TY - JOUR

T1 - Relaxation in a Duffing potential

AU - Sen, Surajit

AU - Phillips, James Christopher

N1 - Funding Information:
SS acknowledgepsa rtials upporot f an All UniversityR esearchIn itiationG rantw hile at Michigan StateU niversityw heret his work was beguna nd the PhysicsD epartment at S.U.N.Y. - Buffalo where this work has been completedJC. P has been supported by the U.S. National ScienceF oundationR esearchE xperiencefso r Undergraduates programa nd by a Hertz FellowshipW. e warmlyt hankP rofessoSr oumyaC hakravarti for numerouhs elpfuld iscussionds uringt he courseo f this work and for much help in performingth e Fourier transformsW. e acknowledgoeu r gratitudeto ProfessoPr aolo Grigolini for kindly bringingh is early work on this subjectt o our attentiona nd for answeringn umerouqsu estionosn the dynamicso f the Duffingo scillator.

PY - 1995/6/15

Y1 - 1995/6/15

N2 - The solution of the equation of motion for a particle in a Duffing potential, V(x) = α1x2/2 + α2x4/4 (α1, α2 > 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 microcanonical 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.

AB - The solution of the equation of motion for a particle in a Duffing potential, V(x) = α1x2/2 + α2x4/4 (α1, α2 > 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 microcanonical 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.

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U2 - 10.1016/0378-4371(95)00033-4

DO - 10.1016/0378-4371(95)00033-4

M3 - Article

AN - SCOPUS:0039081136

VL - 216

SP - 271

EP - 287

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 3

ER -