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RESEARCH PRODUCT
How to solve Fokker-Planck equation treating mixed eigenvalue spectrum?
M. BricsJ. KaupuzsR. Mahnkesubject
PhysicsStatistical Mechanics (cond-mat.stat-mech)Physics and Astronomy (miscellaneous)Spectrum (functional analysis)FOS: Physical sciencesFokker-Planck equationSchrödinger equationMathematical Physics (math-ph)Mathematics::Spectral TheoryCondensed Matter Physicslcsh:QC1-999Pöschl-Teller potentialFokker–Planck equationEigenvalues and eigenvectorsCondensed Matter - Statistical MechanicsMathematical Physicslcsh:PhysicsMathematical physicsdescription
An analogy of the Fokker-Planck equation (FPE) with the Schr\"odinger equation allows us to use quantum mechanics technique to find the analytical solution of the FPE in a number of cases. However, previous studies have been limited to the Schr\"odinger potential with a discrete eigenvalue spectrum. Here, we will show how this approach can be also applied to a mixed eigenvalue spectrum with bounded and free states. We solve the FPE with boundaries located at x=\pm L/2 and take the limit L\rightarrow\infty, considering the examples with constant Schr\"{o}dinger potential and with P\"{o}schl-Teller potential. An oversimplified approach was proposed earlier by M.T. Araujo and E. Drigo Filho. A detailed investigation of the two examples shows that the correct solution, obtained in this paper, is consistent with the expected Fokker-Planck dynamics.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-03-01 |