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Volumn 66, Issue 4, 2002, Pages 7-

Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states

Author keywords

[No Author keywords available]

Indexed keywords

FOURIER TRANSFORMS; HAMILTONIANS; LYAPUNOV METHODS; NUMERICAL METHODS; PERTURBATION TECHNIQUES; PROBABILITY;

EID: 41349094517     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.046209     Document Type: Article
Times cited : (61)

References (37)
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    • Phys. Rev. E For details on the numerics see D.A. Wisniacki and E. Vergini, 59, 6579 (1999). Note that we use in this paper the same deformation of the billiard shape, which is effectively achieved by using mixed boundary conditions. On the other hand, we work here in the (Formula presented) region.
    • (1999) , vol.59 , pp. 6579
    • Wisniacki, D.A.1    Vergini, E.2
  • 13
  • 15
    • 85036345389 scopus 로고    scopus 로고
    • D. Cohen, in Dynamical Semigroups: Dissipation, Chaos, Quanta, edited by P. Garbaczewski and R. Olkiewicz, Proceedings of the 38th Winter School of Theoretical Physics (Springer-Verlag, Berlin, in press). Also available at http://www.bgu.ac.il/∼dcohen
    • D. Cohen, in Dynamical Semigroups: Dissipation, Chaos, Quanta, edited by P. Garbaczewski and R. Olkiewicz, Proceedings of the 38th Winter School of Theoretical Physics (Springer-Verlag, Berlin, in press). Also available at http://www.bgu.ac.il/∼dcohen.
  • 16
    • 85036413820 scopus 로고    scopus 로고
    • E. J. Heller, in Chaos and Quantum Systems, edited by M.-J. Giannoni et al. (Elsevier, Amsterdam, 1991)
    • E. J. Heller, in Chaos and Quantum Systems, edited by M.-J. Giannoni et al. (Elsevier, Amsterdam, 1991).
  • 19
    • 0034428628 scopus 로고    scopus 로고
    • Phys. Rev. Lett.D. Cohen and T. Kottos, 85, 4839 (2000).
    • (2000) , vol.85 , pp. 4839
    • Cohen, D.1    Kottos, T.2
  • 20
    • 85036273292 scopus 로고    scopus 로고
    • We use (Formula presented) units, but later in some formulas we include (Formula presented) in order to make it easy for the reader to make comparisons with other publications
    • We use (Formula presented) units, but later in some formulas we include (Formula presented) in order to make it easy for the reader to make comparisons with other publications.
  • 22
    • 0000044024 scopus 로고
    • Ann. Math.E. Wigner65, 203 (1957);
    • (1957) , vol.65 , pp. 203
    • Wigner, E.1
  • 28
    • 85036160531 scopus 로고    scopus 로고
    • The term “parametric evolution” refers to the (Formula presented) dependence of the LDOS profile, which starts as a delta distribution at (Formula presented) It can be formally obtained as the solution of a Schrödinger-like equation, where (Formula presented) plays the role of fictitious time
    • The term “parametric evolution” refers to the (Formula presented) dependence of the LDOS profile, which starts as a delta distribution at (Formula presented) It can be formally obtained as the solution of a Schrödinger-like equation, where (Formula presented) plays the role of fictitious time.
  • 29
    • 85036409925 scopus 로고    scopus 로고
    • The saturation of (Formula presented) is just “postponed” by the cutoff procedure. This means that by looking on a large enough (Formula presented) range we can still observe reminisces of saturation. For stronger cutoff, a larger range is required to see deviation from the approximately linear behavior of (Formula presented)
    • The saturation of (Formula presented) is just “postponed” by the cutoff procedure. This means that by looking on a large enough (Formula presented) range we can still observe reminisces of saturation. For stronger cutoff, a larger range is required to see deviation from the approximately linear behavior of (Formula presented)
  • 30
    • 85036234034 scopus 로고    scopus 로고
    • D. Cohen, in Proceedings of the International School of Physics Enrico Fermi Course CXLIII, edited by G. Casati et al. (IOS Press, Amsterdam, 2000)
    • D. Cohen, in Proceedings of the International School of Physics Enrico Fermi Course CXLIII, edited by G. Casati et al. (IOS Press, Amsterdam, 2000).
  • 31
    • 85036398110 scopus 로고    scopus 로고
    • If the perturbative tails effectively disappear, then we say that the LDOS has a purely “nonperturbative” structure. For large enough (Formula presented) the nonperturbative structure becomes purely semiclassical
    • If the perturbative tails effectively disappear, then we say that the LDOS has a purely “nonperturbative” structure. For large enough (Formula presented) the nonperturbative structure becomes purely semiclassical.
  • 32
    • 85036270030 scopus 로고    scopus 로고
    • M. V. Berry, in Chaos and Quantum Systems, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam, 1991)
    • M. V. Berry, in Chaos and Quantum Systems, edited by M.-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam, 1991).
  • 37
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    • The following remark is important [B. Eckhardt (private communication)]: The naive identification of (Formula presented) as the Lyapunov exponent is not obvious, and involves some hidden assumptions regarding the phase space structure of evolving manifolds
    • The following remark is important [B. Eckhardt (private communication)]: The naive identification of (Formula presented) as the Lyapunov exponent is not obvious, and involves some hidden assumptions regarding the phase space structure of evolving manifolds.


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