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Escape or switching at short times.

G Grinstein¹, R H Koch

¹IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|December 31, 2005

Summary

This study extends the Arrhenius theory of thermal switching, revealing that escape probability can peak over time, not just decrease. The peak time is logarithmically related to the standard decay time, offering new insights into metastable state escape dynamics.

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Area of Science:

Physics
Physical Chemistry
Materials Science

Background:

The standard Arrhenius picture describes thermal escape from metastable states as monotonically decreasing over time.
This model is crucial for understanding phenomena like magnetic switching and chemical reactions.

Purpose of the Study:

To extend the Arrhenius picture to shorter timescales.
To derive conditions for non-monotonic escape probability.
To investigate the relationship between peak escape time and thermal decay time.

Main Methods:

Theoretical derivation of escape probability under general conditions.
Analysis of the Arrhenius equation for thermal switching dynamics.
Mathematical modeling of escape probability as a function of time.

Main Results:

Established conditions for peaked, rather than monotonic, escape probability over time.
Derived a relationship where the peak time (tau(P)) diverges logarithmically with the decay time (tau(D)).
The findings challenge the monotonic decay assumption in the standard Arrhenius model at shorter timescales.

Conclusions:

The Arrhenius picture can be extended to predict peaked escape probabilities.
This provides a more nuanced understanding of thermal switching and escape dynamics.
The derived relationship offers a new parameter for characterizing metastable state behavior.

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