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This study analyzes the random charging and discharging times of molecules in electric current flow. A new formula for the distribution of these time intervals, crucial for understanding charge dwelling, is derived using a Markovian master equation.

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Area of Science:

  • Quantum Transport
  • Molecular Electronics
  • Statistical Mechanics

Background:

  • Electric current through molecular junctions involves frequent electron tunneling, leading to molecular charging and discharging.
  • These events occur at random times, creating stochastic intervals that represent charge dwelling times on the molecule.
  • Understanding the statistical properties of these intervals is key to characterizing charge dynamics in molecular systems.

Purpose of the Study:

  • To investigate the statistical properties of time intervals between molecular charging and discharging events.
  • To derive a general formula for the distribution of these stochastic time intervals.
  • To provide a theoretical framework for analyzing charge dwelling times in molecular junctions.

Main Methods:

  • Utilized the Markovian master equation to model transitions between charged and neutral molecular vibrational states.
  • Identified two quantum jump operators from the Liouvillian: one for charging and one for discharging.
  • Derived a conditional probability distribution for the time interval (τ) until a charged molecule becomes neutral.

Main Results:

  • A general formula for the distribution of charge dwelling time intervals (τ) was successfully derived.
  • The quantum jump operators provide a clear mechanism for describing the charging and discharging processes.
  • The derived distribution allows for detailed statistical analysis of charge dynamics in molecular junctions.

Conclusions:

  • The study provides a robust theoretical framework for understanding stochastic charge dynamics in molecular junctions.
  • The derived distribution of time intervals offers new insights into electron tunneling and charge residence times.
  • This work advances the fundamental understanding of charge transport at the molecular level.