Classical and quantum dynamics of a periodically driven particle in a triangular well

被引:24
作者
Flatte, ME
Holthaus, M
机构
[1] HARVARD UNIV,DIV APPL SCI,CAMBRIDGE,MA 02138
[2] UNIV MARBURG,FACHBEREICH PHYS,D-35032 MARBURG,GERMANY
关键词
D O I
10.1006/aphy.1996.0005
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We investigate the correspondence between classical and quantum mechanics for periodically time dependent Hamiltonian systems, using the example of a periodically forced particle in a one-dimensional triangular well potential. In particular, we consider quantum mechanical Floquet states associated with resonances in the classical phase space. When the classical motion exhibits subharmonic resonances, the corresponding Floquet states maintain the driving field's periodicity through dynamical tunneling. This principle applies both to Floquet states associated with classical invariant vortex tubes surrounding stable, elliptic periodic orbits and to Floquet states that are associated with unstable, hyperbolic periodic orbits. The triangular well model also poses a yet unsolved mathematical problem, related to perturbation theory for systems with a dense pure point spectrum. The present approximate analytical and numerical results indicate that quantum tunneling between different resonance zones is of crucial importance for the question whether the driven triangular well has a dense point or an absolutely continuous quasienergy spectrum, or whether there is a transition from the one to the other. (C) 1996 Academic Press, Inc.
引用
收藏
页码:113 / 146
页数:34
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