메뉴 건너뛰기




Volumn 80, Issue 4, 2009, Pages

Recovery of chaotic tunneling due to destruction of dynamical localization by external noise

Author keywords

[No Author keywords available]

Indexed keywords

CHAOTIC REGIONS; CHAOTIC SEA; CHAOTIC STATE; DESTRUCTIVE INTERFERENCE; DYNAMICAL LOCALIZATION; EXTERNAL NOISE; INCREASING FUNCTIONS; LOCALIZATION LENGTH; NOISE INTENSITIES; PERTURBATIVE SCALING; PLANCK'S CONSTANTS; QUANTUM TUNNELING; TUNNELING AMPLITUDE; TUNNELING RATES;

EID: 70350068132     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.046204     Document Type: Article
Times cited : (4)

References (55)
  • 2
    • 0003870238 scopus 로고    scopus 로고
    • edited by S. Tomsovic (World Scientific, Singapore
    • S. C. Creagh, in Tunneling in Complex Systems, edited by, S. Tomsovic, (World Scientific, Singapore, 1998) p. 35.
    • (1998) Tunneling in Complex Systems
    • Creagh, S.C.1
  • 3
    • 26144436679 scopus 로고
    • 10.1103/PhysRevE.50.145
    • S. Tomsovic and D. Ullmo, Phys. Rev. E 50, 145 (1994). 10.1103/PhysRevE.50.145
    • (1994) Phys. Rev. e , vol.50 , pp. 145
    • Tomsovic, S.1    Ullmo, D.2
  • 5
    • 0343861171 scopus 로고    scopus 로고
    • 10.1103/PhysRevE.57.1421
    • S. D. Frischat and E. Doron, Phys. Rev. E 57, 1421 (1998). 10.1103/PhysRevE.57.1421
    • (1998) Phys. Rev. e , vol.57 , pp. 1421
    • Frischat, S.D.1    Doron, E.2
  • 9
    • 33745296293 scopus 로고    scopus 로고
    • 10.1088/0305-4470/39/26/003
    • G. C. Smith and S. C. Creagh, J. Phys. A 39, 8283 (2006). 10.1088/0305-4470/39/26/003
    • (2006) J. Phys. A , vol.39 , pp. 8283
    • Smith, G.C.1    Creagh, S.C.2
  • 10
    • 0000233976 scopus 로고
    • 10.1103/PhysRevLett.74.682;
    • A. Shudo and K. S. Ikeda, Phys. Rev. Lett. 74, 682 (1995) 10.1103/PhysRevLett.74.682
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 682
    • Shudo, A.1    Ikeda, K.S.2
  • 11
    • 22244458303 scopus 로고    scopus 로고
    • 10.1016/S0167-2789(97)00239-X;
    • A. Shudo and K. S. Ikeda, Physica D 115, 234 (1998) 10.1016/S0167- 2789(97)00239-X
    • (1998) Physica D , vol.115 , pp. 234
    • Shudo, A.1    Ikeda, K.S.2
  • 13
    • 0009148023 scopus 로고    scopus 로고
    • 10.1006/aphy.2000.6050;
    • K. Takahashi and K. S. Ikeda, Ann. Phys. 283, 94 (2000) 10.1006/aphy.2000.6050
    • (2000) Ann. Phys. , vol.283 , pp. 94
    • Takahashi, K.1    Ikeda, K.S.2
  • 14
    • 0042342514 scopus 로고    scopus 로고
    • 10.1088/0305-4470/36/29/305;
    • K. Takahashi and K. S. Ikeda, J. Phys. A 36, 7953 (2003) 10.1088/0305-4470/36/29/305
    • (2003) J. Phys. A , vol.36 , pp. 7953
    • Takahashi, K.1    Ikeda, K.S.2
  • 16
    • 33845387099 scopus 로고    scopus 로고
    • 10.1103/PhysRevLett.97.240403
    • K. Takahashi and K. S. Ikeda, Phys. Rev. Lett. 97, 240403 (2006). 10.1103/PhysRevLett.97.240403
    • (2006) Phys. Rev. Lett. , vol.97 , pp. 240403
    • Takahashi, K.1    Ikeda, K.S.2
  • 23
    • 0042970386 scopus 로고    scopus 로고
    • 10.1088/0305-4470/35/17/101;
    • A. Shudo, Y. Ishii, and K. S. Ikeda, J. Phys. A 35, L225 (2002) 10.1088/0305-4470/35/17/101
    • (2002) J. Phys. A , vol.35 , pp. 225
    • Shudo, A.1    Ishii, Y.2    Ikeda, K.S.3
  • 27
    • 5844383842 scopus 로고
    • 10.1103/PhysRevLett.56.677
    • D. L. Shepelyansky, Phys. Rev. Lett. 56, 677 (1986). 10.1103/PhysRevLett. 56.677
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 677
    • Shepelyansky, D.L.1
  • 35
    • 0035648602 scopus 로고    scopus 로고
    • 10.1063/1.1418763
    • L. A. Bunimovich, Chaos 11, 802 (2001). 10.1063/1.1418763
    • (2001) Chaos , vol.11 , pp. 802
    • Bunimovich, L.A.1
  • 36
    • 70350075038 scopus 로고    scopus 로고
    • More precisely, pcutoff is kept large enough so as to preserve the dynamical localization that occurs in the vicinity of the torus region when the noise term is absent. As shown in Sec. we have nonzero decay rate from torus to chaotic region under the presence of noise. Hence, we choose pcutoff so as to obtain the converged decay rate.
    • More precisely, pcutoff is kept large enough so as to preserve the dynamical localization that occurs in the vicinity of the torus region when the noise term is absent. As shown in Sec., we have nonzero decay rate from torus to chaotic region under the presence of noise. Hence, we choose pcutoff so as to obtain the converged decay rate.
  • 37
    • 70350043110 scopus 로고    scopus 로고
    • Precisely speaking, Pn torus also contains the probability at the chaotic sea near the torus. However the contribution from the chaotic sea is negligible on average, since probability in that region escapes quickly.
