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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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Related Experiment Video

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Chronic Unpredictable Mild Stress in Rats based on the Mongolian medicine
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On stochastic models of dynamic disorder.

David R Reichman1

  • 1Department of Chemistry, Columbia University, 3000 Broadway, New York, New York, 10025, USA.

The Journal of Physical Chemistry. B
|September 22, 2006
PubMed
Summary

This study connects dynamic disorder models, like the Zwanzig model, to crystal zero-phonon line broadening. It offers new insights into escape rates with non-Markovian fluctuations, inspired by single-molecule experiments.

Area of Science:

  • Statistical Physics
  • Physical Chemistry
  • Biophysics

Background:

  • Dynamic disorder is crucial in various physical and biological systems.
  • Stochastic models help understand complex phenomena like escape kinetics and spectral broadening.
  • Single-molecule experiments provide new avenues for studying dynamic processes.

Purpose of the Study:

  • To investigate general aspects of stochastic models for dynamic disorder.
  • To reexamine the Zwanzig model and its connection to zero-phonon line broadening.
  • To explore fluctuation processes using cumulant expansions, inspired by single-molecule experiments.

Main Methods:

  • Reexamination of the Zwanzig model for escape kinetics.
  • Connecting the Zwanzig model to the canonical model of zero-phonon line (ZPL) broadening.

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Published on: October 27, 2023

  • Application of cumulant expansions to analyze fluctuation processes.

    • Main Results:

    • Demonstrated a trivial connection between the Zwanzig model and ZPL broadening.
    • Provided a new perspective on the Wang-Wolynes expression for escape rates with non-Markovian Gaussian fluctuations.
    • Examined general fluctuation processes relevant to single-molecule experiments.

    Conclusions:

    • The study establishes a link between seemingly different stochastic models.
    • Offers a unified view on escape dynamics and spectral line broadening.
    • Highlights the utility of cumulant expansions for analyzing complex fluctuations in dynamic disorder systems.