Exact dynamics of XX central spin models

TL;DR

This paper provides an exact analytical solution for the time evolution of a star network of spins with a central spin interacting via non-uniform Heisenberg XX interactions, starting from arbitrary initial states.

Contribution

It presents an exact solution to the dynamics of XX central spin models, which was previously not fully characterized for arbitrary initial states.

Findings

Exact time-dependent solutions derived for the spin system.

Analysis of the dynamical behavior based on the exact solutions.

Discussion of implications for quantum information processing.

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 Schrodinger equation of the spin system model is solved starting from an arbitrary initial state. The resulting solution is analyzed and briefly discussed.