Igarashi, A. and McClintock, Peter V. E. and Stocks, N. G.
(1992)
*Velocity spectrum for non-Markovian Brownian motion in a periodic potential.*
Journal of Statistical Physics, 66 (3/4).
pp. 1059-1070.
ISSN 0022-4715

## 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.