Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation

Journal Of Physics-Condensed Matter 26, 395303 (2014)

Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation

Robert Biele, Carsten Timm, Roberto D'Agosta

Quantum 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.

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Doi
http://dx.doi.org/10.1088/0953-8984/26/39/395303
arxiv
http://arxiv.org/abs/1203.3785

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