Biorthonormal eigenbasis of a Markovian master equation for the quantum Brownian motion
- Department of Physics, Faculty of Science, Universiti Putra Malaysia, Serdang, 43400 UPM Selangor, Malaysia and Laboratory of Computational Science and Informatics, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, 43400 UPM Selangor (Malaysia)
- Center for Complex Quantum Systems, University of Texas at Austin, 1 University Station C1600 Austin, Texas 78712 (United States)
The solution to a quantum Markovian master equation of a harmonic oscillator weakly coupled to a thermal reservoir is investigated as a non-Hermitian eigenvalue problem in space coordinates. In terms of a pair of quantum action-angle variables, the equation becomes separable and a complete set of biorthogonal eigenfunctions can be constructed. Properties of quantum states, such as the change in the quantum coherence length, damping in the motion, and disappearance of the spatial interference pattern, can then be described as the decay of the nonequilibrium modes in the eigenbasis expansion. It is found that the process of gaining quantum coherence from the environment takes a longer time than the opposite process of losing quantum coherence to the environment. An estimate of the time scales of these processes is obtained.
- OSTI ID:
- 21175775
- Journal Information:
- Journal of Mathematical Physics, Vol. 49, Issue 11; Other Information: DOI: 10.1063/1.3005968; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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