arXiv:1203.3785v3Quantum stochastic methods based on effective wave functions form a framework for investigating the generally non-Markovian dynamics of a quantum-mechanical system coupled to a bath. They promise to be computationally superior to the master-equation approach, which is numerically expensive for large dimensions of the Hilbert space. Here, we numerically investigate the suitability of a known stochastic Schrödinger equation that is local in time to give a description of thermal relaxation and energy transport. This stochastic Schrödinger equation can be solved with a moderate numerical cost, indeed comparable to that of a Markovian system, and reproduces the dynamics of a system evolving according to a general non-Markovian master equation. After verifying that it describes thermal relaxation correctly, we apply it for the first time to the energy transport in a spin chain. We also discuss a portable algorithm for the generation of the coloured noise associated with the numerical solution of the non-Markovian dynamics.RB and RDA acknowledge support from MICINN (FIS2010-21282-C02-01 and PIB2010US-00652), the Grupos Consolidados UPV/EHU del Gobierno Vasco (IT-319-07) and ACI-Promociona (ACI2009-1036), and the financial support of CONSOLIDER-INGENIO 2010 NanoTherm (CSD2010-00044). RB acknowledges financial support from IKERBASQUE, Basque Foundation for Science and the Ministerio de Educación, Cultura y Deporte (FPU12/01576). CT acknowledges financial support from Deutsche Forschungsgemeinschaft, in part through Research Unit FOR 1154 Towards Molecular Spintronics. RD'A acknowledges support from Diputacion Foral de Gipuzkoa via grant number Q4818001B.Peer Reviewe
