Dynamics of the independent-oscillator (IO) model in the Einstein and pseudo-Debye limits

The independent-oscillator model is thought to be a simple model for Brownian motion, explored extensively by Ford, Lewis and O'Connell. This model does not specify the distribution of the oscillators’ frequencies. By considering the distribution to be of two standard limits, otherwise preservi...

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Bibliographic Details
Published inPhysica A Vol. 304; no. 3; pp. 409 - 420
Main Authors Kim, Jangil, Howard Lee, M
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.02.2002
Subjects
Independent-oscillator model
Memory function
Recurrence relations
05.60.−k
05.40.−a
Independent-oscillator model
05.20.−y
Memory function
Recurrence relations
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Summary:The independent-oscillator model is thought to be a simple model for Brownian motion, explored extensively by Ford, Lewis and O'Connell. This model does not specify the distribution of the oscillators’ frequencies. By considering the distribution to be of two standard limits, otherwise preserving the Hermiticity of the model, we obtain the memory function exactly by the method of recurrence relations. In one limit the memory function is purely oscillatory while in the other limit it shows a decreasing amplitude with an oscillation. Relevance to transport theory is briefly pointed out.
ISSN:0378-4371
1873-2119
DOI:10.1016/S0378-4371(01)00551-9