Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 43: Anomalous diffusion / Brownian motion

DY 43.1: Talk

Thursday, April 4, 2019, 10:00–10:15, H3

Fractional electron transfer kinetics and a quantum breaking of ergodicity — •Igor Goychuk — Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany

The dissipative curve-crossing problem provides a paradigm for electron-transfer (ET) processes in condensed media. It is studied both analytically and numerically for subdiffusive or sub-Ohmic dynamics of the reaction coordinate in the contact approximation, both from the ensemble and single-trajectory perspectives [1]. Depending on the electron coupling strength, the transfer occurs either in non-adiabatic or in a solvent-controlled adiabatic regime. It is shown that the relaxation of electronic populations has universally a power law tail even in a deeply non-adiabatic regime. For a sufficiently strong tunnel coupling, it is described by a Mittag-Leffler function. The statistics of electron transitions is, however, very different from both the ensemble and single-trajectory perspective. For large sojourn times, it is featured by a stretched exponential Weibull distribution and not by a power law dependence. Moreover, a profound difference occurs for the distribution of residence times in the electronic states on the ensemble level and on the level of single trajectories. Ergodicity is broken dynamically even in a more spectacular way than in the memoryless case [2].
[1] I. Goychuk, arXiv:1811.03838 [cond-mat.stat-mech] (2018).
[2] I. Goychuk, Phys. Chem. Chem. Phys. 19, 3056 (2017).