Remarks concerning the derivation and the expansion of the master equation |
| |
Authors: | M Razavy |
| |
Institution: | Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada |
| |
Abstract: | The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q′), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q′), the master equation can be transformed exactly to partial differential equations of finite order. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|