TY - JOUR
T1 - Path integrals and non-Markov processes. II. Escape rates and stationary distributions in the weak-noise limit
AU - Bray, A. J.
AU - McKane, A. J.
AU - Newman, T. J.
PY - 1990/1
Y1 - 1990/1
N2 - The path-integral formalism developed in the preceding paper [McKane, Luckock, and Bray, Phys. Rev. A 41, 644 (1990)] is used to calculate, in the weak-noise limit, the rate of escape of a particle over a one-dimensional potential barrier, for exponentially correlated noise (t)(t) =(D/)exp{-t-t/}. For small D, a steepest-descent evaluation of the appropriate path integral yields exp(-S/D), where S is the action associated with the dominant (instanton) path. Analytical results for S are obtained for small and large , and (essentially exact) numerical results for intermediate. The stationary joint probability density for the position and velocity of the particle is also calculated for small D: it has the form Pst (x,xI)exp[-S(x,xI)/D]. Results are presented for the marginal probability density Pst(x) for the position of the particle.
AB - The path-integral formalism developed in the preceding paper [McKane, Luckock, and Bray, Phys. Rev. A 41, 644 (1990)] is used to calculate, in the weak-noise limit, the rate of escape of a particle over a one-dimensional potential barrier, for exponentially correlated noise (t)(t) =(D/)exp{-t-t/}. For small D, a steepest-descent evaluation of the appropriate path integral yields exp(-S/D), where S is the action associated with the dominant (instanton) path. Analytical results for S are obtained for small and large , and (essentially exact) numerical results for intermediate. The stationary joint probability density for the position and velocity of the particle is also calculated for small D: it has the form Pst (x,xI)exp[-S(x,xI)/D]. Results are presented for the marginal probability density Pst(x) for the position of the particle.
UR - http://www.scopus.com/inward/record.url?scp=25944451974&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.41.657
DO - 10.1103/PhysRevA.41.657
M3 - Article
AN - SCOPUS:25944451974
SN - 1050-2947
VL - 41
SP - 657
EP - 667
JO - Physical Review A
JF - Physical Review A
IS - 2
ER -