The non-Markovian relaxation process as a ‘‘contraction’’ of a multidimensional one of Markovian type
- 1 December 1979
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 20 (12) , 2567-2572
- https://doi.org/10.1063/1.524019
Abstract
A new approach for obtaining the Fokker–Planck equation to be associated with the generalized Langevin equation is discussed. By using the Mori expansion of the ’’memory kernel,’’ it is shown that any information of interest may be provided by a suitable multidimensional Fokker–Planck equation of Markovian type. A suitable ’’contraction’’ process, furthermore, enables us to find the same two‐point conditional probability as the one recently obtained by Fox. This approach may be useful to overcome the Markov approximation which is present in the stochastic Liouville equation theoryKeywords
This publication has 17 references indexed in Scilit:
- Preparation and decay of unstable molecular states undergoing memory effects: Excitation by coherent electromagnetic pulses of arbitrary strengthChemical Physics, 1978
- Molecular dynamics and interactions in liquids, molecular crystals and molecular complexesJournal of Molecular Structure, 1978
- A “reduced” model theory for molecular decay processesChemical Physics Letters, 1977
- Analysis of nonstationary, Gaussian and non-Gaussian, generalized Langevin equations using methods of multiplicative stochastic processesJournal of Statistical Physics, 1977
- The electrical polarizability of a two-dimensional itinerant oscillatorJournal of Physics D: Applied Physics, 1976
- Stochastic differential equationsPhysics Reports, 1976
- On the Calculation of Time Correlation FunctionsAdvances in Chemical Physics, 1970
- A Stochastic Theory of Line ShapeAdvances in Chemical Physics, 1969
- Transport, Collective Motion, and Brownian MotionProgress of Theoretical Physics, 1965
- A Possible Second Dielectric Dispersion Region in Polar LiquidsProceedings of the Physical Society, 1963