Abstract
The Brownian motion is studied within a modification of the Zwanzig-Caldeira-Legget model when both the Brownian particle and the surrounding bath particles respond to an external harmonic field. It is shown for the derived generalized Langevin equation that the second fluctuation-dissipation theorem remains valid but, as distinct from the usual consideration, with the thermal random force depending on the strength of the confinement potential. An approximate method to evaluate the memory function, the apparent stiffness of the external potential, and the time correlation functions used in the description of the Brownian motion is proposed and applied for the frequency distribution of the bath oscillators, which in the absence of external forces corresponds to the exponentially decaying memory function.
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