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Volumn 71, Issue 3, 2005, Pages

Quantum-mechanical cumulant dynamics near stable periodic orbits in phase space: Application to the classical-like dynamics of quantum accelerator modes

Author keywords

[No Author keywords available]

Indexed keywords

CUMULANT-BASED FORMALISM; GAUSSIAN WAVE PACKETS; QUANTUM ACCELERATOR MODES; ROBUST QUANTUM RESONANCE EFFECTS;

EID: 18544371302     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.71.033417     Document Type: Article
Times cited : (17)

References (81)
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    • A. Buchleitner, M. B. d'Arcy, S. Fishman, S. A. Gardiner, I. Guarneri, Z.-Y. Ma, L. Rebuzzini, and G. S. Summy, eprint physics/0501146
    • A. Buchleitner, M. B. d'Arcy, S. Fishman, S. A. Gardiner, I. Guarneri, Z.-Y. Ma, L. Rebuzzini, and G. S. Summy, eprint physics/0501146.
  • 45
    • 84856127108 scopus 로고    scopus 로고
    • M. F. Andersen, A. Kaplan, T. Grünzweig, and N. Davidson, e-print quant-ph/0404118
    • M. F. Andersen, A. Kaplan, T. Grünzweig, and N. Davidson, e-print quant-ph/0404118.
  • 51
    • 84856123628 scopus 로고
    • Proceedings of the International School of Physics "Enrico Fermi," Course CXIX, edited by G. Casati, I. Guarneri, and U. Smilansky (IOS Press, Amsterdam)
    • S. Fishman in Quantum Chaos, Proceedings of the International School of Physics "Enrico Fermi," Course CXIX, edited by G. Casati, I. Guarneri, and U. Smilansky (IOS Press, Amsterdam, 1993);
    • (1993) Quantum Chaos
    • Fishman, S.1
  • 56
    • 0037279688 scopus 로고    scopus 로고
    • J. Stat. Phys. 110, 911 (2003).
    • (2003) J. Stat. Phys. , vol.110 , pp. 911
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    • 1842609871 scopus 로고    scopus 로고
    • Phys. Rev. Lett. 92, 084102 (2004).
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 084102
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    • 0001322445 scopus 로고
    • and references therein
    • D. Huber and E. J. Heller, J. Chem. Phys. 87, 5302 (1987), and references therein;
    • (1987) J. Chem. Phys. , vol.87 , pp. 5302
    • Huber, D.1    Heller, E.J.2
  • 62
    • 18544373254 scopus 로고    scopus 로고
    • note
    • This in principle assumes both ξ̂ and ζ̂ to be continuously defined on (-∞,∞), although in practice this restriction can frequently be softened.
  • 69
    • 34250967320 scopus 로고
    • deter mined that there are no well-defined distributions that are completely described by a finite number of greater than two cumulants. In this sense, the truncation at second order, as used here, is somewhat special. See also Ref. [24]
    • Although cumulant expansions can be extended indefinitely, note that J. Marcienkiewicz, Math. Z. 44, 612 (1939), deter mined that there are no well-defined distributions that are completely described by a finite number of greater than two cumulants. In this sense, the truncation at second order, as used here, is somewhat special. See also Ref. [24].
    • (1939) Math. Z. , vol.44 , pp. 612
    • Marcienkiewicz, J.1
  • 72
    • 84856127167 scopus 로고    scopus 로고
    • The quantity ℏG, used as the basic unit of momentum in much of this paper, is equal to two photon recoils
    • The quantity ℏG, used as the basic unit of momentum in much of this paper, is equal to two photon recoils.
  • 74
    • 0001100551 scopus 로고    scopus 로고
    • Related effects in the context of classical optics are discussed in M. V. Berry and E. Bodenschatz, J. Mod. Opt. 46, 349 (1999).
    • (1999) J. Mod. Opt. , vol.46 , pp. 349
    • Berry, M.V.1    Bodenschatz, E.2
  • 77
    • 18544370295 scopus 로고    scopus 로고
    • note
    • A consequence of the ℑ(β) periodicity of the phase space is that it can be mapped onto a torus, in which case j/p can be considered a winding number.
  • 79
    • 18544364099 scopus 로고    scopus 로고
    • note
    • As the Wigner function is only for illustrative purposes, we have simplified by allowing both dynamical variables to be infinite and continuous for its determination.
  • 81
    • 18544371393 scopus 로고    scopus 로고
    • note
    • Equation (A2) has clearly a very similar form to Eq. (34). While this similarity is obviously not coincidental, one should nevertheless bear in mind that the interpretation of these equations is rather different.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.