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.

Item Type: | Article |
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Journal or Publication Title: | Journal of Statistical Physics |

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

Subjects: | ?? qc ?? |

Departments: | Faculty of Science and Technology > Physics |

ID Code: | 32191 |

Deposited By: | Professor P. V. E. McClintock |

Deposited On: | 18 Mar 2010 11:52 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 23 Mar 2017 17:34 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/32191 |

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