Semiclassical Klein–Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential
| Autor: | B. P. Mulligan, William T. Coffey, Yu. P. Kalmykov, Serguey V. Titov |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Statistics and Probability
Smoluchowski coagulation equation General Physics and Astronomy Semiclassical physics Statistical and Nonlinear Physics Classical limit symbols.namesake Quantum harmonic oscillator Modeling and Simulation Quantum mechanics Master equation symbols Wigner distribution function Fokker–Planck equation Mathematical Physics Brownian motion Mathematics Mathematical physics |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 40:F91-F98 |
| ISSN: | 1751-8121 1751-8113 |
| DOI: | 10.1088/1751-8113/40/3/f02 |
| Popis: | The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(4) and in the classical limit, → 0, reduces to the Klein–Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|