ISSN:
1089-7690
Source:
AIP Digital Archive
Topics:
Physics
,
Chemistry and Pharmacology
Notes:
General formulas are found for all the multitime correlation functions and susceptibilities of a simple two-dimensional rotor, the motion of which is governed by a Langevin equation containing Gaussian white noise as the torque. A sufficient condition that the equal time Poisson bracket of the angle with its conjugate momentum be satisfied at all times is inferred from the fluctuation–dissipation theorem applied to the fluctuating torque. The formulas include inertial effects, a necessity if high frequency behavior is to be correctly reproduced. The Fourier transforms of the two- and four-time dipole susceptibilities are extracted from the general results in the large friction constant limit. For the particular case of the rotor subjected to a strong constant background field and a weak time dependent probe field, we find that at low frequencies, the rotor exhibits saturation as measured by the real component of the four-time susceptibility. The imaginary part of the parallel component of the four-time susceptibility is found to be negative over the entire range of frequencies, this merely indicating that the overall dissipation in the system is decreased in the presence of a strong field. The Appendix determines the most general form of the correlation functions of the torque when it is specified that the two-time Poisson bracket of the torque is independent of the torque and of the system variables and that the fluctuation–dissipation theorem holds. They are a bit more general than Gaussian.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.454975
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