The Kramers Problem: Beyond Quasi-Stationarity
نویسندگان
چکیده
Noise-induced escape from a metastable potential is considered on timescales preceding the formation of quasi-equilibrium within the metastable part of the potential. It is shown that the escape flux may then depend exponentially strongly, and in a complicated manner, on time and friction.
منابع مشابه
Strong Stationarity for Optimal Control of the Obstacle Problem with Control Constraints
We consider the distributed optimal control of the obstacle problem with control constraints. Since Mignot proved in 1976 the necessity of a system which is equivalent to strong stationarity, it has been an open problem whether such a system is still necessary in the presence of control constraints. Using moderate regularity of the optimal control and an assumption on the control bounds (which ...
متن کاملSmoluchowski–kramers Approximation and Large Deviations for Infinite-dimensional Nongradient Systems with Applications to the Exit Problem1 by Sandra Cerrai
In this paper, we study the quasi-potential for a general class of damped semilinear stochastic wave equations. We show that as the density of the mass converges to zero, the infimum of the quasi-potential with respect to all possible velocities converges to the quasi-potential of the corresponding stochastic heat equation, that one obtains from the zero mass limit. This shows in particular tha...
متن کاملShort time-scales in the Kramers problem
Escape from a metastable potential is considered on time-scales less than are needed for the creation of quasi-equilibrium within the well. It is shown that the escape flux may then depend exponentially strongly, and in a complicated way, on friction and time.
متن کاملOne-sided asymptotically mean stationary channels
This paper proposes an analysis of asymptotically mean stationary (AMS) communication channels. A hierarchy based on stability properties (stationarity, quasi-stationarity, recurrence and asymptotically mean stationarity) of channels is identified. Stationary channels are a subclass of quasi-stationary channels which are a subclass of recurrent AMS channels which are a subclass of AMS channels....
متن کاملA new look at the critical community size for childhood infections.
Quasi-stationarity and time to extinction are studied for the classic endemic model. Attention is restricted to the transition region in parameter space where the quasi-stationary distribution is non-normal. A new approximation of the marginal distribution of infected individuals in quasi-stationarity is presented. It leads to a simple explicit expression for an approximation of the critical co...
متن کامل