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Title: Diffusion in very chaotic hamiltonian systems

Abstract

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.

Authors:
 [1];  [1]
  1. 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):
LBL-11889
Journal ID: ISSN 0375-9601
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
Physics Letters. A
Additional Journal Information:
Journal Volume: 82; Journal Issue: 8; Journal ID: ISSN 0375-9601
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:10.1016/0375-9601(81)90781-7.
Abarbanel, Henry D. I., & Crawford, John David. Diffusion in very chaotic hamiltonian systems. United States. https://doi.org/10.1016/0375-9601(81)90781-7
Abarbanel, Henry D. I., and Crawford, John David. 1981. "Diffusion in very chaotic hamiltonian systems". United States. https://doi.org/10.1016/0375-9601(81)90781-7. 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 = {10.1016/0375-9601(81)90781-7},
url = {https://www.osti.gov/biblio/1109132}, journal = {Physics Letters. A},
issn = {0375-9601},
number = 8,
volume = 82,
place = {United States},
year = {1981},
month = {4}
}