James Phillips' Publications
Surajit Sen and James Christopher Phillips.
Relaxation in a Duffing potential.
Physica A 216:271-287, 1995.
The solution of the equation of motion for a particle in a
Duffing potential, V(x) = alpha1chi2/2+ alpha2chi4/4 (alpha1, alpha2 > 0) for
arbitrary anharmonicity strength is characterized by the presence of odd
frequencies which implies that velocity and position autocorrelation functions
of such an oscillator in a microanonical ensemble are also characterized by odd
frequencies. It is, however, non-trivial to determine whether such ''discrete''
frequencies also characterize the autocorrelation functions in a canonical
ensemble as discussed recently by Fronzoni et al. (J. Stat. Phys. 41 (1985)
553). We recover and extend upon the results of Fronzoni et al. to show
analytically, via Mori-Lee theory, that ''essentially discrete'' (i.e.
well-defined peaks with finite but ''small'' width) temperature-dependent
frequencies characterize the autocorrelation functions in a canonical ensemble.
