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 theory.
The non‐Markovian relaxation process as a ‘‘contraction’’ of a multidimensional one of Markovian type / Ferrario, Mauro; P., Grigolini. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 20:(1979), pp. 2567-2572. [10.1063/1.524019]
The non‐Markovian relaxation process as a ‘‘contraction’’ of a multidimensional one of Markovian type
FERRARIO, Mauro;
1979
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 theory.
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