Arbitrary length XX spin chains boundary-driven by non-Markovian environments

TL;DR

This paper introduces a recursive method to compute the wavefunction of boundary-driven XX spin chains coupled to non-Markovian environments, enabling analysis of dynamics and state transfer for arbitrary chain lengths and reservoir types.

Contribution

The authors develop a novel recursive approach for solving the wavefunction of XX spin chains with non-Markovian boundary reservoirs, accommodating arbitrary spectral densities and initial conditions.

Findings

The method provides closed-form solutions for chain lengths and initial states.

Analysis of dynamical behavior under different reservoir spectral densities.

Quantitative comparisons between Lorentzian and Ohmic reservoirs.

Abstract

In this work we provide a recursive method of calculating the wavefunction of a XX spin chain coupled at both ends to non-Markovian reservoirs with arbitrary spectral density. The method is based on the appropriate handling of the time-dependent Schrodinger's equations of motion in Laplace space and leads to closed form solutions of the transformed amplitudes, for arbitrary chain lengths as well as arbitrary initial conditions, within the single-excitation subspace. Results on the dynamical as well as state transfer properties of the system for various combinations of parameters are also presented. In particular, detailed quantitative comparisons for Lorentzian and Ohmic reservoirs are illustrated.