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arXiv:1407.6171 · Physica Scripta

On oscillator–bath system: exact propagator, reduced density matrix and Greenʼs function

A Refaei, F Kheirandish

Published Jan 26, 2015• 0 citations
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Abstract

The exact form of a quantum propagator of a quantum oscillator, interacting with a bosonic bath consisting of N -distinguished quantum oscillators with different frequencies, is obtained in the Heisenberg picture. A reduced density matrix for the oscillator is obtained. The kernel or Greenʼs function connecting the initial density matrix of the oscillator to the density matrix in an arbitrary time is obtained, and its connection to the Feynman–Vernon influence functional is discussed. A weak coupling regime and squared mean values for position, momentum, and energy of the oscillator are obtained in equilibrium.

DOI
10.1088/0031-8949/90/2/025206

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The exact form of a quantum propagator of a quantum oscillator, interacting with a bosonic bath consisting of N -distinguished quantum oscillators with different frequencies, is obtained in the Heisenberg picture. A reduced density matrix for the oscillator is obtained. The kernel or Greenʼs function connecting the initial density matrix of the oscillator to the density matrix in an arbitrary time is obtained, and its connection to the Feynman–Vernon influence functional is discussed. A weak coupling regime and squared mean values for position, momentum, and energy of the oscillator are obtained in equilibrium.
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