Chaotic Behavior in a Dynamic System Related to the Stationary Path of the Path-Integral for a Brownian Particle in a Double-Well Potential

Abstract

Considering the path-integral approach to the Brownian motion of a particle in a double-well potential, the joint probability for a possible trajectory (path) is a positive definite functional of the path. In the practically important low temperature or low friction regime, the probability functional is found to comprise dominant contributions from the stationary paths. The corresponding dynamics behaves chaotically, exhibiting intermittency as well as sensitivity to the initial conditions. The first Lyapunov exponent is found to be positive and the attractor in the phase space to be of fractal structure.