Berlin 2012 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 27: Transport and Anomalous Diffusion

DY 27.10: Talk

Thursday, March 29, 2012, 17:00–17:15, MA 004

Minimal mean first passage time in a piecewise linear potential landscape — •Vladimir V. Palyulin¹ and Ralf Metzler² — ¹Physik Department (T30g), Technical University of Munich, James Franck Strasse, 85747 Garching, Germany — ²Chair for Theoretical Physics, Inst for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany

How can we minimize the mean first passage time between two points x₁ and x₂, whose energies are E₁ and E₂ (E₁>E₂)? Naively, one might suppose that the solution is a linear potential drop between the two points. However, in our analysis we show that for an energy landscape consisting of two linear parts, a potential barrier with height E_b>E₁ leads to a decrease of the mean first passage time. Similar results hold for subdiffusive conditions.

Our a priori surprising findings are obtained analytically and supported by numerical analysis. Several approaches were used, namely, direct numerical solution of fractional Fokker-Planck equation with Gruenwald-Letnikov representation of the fractional derivative, numerical inverse Laplace transform of first passage time density obtained by solution of equation in Laplace space, and Monte Carlo simulation approach.