Resonance-assisted tunneling in near-integrable systems

被引:94
作者
Brodier, O [1 ]
Schlagheck, P [1 ]
Ullmo, D [1 ]
机构
[1] Lab Phys Theor & Modeles Stat, F-91405 Orsay, France
关键词
D O I
10.1103/PhysRevLett.87.064101
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasidegenerate eigenvalues from the purely exponential decrease with 1/(h) over bar obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the invariant tori, allows one to quantitatively reproduce the behavior of the eigenvalue splittings.
引用
收藏
页码:641011 / 641014
页数:4
相关论文
共 23 条
[1]   QUANTUM TUNNELING AND CHAOTIC DYNAMICS [J].
BOHIGAS, O ;
BOOSE, D ;
DECARVALHO, RE ;
MARVULLE, V .
NUCLEAR PHYSICS A, 1993, 560 (01) :197-210
[2]   Tunneling rate fluctuations induced by nonlinear resonances: A quantitative treatment based on semiclassical arguments [J].
Bonci, L ;
Farusi, A ;
Grigolini, P ;
Roncaglia, R .
PHYSICAL REVIEW E, 1998, 58 (05) :5689-5692
[3]  
CREAGH S, 1998, TUNNELING COMPLEX SY, P1
[4]   Complex periodic orbits and tunneling in chaotic potentials [J].
Creagh, SC ;
Whelan, ND .
PHYSICAL REVIEW LETTERS, 1996, 77 (25) :4975-4979
[5]   Homoclinic structure controls chaotic tunneling [J].
Creagh, SC ;
Whelan, ND .
PHYSICAL REVIEW LETTERS, 1999, 82 (26) :5237-5240
[6]   QUANTUM DYNAMICAL TUNNELING IN BOUND-STATES [J].
DAVIS, MJ ;
HELLER, EJ .
JOURNAL OF CHEMICAL PHYSICS, 1981, 75 (01) :246-254
[7]  
DEALMEIDA AMO, 1984, J PHYS CHEM-US, V88, P6139
[8]   First experimental evidence for chaos-assisted tunneling in a microwave annular billiard [J].
Dembowski, C ;
Gräf, HD ;
Heine, A ;
Hofferbert, R ;
Rehfeld, F ;
Richter, A .
PHYSICAL REVIEW LETTERS, 2000, 84 (05) :867-870
[9]   SEMICLASSICAL DESCRIPTION OF TUNNELING IN MIXED SYSTEMS - CASE OF THE ANNULAR BILLIARD [J].
DORON, E ;
FRISCHAT, SD .
PHYSICAL REVIEW LETTERS, 1995, 75 (20) :3661-3664
[10]   Dynamical tunneling in mixed systems [J].
Frischat, SD ;
Doron, E .
PHYSICAL REVIEW E, 1998, 57 (02) :1421-1443