Exact analytical solutions to the master equation of quantum Brownian motion 
for a general environment

Fleming, C. H.; Roura, Albert; Hu, B. L.

doi:doi:10.1016/j.aop.2010.12.003

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Exact analytical solutions to the master equation of quantum Brownian motion for a general environment

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Roura, Albert
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Fleming, C. H., Roura, A., & Hu, B. L. (2011). Exact analytical solutions to the master equation of quantum Brownian motion for a general environment. Annals of Physics, 326(5), 1207-1258. doi:doi:10.1016/j.aop.2010.12.003.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-BC00-8

Abstract

We revisit the model of a quantum Brownian oscillator linearly coupled to an environment of quantum oscillators at finite temperature. By introducing a compact and particularly well-suited formulation, we give a rather quick and direct derivation of the master equation and its solutions for general spectral functions and arbitrary temperatures. The flexibility of our approach allows for an immediate generalization to cases with an external force and with an arbitrary number of Brownian oscillators. More importantly, we point out an important mathematical subtlety concerning boundary-value problems for integro-differential equations which led to incorrect master equation coefficients and impacts on the description of nonlocal dissipation effects in all earlier derivations. Furthermore, we provide explicit, exact analytical results for the master equation coefficients and its solutions in a wide variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with a finite cut-off.