Mathematics – Probability
Scientific paper
Dec 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004phrve..70f6103k&link_type=abstract
Physical Review E, vol. 70, Issue 6, id. 066103
Mathematics
Probability
Nucleation, Fluctuation Phenomena, Random Processes, Noise, And Brownian Motion, Nonlinear Or Nonlocal Theories And Models, 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 ϕ6 local potential and subject to noise and damping forces. The critical droplet is a bound soliton-antisoliton pair that carries a section of the string out of the metastable central minimum into one of the stable side minima. 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 it onto the eigenfunction basis obtained from the Heun equation. We employ Farkas’ “flux-overpopulation” method to obtain boundary conditions for solving the Fokker-Planck equation; these restrict the validity of our solution to the moderate to heavy damping regime. We present results for the rate as a function of temperature, well depth, and damping.
Graham John A.
Kerr W. C.
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