Relaxation time stochastic resonance

But, as mentioned above in Sec. I, the mechanism of bistable stochastic resonance requires that the frequency of the input signal is much less than reciprocal relaxation time of the system. 

Vibrational Relaxation. Stochastic processes, including vibrational relaxation in condensed media, have been considered from a theoretical standpoint in an extensive review,502 and a further review has considered measurement of such processes also.503 Models have been presented for vibrational relaxation in diatomic liquids 504 and in condensed media,505 using a master-equation approach. An extensive development of quantum ergodic theory for relaxation processes has been published,506 and quantum resonance effects in electronic to vibrational energy transfer have been considered.507 A paper has also considered the coupling between vibrational relaxation and molecular electronic transitions.508 A theory has also been outlined for the time-resolved electronic absorption spectrum of a molecule undergoing collisional vibrational relaxation.509... 

For an external magnetic field Bo along the z direction, the electron spins are oriented parallel or antiparallel to the z direction. Modulation of the components of the local field in the xy plane due to a stochastic process then induces stochastic electron spin transitions (spin flips) that contribute to longitudinal relaxation with time constant T. For historical reasons longitudinal relaxation is often termed spin-lattice relaxation. The relaxation rate T is proportional to the spectral density /(co) of the stochastic process at the resonance frequency Mo of the transition under consideration. This spectral density is maximum for a correlation time Tc of the stochastic process that fulfils the condition wqTc = 1. As correlation times usually are a monotonic function of temperature, there is a temperature for which the relaxation rate attains a maximum and T attains a minimum. Measurements of 7] as a function of temperature can thus be used to infer the correlation time of a dynamic process. By varying the external field Bo and thus mq, the time scale can be shifted to which EPR experiments are most sensitive. 

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