In this work we provide a recursive method of calculating the wave function of an $XX$ 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 Schrödinger'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.

• Received 15 November 2021
• Accepted 14 January 2022

DOI:https://doi.org/10.1103/PhysRevA.105.012429