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Remarks concerning the derivation and the expansion of the master equation

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  • Razavy, M.

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.

Suggested Citation

  • Razavy, M., 1976. "Remarks concerning the derivation and the expansion of the master equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 84(3), pages 591-602.
    • Handle: RePEc:eee:phsmap:v:84:y:1976:i:3:p:591-602
    DOI: 10.1016/0378-4371(76)90107-2
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