Statistics of quasienergies in chaotic and random systems

Mario Feingold; Shmuel Fishman

doi:10.1016/0167-2789(87)90101-1

Statistics of quasienergies in chaotic and random systems

Mario Feingold, Shmuel Fishman

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

The statistics of quasienergies are analyzed for periodically driven chaotic systems and found to be similar to those of truly random models. These differ from the results that were obtained so far, for chaotic systems with time-independent Hamiltonians. The separations of the quasienergies and the Δ₃-statistic are calculated numerically for chaotic, as well as for truly random models. Local statistical measures are introduced in order to investigate the repulsion of quasienergies. The results provide further evidence for Anderson localization in chaotic systems with Hamiltonians that are periodic in time.

Original language	English
Pages (from-to)	181-195
Number of pages	15
Journal	Physica D: Nonlinear Phenomena
Volume	25
Issue number	1-3
DOIs	https://doi.org/10.1016/0167-2789(87)90101-1
State	Published - 1 Jan 1987
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(87)90101-1

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title = "Statistics of quasienergies in chaotic and random systems",

abstract = "The statistics of quasienergies are analyzed for periodically driven chaotic systems and found to be similar to those of truly random models. These differ from the results that were obtained so far, for chaotic systems with time-independent Hamiltonians. The separations of the quasienergies and the Δ3-statistic are calculated numerically for chaotic, as well as for truly random models. Local statistical measures are introduced in order to investigate the repulsion of quasienergies. The results provide further evidence for Anderson localization in chaotic systems with Hamiltonians that are periodic in time.",

author = "Mario Feingold and Shmuel Fishman",

note = "Funding Information: We thank D.R. Grempel, N. Moiseyev and R.E. Prange for useful suggestions and comments. The work was supported in part by the U.S.-Israel Binational Science Foundation (BSF), by the Bat-Sheva de-Rothschild Fund for Advancement of Science and Technology and by the Technion VPR-L. Deutsch Research Fund.",

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AU - Fishman, Shmuel

N1 - Funding Information: We thank D.R. Grempel, N. Moiseyev and R.E. Prange for useful suggestions and comments. The work was supported in part by the U.S.-Israel Binational Science Foundation (BSF), by the Bat-Sheva de-Rothschild Fund for Advancement of Science and Technology and by the Technion VPR-L. Deutsch Research Fund.

PY - 1987/1/1

Y1 - 1987/1/1

N2 - The statistics of quasienergies are analyzed for periodically driven chaotic systems and found to be similar to those of truly random models. These differ from the results that were obtained so far, for chaotic systems with time-independent Hamiltonians. The separations of the quasienergies and the Δ3-statistic are calculated numerically for chaotic, as well as for truly random models. Local statistical measures are introduced in order to investigate the repulsion of quasienergies. The results provide further evidence for Anderson localization in chaotic systems with Hamiltonians that are periodic in time.

AB - The statistics of quasienergies are analyzed for periodically driven chaotic systems and found to be similar to those of truly random models. These differ from the results that were obtained so far, for chaotic systems with time-independent Hamiltonians. The separations of the quasienergies and the Δ3-statistic are calculated numerically for chaotic, as well as for truly random models. Local statistical measures are introduced in order to investigate the repulsion of quasienergies. The results provide further evidence for Anderson localization in chaotic systems with Hamiltonians that are periodic in time.

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Statistics of quasienergies in chaotic and random systems

Abstract

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