Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 19: Complex Systems

DY 19.3: Talk

Tuesday, April 2, 2019, 12:15–12:30, H6

WKB-type-of approximation for probabilistic description of rare events in reaction systems — •Andreas Mühlbacher and Thomas Guhr — Fakultät für Physik, Universität Duisburg-Essen

We calculate the probabilities to find systems of reacting particles in states which largely deviate from typical behavior. The rare event statistics is obtained from the master equation which describes the dynamics of the probability distribution of the particle number. We transform the master equation by means of a generating function into a time-dependent "Schrödinger equation". Its solution is provided by a separation ansatz and a WKB-approximation for the stationary part. The classical equations of motions are formulated. We calcutate the probabilities employing a saddle-point approximation. Hereby, we switch from a deterministic to a probabilistic description which has important repercussions on the system dynamics. We present a method to calculate the rare event statistics for systems where the dynamics cannot be entirely analyzed in an analytical manner. The method is applied to a set of different examples.