DOI: 10.1063/1.524019. The non-Markovian relaxation process as a ‘‘contraction’’ of a multidimensional one of Markovian type

The non-Markovian relaxation process as a ‘‘contraction’’ of a multidimensional one of Markovian type

10.1063/1.524019

Crossref journal-article

AIP Publishing

Journal of Mathematical Physics (317)

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.

Bibliography

Ferrario, M., & Grigolini, P. (1979). The non-Markovian relaxation process as a ââcontractionââ of a multidimensional one of Markovian type. Journal of Mathematical Physics, 20(12), 2567â2572.

Authors 2

Mauro Ferrario (first)
Paolo Grigolini (additional)

References 19 Referenced 71

10.1143/PTP.33.423 / Prog. Theor. Phys. (1965)
10.1063/1.431961 / J. Chem. Phys. (1976)
10.1007/BF01020382 / J. Stat. Phys. (1977)
10.1063/1.523242 / J. Math. Phys. Phys. (1977)
10.1063/1.1693183 / Phys. Fluids (1970)
10.1063/1.1666123 / J. Math. Phys. (1972)
{'key': '2024020710255091800_r7'}
10.1143/PTP.34.399 / Prog. Theor. Phys. (1965)
{'key': '2024020710255091800_r9', 'first-page': '63', 'volume': '62', 'year': '1970', 'journal-title': 'Advan. Chem. Phys.'} / Advan. Chem. Phys. (1970)
10.1103/PhysRev.36.823 / Phys. Rev. (1930)
10.1016/0009-2614(77)85021-5 / Chem. Phys. Lett. (1977)
10.1016/0301-0104(78)85107-6 / Chem. Phys. (1978)
{'key': '2024020710255091800_r12'}
10.1088/0370-1328/82/5/309 / Proc. Phys. Soc. (1963)
10.1016/0022-2860(78)87161-0 / J. Mol. Struct. (1978)
10.1088/0022-3727/9/10/004 / J. Phys. D (1976)
{'key': '2024020710255091800_r15', 'first-page': '101', 'volume': '15', 'year': '1969', 'journal-title': 'Advan. Chem. Phys.'} / Advan. Chem. Phys. (1969)
10.1016/0370-1573(76)90029-6 / Phys. Rep. C (1976)
10.1143/JPSJ.26.1 / J. Phys. Soc. Japan (1969)

Dates

Type	When
Created	22 years, 5 months ago (March 7, 2003, 12:31 p.m.)
Deposited	1 year, 6 months ago (Feb. 7, 2024, 11:17 a.m.)
Indexed	1 year ago (Aug. 27, 2024, 9:04 a.m.)
Issued	45 years, 8 months ago (Dec. 1, 1979)
Published	45 years, 8 months ago (Dec. 1, 1979)
Published Print	45 years, 8 months ago (Dec. 1, 1979)

Funders 0

None

BibTeX

@article{Ferrario_1979, title={The non-Markovian relaxation process as a ‘“contraction”’ of a multidimensional one of Markovian type}, volume={20}, ISSN={1089-7658}, url={http://dx.doi.org/10.1063/1.524019}, DOI={10.1063/1.524019}, number={12}, journal={Journal of Mathematical Physics}, publisher={AIP Publishing}, author={Ferrario, Mauro and Grigolini, Paolo}, year={1979}, month=dec, pages={2567–2572} }

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