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Exact dynamics of XX central spin models

Maria Anastasia Jivulescu, Elena Ferraro, Anna Napoli, ANTONINO MESSINA

Published Aug 5, 2013• 6 citations
OpenAlex

Abstract

The dynamical behavior of a star network of spins, wherein each of N decoupled spins interact with a central spin through non uniform Heisenberg XX interaction is exactly studied. The time-dependent Schrödinger equation of the spin system model is solved starting from an arbitrary initial state. The resulting solution is analyzed and briefly discussed. PACS numbers: 02.30.Ik, 73.21.La, 71.70.Jp, 31.30.GsExact dynamics of XX central spin models 2 1.

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A model of an arbitrary spin coupled to a bath of spins 12\frac{1}{2}21​ 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)1/(A\sqrt{N})1/(AN​), where AAA is the coupling constant and NNN is the number of spins in the bath.
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