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Quantum ergodicity breaking in semi-classical electron transfer dynamics.

Igor Goychuk1

  • 1Institute for Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476 Potsdam-Golm, Germany. igoychuk@uni-potsdam.de.

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Summary
This summary is machine-generated.

Ergodic behavior in electron transfer is predictable under non-adiabatic conditions but breaks down in the adiabatic regime. Single-electron transfer statistics deviate from ensemble predictions in classical solvent-controlled electron transfer.

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Area of Science:

  • Physical Chemistry
  • Chemical Physics
  • Theoretical Chemistry

Background:

  • Ergodic behavior is a fundamental concept in statistical mechanics.
  • Understanding electron transfer statistics is crucial in nanoworld applications.
  • Equilibrium ensemble descriptions are commonly used to model chemical reactions.

Purpose of the Study:

  • To investigate the validity of equilibrium ensemble descriptions for predicting single-electron transfer statistics.
  • To scrutinize ergodic behavior in semi-classical curve-crossing models.
  • To identify conditions under which ensemble and single-trajectory descriptions diverge.

Main Methods:

  • Semi-classical curve-crossing model.
  • Analysis of non-adiabatic (Marcus-Levich-Dogonadze rate) and adiabatic electron transfer regimes.
  • Stochastic simulations.
  • Development of an analytical theory.

Main Results:

  • Ergodicity holds for non-adiabatic electron transfer, aligning with Marcus-Levich-Dogonadze (MLD) rate predictions.
  • A profound breaking of ergodicity occurs in solvent-controlled adiabatic electron transfer.
  • Single-electron survival probability becomes non-exponential near the adiabatic regime, described by a Mittag-Leffler distribution.
  • Ensemble survival probability remains nearly exponential for large activation barriers.
  • Mean transfer time paradoxically aligns with non-adiabatic quantum tunneling rates.

Conclusions:

  • Equilibrium ensemble descriptions fail to capture single-electron transfer statistics in the adiabatic regime.
  • The breakdown of ergodicity highlights limitations of classical ensemble approaches for certain electron transfer dynamics.
  • A new analytical theory accurately explains simulation results and the observed deviations.