The nonstationary diffusion by phase transitions
of II order: analytical description
A.V. Polovinkin
University of Nizhny Novgorod, Russia
The nonstationary diffusion of physical variables after instantaneous switching of potential profile U(x) of a system being investigated is considered. With the aid of cumulant equations in small-noise limit the analytical expressions are derived for:
1) the first passage time probability density,
2) the nonstationary probability density,
3) the mean passage time 
of fixed x-value,
4) the mean transition time.
It is shown, that
where C=0.577 is Euler's constant, and variable z equals:
b is the white noise intensity, 
is the initial x-dispersion and 
is the point of the potential maximum.
The obtained expressions generalize results of Susuki and of Roy R., Yu A.W. and Zhu S.
The analytical description of fluctuation phenomena by switching parameter in laser generating system and in nematic liquid crystals for illustration of the elaborated method is proposed.
