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Velocity spectrum for non-Markovian Brownian motion in a periodic potential.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>02/1992
<mark>Journal</mark>Journal of Statistical Physics
Issue number3/4
Number of pages12
Pages (from-to)1059-1070
Publication StatusPublished
<mark>Original language</mark>English


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.