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Classical non-conservative equations of motion are inapplicable in quantum mechanics. This constitutes a major problem in the study of quantum systems, that can not be regarded as isolated from their environment. The standard method of implementing dissipation in quantum mechanics is to include the environment as infinitely many degrees of freedom, which are linearly coupled to the system of interest. By applying reduced system descriptions, where the infinite degrees of freedom in the environment is encapsulated in scalar functions such as the spectral density, dissipative dynamics can be included in quantum descriptions. However, this is often achieved with assumptions that are justified a posteriori in the phenomonological modelling of dissipative quantum mechanics. As an alternative, it can be shown that dissipative dynamics can be derived from a microscopic model of a quantum system. By applying circuit quantum electrodynamics to circuit diagrams, a spectral density corresponding to Drude dampening is derived from an infinite transmission line in the continuum limit acting as a dissipative environment. The resulting dynamics is captured in a Heisenberg-Langevin equation for the flux of a resonator circuit, and the correlation function of its stochastic noise is demonstrated to be an example of the fluctuation-dissipation theorem. Along the way the physical justification of the rotating-wave approximation is touched upon, and Poincaré recurrences are demonstrated as a feature of environments with finite degrees of freedom.

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Magnus Vigsø, Niels Bohr Institute/University of Copenhagen
Seminar Room 0.03, ETP
Contact: Urban Seifert