Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Statistical Physics II (General)

DY 25.1: Talk

Tuesday, March 13, 2018, 10:00–10:15, BH-N 243

Analyzing tunneling time distributions on the basis of first passage time problems — •Jeanette Köppe¹, Michael Beyer¹, Markus Patzold¹, Wilfried Grecksch², and Wolfgang Paul¹ — ¹Institut für Physik, MLU Halle-Wittenberg — ²Institut für Mathematik, MLU Halle-Wittenberg

In 1966, E. Nelson established a new interpretation of quantum mechanics, whereby the particles follow some conservative diffusion process, i.e. forward-backward stochastic differential equations (FBSDEs), which are equivalent to the Schrödinger equation. In analogy to classical mechanics, we show that finding the Nash equilibrium for a stochastic optimal control problem, which is the quantum equivalent to Hamilton’s principle of least action, a set of quantum dynamical equations can be derived, which are the generalization of Hamilton’s equations of motion to the quantum world.

On the basis of these quantum Hamilton equations, it was possible to study tunneling processes in a one-dimensional double-well potential by analyzing first passage times of the respective diffusion processes. We show that the energy splitting between the two lowest energy states Δ E= E₁− E₀ can be predicted based upon mean first passage times. Moreover, the probability density function of these first passage times is analyzed. The general form of this empircal determined distribution can be motivated by the definition of first passage times and it turns out that, independent of the considered system, tunnel times follow the same distribution qualitatively.