-
2
-
-
0003870238
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
12
-
-
0942267628
-
-
10.1103/PhysRevE.68.056211
-
T. Onishi, A. Shudo, K. S. Ikeda, and K. Takahashi, Phys. Rev. E 68, 056211 (2003). 10.1103/PhysRevE.68.056211
-
(2003)
Phys. Rev. e
, vol.68
, pp. 056211
-
-
Onishi, T.1
Shudo, A.2
Ikeda, K.S.3
Takahashi, K.4
-
14
-
-
0042342514
-
-
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
-
-
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
-
19
-
-
45849154676
-
-
10.1103/PhysRevE.64.016221
-
A. Mouchet, C. Miniatura, R. Kaiser, B. Gremaud, and D. Delande, Phys. Rev. E 64, 016221 (2001). 10.1103/PhysRevE.64.016221
-
(2001)
Phys. Rev. e
, vol.64
, pp. 016221
-
-
Mouchet, A.1
Miniatura, C.2
Kaiser, R.3
Gremaud, B.4
Delande, D.5
-
26
-
-
0003973169
-
-
Springer, Berlin
-
G. Casati, B. V. Chirikov, J. Ford, and F. M. Izrailev, Stochastic Behavior in Classical and Quantum Hamiltonian Systems (Springer, Berlin, 1979), p. 334.
-
(1979)
Stochastic Behavior in Classical and Quantum Hamiltonian Systems
, pp. 334
-
-
Casati, G.1
Chirikov, B.V.2
Ford, J.3
Izrailev, F.M.4
-
27
-
-
5844383842
-
-
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
-
30
-
-
0000876402
-
-
10.1103/PhysRevLett.53.2187
-
E. Ott, T. M. Antonsen, Jr., and J. D. Hanson, Phys. Rev. Lett. 53, 2187 (1984). 10.1103/PhysRevLett.53.2187
-
(1984)
Phys. Rev. Lett.
, vol.53
, pp. 2187
-
-
Ott, E.1
Antonsen, Jr.T.M.2
Hanson, J.D.3
-
32
-
-
0037037901
-
-
10.1103/PhysRevLett.89.154101
-
L. Hufnagel, R. Ketzmerick, M.-F. Otto, and H. Schanz, Phys. Rev. Lett. 89, 154101 (2002). 10.1103/PhysRevLett.89.154101
-
(2002)
Phys. Rev. Lett.
, vol.89
, pp. 154101
-
-
Hufnagel, L.1
Ketzmerick, R.2
Otto, M.-F.3
Schanz, H.4
-
35
-
-
0035648602
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
Academic Press, New York
-
A. Sommerfeld, Optics (Academic Press, New York, 1954)
-
(1954)
Optics
-
-
Sommerfeld, A.1
-
46
-
-
0034248195
-
-
10.1103/PhysRevLett.85.1214
-
R. Ketzmerick, L. Hufnagel, F. Steinbach, and M. Weiss, Phys. Rev. Lett. 85, 1214 (2000). 10.1103/PhysRevLett.85.1214
-
(2000)
Phys. Rev. Lett.
, vol.85
, pp. 1214
-
-
Ketzmerick, R.1
Hufnagel, L.2
Steinbach, F.3
Weiss, M.4
-
47
-
-
70350043099
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
-
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
-
55
-
-
40849102645
-
-
10.1103/PhysRevLett.100.104101
-
A. Bäcker, R. Ketzmerick, S. Löck, and L. Schilling, Phys. Rev. Lett. 100, 104101 (2008). 10.1103/PhysRevLett.100.104101
-
(2008)
Phys. Rev. Lett.
, vol.100
, pp. 104101
-
-
Bäcker, A.1
Ketzmerick, R.2
Löck, S.3
Schilling, L.4
|