Diffusion in very chaotic hamiltonian systems
Abstract
In this paper, we study nonintegrable hamiltonian dynamics: H(I,θ) = H_{0}(I) + kH_{1}(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I_{0}, θ_{0}, t_{0}) that the system is at I, θ at t, given it was at I_{0}, θ_{0} at t_{0}. By discretizing time into steps of size ϵ, we show how to evaluate physical observables for large k, fixed ϵ. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Finally, passage to ϵ = 0, the original hamiltonian flow, is discussed.
 Authors:

 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1109132
 Report Number(s):
 LBL11889
Journal ID: ISSN 03759601
 DOE Contract Number:
 W7405ENG48
 Resource Type:
 Journal Article
 Journal Name:
 Physics Letters. A
 Additional Journal Information:
 Journal Volume: 82; Journal Issue: 8; Journal ID: ISSN 03759601
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Abarbanel, Henry D. I., and Crawford, John David. Diffusion in very chaotic hamiltonian systems. United States: N. p., 1981.
Web. doi:10.1016/03759601(81)907817.
Abarbanel, Henry D. I., & Crawford, John David. Diffusion in very chaotic hamiltonian systems. United States. https://doi.org/10.1016/03759601(81)907817
Abarbanel, Henry D. I., and Crawford, John David. 1981.
"Diffusion in very chaotic hamiltonian systems". United States. https://doi.org/10.1016/03759601(81)907817. https://www.osti.gov/servlets/purl/1109132.
@article{osti_1109132,
title = {Diffusion in very chaotic hamiltonian systems},
author = {Abarbanel, Henry D. I. and Crawford, John David},
abstractNote = {In this paper, we study nonintegrable hamiltonian dynamics: H(I,θ) = H0(I) + kH1(I,θ), for large k, that is, far from integrability. An integral representation is given for the conditional probability P(I,θ, t¦I0, θ0, t0) that the system is at I, θ at t, given it was at I0, θ0 at t0. By discretizing time into steps of size ϵ, we show how to evaluate physical observables for large k, fixed ϵ. An explicit calculation of a diffusion coefficient in a two degrees of freedom problem is reported. Finally, passage to ϵ = 0, the original hamiltonian flow, is discussed.},
doi = {10.1016/03759601(81)907817},
url = {https://www.osti.gov/biblio/1109132},
journal = {Physics Letters. A},
issn = {03759601},
number = 8,
volume = 82,
place = {United States},
year = {1981},
month = {4}
}
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