9 - Colored noise in continuous dynamical systems: a functional calculus approach

Summary

Introduction

Recent work on dye lasers (Fox and Roy, 1987; Jung and Risken, 1984; Lett, Short and Mandel, 1984; Roy, Yu and Zhu, 1985; Short, Mandel and Roy, 1982) and the optical ring laser gyroscope (Vogel et al., 1987a, b) has emphasized the physically important role of colored noise sources. A well-known classical situation in which strongly colored noise has an impact on the physics is the phenomenon of motional narrowing in magnetic resonance (Kubo, 1962). Kubo has shown that a fluctuating magnetic field with very short noise correlation time (almost white noise) does typically not manifestly affect the motion of spins; on the contrary, if the fluctuations are correlated over a long time scale (colored noise) the motion of the spin becomes greatly modified.

Another area where there has been much recent activity addresses escape problems. These are currently in the limelight both from the theoretical viewpoint (Grote and Hynes,1980; Hänggi, 1986; Hänggi and Mojtabai, 1982; Hänggi and Riseborough, 1983; Hänggi, Mroczkowski, Moss and McClintock, 1985) as well as from an experimental point of view (Devoret, Martinis, Esteve and Clarke, 1984; Fleming, Courtney and Balk, 1986; Hänggi et al., 1985; Maneke, Schroeder, Troe and Voss, 1985). In this latter case, a frequency-dependent friction, or noise of finite correlation time, can considerably modify the classical barrier transmission. Except for two-state noise (Hänggi and Talkner, 1985; Masoliver, Lindenberg and West, 1986; Rodriguez and Pesquera, 1986; Van den Broeck and Hänggi, 1984) there exist no exact analytic methods for truly nonlinear systems, being driven by correlated noise.