Physics – Condensed Matter
Scientific paper
1994-10-19
Physics
Condensed Matter
25 pages with 5 encapsulted postscript figures appended (need epsf)
Scientific paper
10.1103/PhysRevE.51.2974
The evaluation of the path-integral representation for stochastic processes in the weak-noise limit shows that these systems are governed by a set of equations which are those of a classical dynamics. We show that, even when the noise is colored, these may be put into a Hamiltonian form which leads to better insights and improved numerical treatments. We concentrate on solving Hamilton's equations over an infinite time interval, in order to determine the leading order contribution to the mean escape time for a bistable potential. The paths may be oscillatory and inherently unstable, in which case one must use a multiple shooting numerical technique over a truncated time period in order to calculate the infinite time optimal paths to a given accuracy. We look at two systems in some detail: the underdamped Langevin equation driven by external exponentially correlated noise and the overdamped Langevin equation driven by external quasi-monochromatic noise. We deduce that caustics, focusing and bifurcation of the optimal path are general features of all but the simplest stochastic processes.
Einchcomb S. J. B.
McKane Alan J.
No associations
LandOfFree
The Use of Hamiltonian Mechanics in Systems Driven by Colored Noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Use of Hamiltonian Mechanics in Systems Driven by Colored Noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Use of Hamiltonian Mechanics in Systems Driven by Colored Noise will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-686790