ETH Polymer Physics seminar


2010-09-08
9:00 at HCI J 574

Unraveling non-linear quantum master equation : a stochastic simulation

Jérôme Flakowski

Polymer Physics, Department of Materials, ETH Zurich

When considering open quantum systems, the most popular approach is to exploit linear quantum master equation of the Lindblad form[1]. The main drawback of this method is that it invokes an incorrect "quantum-regression hypothesis"[2] and is often not applicable at low temperatures[3]. In this talk, we will outline an alternative approach including non-linearities to overcome the problem. The non-linear quantum master equation investigated here was obtained by an extension of the geometric formulation of non-equilibrium thermodynamic from classical to quantum system[4,5] and was previously derived by time-dependent projection operator techniques[2]. Here a numerical solution of this equation is explored in the case of a damped harmonic oscillator in contact with a heat bath[6]. It is based on stochastic simulation methods with a general class of piecewise deterministic Markovian jump[7]. The talk will be conducted in "a work in progress" style : it will start with a short survey of the formalism, followed by the presentation of the simulation techniques, and end with a discussion on the possible applications of the developed methodology.

[1] Lindblad, G., On the generators of quantum dynamical semigroups, Comm. Math. Phys., Volume 48, Number 2 (1976); [2] Grabert, H., Nonlinear relaxation and fluctuations of damped quantum systems, Z. Physik B 49, (1982); [3] Weiss, U. , Quantum Dissipative Systems, 3rd Edition Series in Modern Condensed Matter Physics, World Scientific, Singapore, (2008); [4] Öttinger, H.C., The geometry and thermodynamics of dissipative quantum systems, Phys. Rev. Lett., (2010) submitted and arXiv:1002.2938;
[5] Öttinger, H.C., The nonlinear thermodynamic quantum master equation, Phys. Rev. A, (2010) submitted and arXiv:1002.5023;
[6] Öttinger, H.C., Nonlinear thermodynamic quantum master equation for the damped harmonic oscillator, Phys. Rev. A, (2010) submitted and arXiv:1004.0652;
[7] Öttinger, H.C., Stochastic process behind nonlinear thermodynamic quantum master equation, EPL, (2010) submitted and arXiv:1005.1190.


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