Reduced density matrices of oscillator systems

V. V. Dodonov; O. V. Man'ko; V. I. Man'ko

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arXiv · quant-ph/0210030

Reduced density matrices of oscillator systems

V. V. Dodonov·O. V. Man'ko·V. I. Man'ko

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Abstract

We study the evolution of an oscillator interacting via the most general bilinear coupling (with time-independent coefficients) with an ``environment'' consisting of a set of other harmonic oscillators. We are mainly interested in a possibility of using the Fokker-Planck equation to describe this evolution. Studying different interaction Hamiltonians, we show that unambiguous reduction to the Fokker-Planck equation is possible only within the framework of the so called rotating-wave approximation. As special cases we consider in detail the evolution of two coupled oscillators and relaxation of a charged oscillator in a uniform magnetic field.

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V. V. Dodonov, O. V. Man'ko, V. I. Man'ko. 2002-10-04. Reduced density matrices of oscillator systems. https://arxiv.org/abs/quant-ph/0210030

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