Where is the boundary of adiabatic approximation
(of quasi-statics) by stochastic resonance consideration?
A.V. Polovinkin
University of Nizhny Novgorod, Russia
There is considered the periodically driven stochastic system, given by equation:
where:
-U(x) is a bistable potential having a maximum at 
and
minimum at 
,
-h(t) is the periodic function,
-and 
is white gaussian noise with
intensity equals b.
In the case when h(t) is the sequence of rectangular pulses with the aid of detailed balance condition it is shown, that the seting-up-time for quasistatical probability flow over the potential barrier can be estimated as the mean relaxation time of a brownian particle initially placed at the barrier's top:
where R is the scale of U(x) - dependence,
This result suggests, that adiabatic approximation for
stochastic resonance consideration can be used at the frequencies
, where 
(1) logarithmically grows
with noise decreasing.