Langevin and Fokker-Planck Equations:

Dr. Andrew J. Graham, a former WFU graduate student, and I have published a paper on a phase space form of Langevin equations and the corresponding Fokker-Planck equations. Here is the reference to the published paper.

W. C. Kerr and A. J. Graham, "Generalized phase space version of Langevin equations and associated Fokker-Planck equations", Eur. Phys. J. B 15, 305-311 (2000).

Here is a link to the paper (scroll through the Table of Contents to page 305).

Nucleation

Dr. Andrew J. Graham, a former WFU graduate student, and I have published a paper that calculates the nucleation rate for critical droplets for an elastic string moving in a local asymmetric f4 potential. The published paper is:

A. J. Graham and W. C. Kerr, "Solution of Kramers' problem for a moderately to heavily damped elastic string", Phys. Rev. E 65, 016106 (2002).

Here is a link to the issue of the journal with the paper.

 

Dr. Graham and I have published a paper that calculates the nucleation rate for critical droplets for an elastic string moving in a local symmetric f6 potential the published paper is

W. C. Kerr and A. J. Graham, "Nucleation rate of critical droplets on an elastic string in a f6 potential", Phys. Rev. E 70, 066103 (2004).

Here is a link to the abstract of the published paper.

Semi-classical electron dynamics

Graduate student Matthew Rave, WFU visiting professor Lukasz A. Turski (from the Polish Academy of Science) and I have published a paper on the effects of the Berry curvature term in the semi-classical equations of motion for an electron on the transport equation for electrons. The published paper is

W. C. Kerr, M. J. Rave, and L. A. Turski, "Phase-Space Dynamics of Semiclassical Spin-1/2 Bloch Electrons", Phys. Rev. Lett. 94, 176403 (2005).

Here is a link to the abstract of the published paper.

 

Berry phase in electronic states

Graduate student Matthew Rave and I have published a paper in which we calculate the Berry's phase for an electron in a one-dimensional model. The model is a Kronig-Penney model, generalized so that it lacks inversion symmetry. The published paper is

M. J. Rave and W. C. Kerr, "Berry's phase for an electron in a periodic potential without inversion symmetry", Eur. Phys. J. B 45, 473 (2005).

Here is a link to the abstract of the published paper.