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Quantum dynamics of a nonintegrable system
Abstract
The quantum motion of a periodically kicked rotator is shown to be related to Anderson's problem of motion of a quantum particle in a one-dimensional lattice in the presence of a static-random potential. Classically, the first problem is nonintegrable and, for certain values of the parameters, exhibits chaos and diffusion in phase space; in the second problem, diffusion takes place in configuration space. Quantum phase interference, however, is known to suppress diffusion in Anderson's problem and to produce quasiperiodic motion. By establishing a mapping between the two systems we show that a similar effect determines the dynamics of the quantum rotator. As a result its wave functions are localized in phase space and their time evolution is quasiperiodic. This result explains the quantum recurrences and boundedness of the energy found in recent numerical work.
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Citations
Cites
Absence of Diffusion in Certain Random Lattices
Anderson, P. W. (1958) · Physical Review · doi:10.1103/physrev.109.1492 · Cited by 12,468
Cited by
Dynamics of Loschmidt echoes and fidelity decay
Gorin, T., Prosen, T., Seligman, T. H., & Žnidarič, M. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.09.003 · Cited by 623
Experimental Observation of the Anderson Metal-Insulator Transition with Atomic Matter Waves
Chabé, J., Lemarié, G., Grémaud, B., Delande, D., Szriftgiser, P., & Garreau, J. C. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.255702 · Cited by 477
Moore, F. L., Robinson, J. C., Bharucha, C., Williams, P. E., & Raizen, M. G. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.2974 · Cited by 391
Dynamical localization in the microwave interaction of Rydberg atoms: The influence of noise
Blümel, R., Buchleitner, A., Graham, R., Sirko, L., Smilansky, U., & Walther, H. (1991) · Physical Review A · doi:10.1103/physreva.44.4521 · Cited by 206
Composed ensembles of random unitary matrices
Pozniak, M., Zyczkowski, K., & Kus, M. (1998) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/31/3/016 · Cited by 128
Metadata
- Authors
- Grempel, D. R., Prange, R. E., & Fishman, S.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1984-04-01
- Volume
- 29
- Issue
- 4
- Pages
- 1639-1647
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2089183178
- Cited by
- 498
- References
- 1
- FWCI
- 17.59
- Type
- journal article
- Language
- en
- Open access
- closed
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- Grempel, D. R., Prange, R. E., & Fishman, S. (1984). Quantum dynamics of a nonintegrable system. Physical Review A. https://doi.org/10.1103/physreva.29.1639
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
