Research output: Contribution to Journal/Magazine › Journal article › peer-review

Published

In: Journal of Statistical Physics, Vol. 66, No. 3/4, 02.1992, p. 1059-1070.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Igarashi, A, McClintock, PVE & Stocks, NG 1992, 'Velocity spectrum for non-Markovian Brownian motion in a periodic potential.', *Journal of Statistical Physics*, vol. 66, no. 3/4, pp. 1059-1070. https://doi.org/10.1007/BF01055716

Igarashi, A., McClintock, P. V. E., & Stocks, N. G. (1992). Velocity spectrum for non-Markovian Brownian motion in a periodic potential. *Journal of Statistical Physics*, *66*(3/4), 1059-1070. https://doi.org/10.1007/BF01055716

Igarashi A, McClintock PVE, Stocks NG. Velocity spectrum for non-Markovian Brownian motion in a periodic potential. Journal of Statistical Physics. 1992 Feb;66(3/4):1059-1070. doi: 10.1007/BF01055716

@article{2aecaf86d7144164998cefb2e8d7c4a8,

title = "Velocity spectrum for non-Markovian Brownian motion in a periodic potential.",

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.",

keywords = "Analog simulation - non-Markovian process - periodic potential - velocity spectrum - colored noise - Brownian motion - Langevin equation - matrix-continued-fraction method",

author = "A. Igarashi and McClintock, {Peter V. E.} and Stocks, {N. G.}",

year = "1992",

month = feb,

doi = "10.1007/BF01055716",

language = "English",

volume = "66",

pages = "1059--1070",

journal = "Journal of Statistical Physics",

issn = "0022-4715",

publisher = "Springer New York",

number = "3/4",

}

TY - JOUR

T1 - Velocity spectrum for non-Markovian Brownian motion in a periodic potential.

AU - Igarashi, A.

AU - McClintock, Peter V. E.

AU - Stocks, N. G.

PY - 1992/2

Y1 - 1992/2

N2 - 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.

AB - 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.

KW - Analog simulation - non-Markovian process - periodic potential - velocity spectrum - colored noise - Brownian motion - Langevin equation - matrix-continued-fraction method

U2 - 10.1007/BF01055716

DO - 10.1007/BF01055716

M3 - Journal article

VL - 66

SP - 1059

EP - 1070

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 3/4

ER -