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We present a general geometrical approach to the problem of escape from ametastable state in the presence of noise. The accompanying analysis leads to asimple condition, based on the norm of the drift field, for determining whethercaustic singularities alter the escape trajectories when detailed balance isabsent. We apply our methods to systems lacking detailed balance, including ananomagnet with a biaxial magnetic anisotropy and subject to a spin transfertorque. The approach described within allows determination of the regions ofexperimental parameter space that admit caustics.

Large Fluctuations and Singular Behavior of Nonequilibrium Systems