IWNET12
IWNET12
Simulation techniques for the nonlinear thermodynamic quantum mas-
ter equation
Flakowski Jérôme1, Schweizer Marco1
1 Polymer Physics, ETH Zurich, D-MATL, Switzerland
Abstract
The great majority of quantum systems exposed to non-equilbirum environments are far too complex to be
numerically solved at the microscopic level. To tackle this problem, various coarse-graining strategies have been
developed with the central idea to reduce the degrees of freedom of the environment to few relevant variables
[1]. The generally obtained linear quantum master equations suer from multiple deciencies such as improper
relaxation behavior [2,3]. Using thermodynamic arguments, an alternative highly nonlinear equation resolving
some of these issues has been proposed recently [4].
We explain here how to simulate the evolution of open quantum systems based on this recent formulation
using deterministic as well as stochastic techniques [5,6]. We conclude by a numerical exploration of the
thermodynamic nature of the nonlinear master equation for heat bath environments by examining the link
between entropy production and loss of quantum coherence, a crucial property for nanoscale applications.
References
[1] Breuer, H.-P., and Petruccione, F., The Theory of Open Quantum System (2002)
[2] Weiss, U., Quantum Dissipative Systems (2008)
[3] Grabert, H., Z. Phys. B, 49, 161 (1982)
[4] Öttinger H.C., Europhys. Lett., 94, 10006 (2011)
[5] Öttinger H.C., Phys. Rev. A, 82, 052119 (2010)
[6] Flakowski, J., Schweizer M. and Öttinger H.C., ready for submission (2012)
E-mail: jerome.flakowski@mat.ethz.ch

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