = {interesting},
note = {cite arxiv:1401.7575Comment: 11 pages, 11 figures; v2: a typo in Eq. (A2) was corrected},
timestamp = {2014-06-20T14:28:32.000+0200},
title = {Arbitrary spin in a spin bath: Exact dynamics and approximation
techniques},
url = {http://arxiv.org/abs/1401.7575},
year = 2014
}