Abstract
Non-Markovian Brownian motion in a periodic potential is studied by means of an electronic analogue simulator. Velocity spectra, the Fourier transforms of velocity autocorrelation functions, are obtained for three types of random force, that is, a white noise, an Ornstein—Uhlenbeck process, and a quasimonochromatic noise. The analogue results are in good agreement both with theoretical ones calculated with the use of a matrix-continued-fraction method, and with the results of digital simulations. An unexpected extra peak in the velocity spectrum is observed for Ornstein-Uhlenbeck noise with large correlation time. The peak is attributed to a slow oscillatory motion of the Brownian particle as it moves back and forth over several lattice spaces. Its relationship to an approximate Langevin equation is discussed.
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Igarashi, A., McClintock, P.V.E. & Stocks, N.G. Velocity spectrum for non-Markovian Brownian motion in a periodic potential. J Stat Phys 66, 1059–1070 (1992). https://doi.org/10.1007/BF01055716
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DOI: https://doi.org/10.1007/BF01055716