Abstract
The low-friction region of an anharmonically bound Brownian particle is examined using systematic elimination procedures. We obtain an asymptotic expression for the spectrum of the Fokker-Planck operator. Asymptotic means both small anharmonicities and small friction constants γ compared to the oscillatory frequency ω. We conclude that Kramers' low-friction equation is generally valid only for 0<γ≲0.01 ω and has to be modified for γ≳0.01 ω by including phase-dependent terms. From these the nonlinear part of the force field in connection with a finite temperature is shown to shorten the correlation time of the equilibrium velocity autocorrelation function and to renormalize the frequency of the corresponding spectral density.
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Renz, W. Derivation and solution of a low-friction Fokker-Planck equation for a bound Brownian particle. Z. Physik B - Condensed Matter 59, 91–102 (1985). https://doi.org/10.1007/BF01325386
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DOI: https://doi.org/10.1007/BF01325386