Solution of Kramers' problem for a moderately to heavily damped elastic string

Details Solution of Kramers' problem for a moderately to heavily damped elastic string Solution of Kramers' problem for a moderately to heavily damped elastic string

Jan 2002

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002phrve..65a6106g&link_type=abstract

Physical Review E, vol. 65, Issue 1, id. 016106

Mathematics

Probability

1

Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion, Nonlinear Or Nonlocal Theories And Models, Nucleation, Particle-Theory And Field-Theory Models Of The Early Universe

Scientific paper

We obtain the nucleation rate of critical droplets for an elastic string moving in a double-well potential and subject to noise and damping forces. We obtain this rate for a class of potentials that includes both the asymmetric φ4 and the φ6 potentials. The frequencies of small oscillations about the critical droplet are obtained from a Heun equation. We solve the Fokker-Planck equation for the phase-space probability density by projecting onto the eigenfunction basis. We present a comparison with simulations for the case of the asymmetric φ4 potential.

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