    • Precisely speaking, Pn torus also contains the probability at the chaotic sea near the torus. However the contribution from the chaotic sea is negligible on average, since probability in that region escapes quickly.
  • 38
    • 70350050402 scopus 로고    scopus 로고
    • We mention that an elaborate construction of torus states for more generic cases has recently been developed by Bäcker
    • We mention that an elaborate construction of torus states for more generic cases has recently been developed by Bäcker.
  • 39
    • 0000260904 scopus 로고
    • We use the term resonance (or off resonance) because the corresponding physical process is governed by the resonance of quasienergies. Note that the quantum resonance often investigated in kicked rotors
    • We use the term resonance (or off resonance) because the corresponding physical process is governed by the resonance of quasienergies. Note that the quantum resonance often investigated in kicked rotors [F. M. Izrailev and D. L. Shepelyanskii, Dokl. Akad. Nauk SSSR 249, 1103 (1979)] is irrelevant in the present study.
    • (1979) Dokl. Akad. Nauk SSSR , vol.249 , pp. 1103
    • Izrailev, F.M.1    Shepelyanskii, D.L.2
  • 40
    • 70350073895 scopus 로고    scopus 로고
    • The discontinuity of the lines of quasienergy is due to artifact of this condition.
    • The discontinuity of the lines of quasienergy is due to artifact of this condition.
  • 41
    • 70350067643 scopus 로고    scopus 로고
    • As the position of the absorbing boundary is set to be pcutoff >L, the probability amplitude obeys a diffusion process in the region of pcutoff >p>L and it escapes through the absorbing boundary.
    • As the position of the absorbing boundary is set to be pcutoff >L, the probability amplitude obeys a diffusion process in the region of pcutoff >p>L and it escapes through the absorbing boundary.
  • 42
    • 33645667614 scopus 로고
    • 10.1364/JOSA.52.000116;
    • J. B. Keller, J. Opt. Soc. Am. 52, 116 (1962) 10.1364/JOSA.52.000116
    • (1962) J. Opt. Soc. Am. , vol.52 , pp. 116
    • Keller, J.B.1
  • 43
    • 0003898664 scopus 로고
    • Academic Press, New York
    • A. Sommerfeld, Optics (Academic Press, New York, 1954)
    • (1954) Optics
    • Sommerfeld, A.1
  • 47
    • 70350043099 scopus 로고    scopus 로고
    • The reason for the choice of d in case of small β is as follows. Since making β small makes the border move "downward" (i.e., toward smaller p), the Lagrangian manifold of the initial state may cross the border. In order to avoid this, we have to move the border upward or the Lagrangian manifold downward. The latter is infeasible because it is impossible to move continuously the Lagrangian manifold due to the quantization condition of ψtorus (q). Hence we move the border upward by increasing d.
    • The reason for the choice of d in case of small β is as follows. Since making β small makes the border move "downward" (i.e., toward smaller p), the Lagrangian manifold of the initial state may cross the border. In order to avoid this, we have to move the border upward or the Lagrangian manifold downward. The latter is infeasible because it is impossible to move continuously the Lagrangian manifold due to the quantization condition of ψtorus (q). Hence we move the border upward by increasing d.
  • 48
    • 70350056636 scopus 로고    scopus 로고
    • The decay rate γ is determined from Pn torus that are not too small (Pn torus >0.1) and n≤ 105, by least square fitting.
    • The decay rate γ is determined from Pn torus that are not too small (Pn torus >0.1) and n≤ 105, by least square fitting.
  • 49
    • 18444380929 scopus 로고
    • 10.1103/PhysRevLett.53.1515
    • E. J. Heller, Phys. Rev. Lett. 53, 1515 (1984). 10.1103/PhysRevLett.53. 1515
    • (1984) Phys. Rev. Lett. , vol.53 , pp. 1515
    • Heller, E.J.1
  • 50
    • 70449490050 scopus 로고    scopus 로고
    • 10.1088/1751-8113/42/26/265101;
    • A. Shudo, Y. Ishii and K. S. Ikeda, J. Phys. A 42, 265101 (2009) 10.1088/1751-8113/42/26/265101
    • (2009) J. Phys. A , vol.42 , pp. 265101
    • Shudo, A.1    Ishii, Y.2    Ikeda, K.S.3
  • 51
    • 70449490050 scopus 로고    scopus 로고
    • 10.1088/1751-8113/42/26/265102
    • A. Shudo, Y. Ishii and K. S. Ikeda, J. Phys. A 42, 265102 (2009). 10.1088/1751-8113/42/26/265102
    • (2009) J. Phys. A , vol.42 , pp. 265102
    • Shudo, A.1    Ishii, Y.2    Ikeda, K.S.3
  • 54
    • 0001349492 scopus 로고    scopus 로고
    • 10.1103/PhysRevE.59.R2516
    • G. Casati and T. Prosen, Phys. Rev. E 59, R2516 (1999). 10.1103/PhysRevE.59.R2516
    • (1999) Phys. Rev. e , vol.59 , pp. 2516
    • Casati, G.1    Prosen, T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.