Localization in strongly chaotic systems

Mario Feingold

doi:10.1088/0305-4470/30/10/032

Localization in strongly chaotic systems

Mario Feingold

Department of Physics

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

2 Scopus citations

Abstract

We discuss the differences and similarities in structure between Hamiltonian matrices of strongly chaotic time-independent systems and the evolution operator matrix for the kicked-rotor model. Since the eigenvectors of the latter are exponentially localized, we study the influence of the differences between the two systems on this property. In particular, the Wigner ensemble is used to show that, for ℏ → 0, the effect of the slow variation of the diagonal matrix elements in the Hamiltonian matrices is restricted to the tails of the eigenvectors.

Original language	English
Pages (from-to)	3603-3612
Number of pages	10
Journal	Journal of Physics A: Mathematical and General
Volume	30
Issue number	10
DOIs	https://doi.org/10.1088/0305-4470/30/10/032
State	Published - 21 May 1997

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy (all)

Access to Document

10.1088/0305-4470/30/10/032

Cite this

@article{c3793f0dc348476fae345606b1f978ad,

title = "Localization in strongly chaotic systems",

abstract = "We discuss the differences and similarities in structure between Hamiltonian matrices of strongly chaotic time-independent systems and the evolution operator matrix for the kicked-rotor model. Since the eigenvectors of the latter are exponentially localized, we study the influence of the differences between the two systems on this property. In particular, the Wigner ensemble is used to show that, for ℏ → 0, the effect of the slow variation of the diagonal matrix elements in the Hamiltonian matrices is restricted to the tails of the eigenvectors.",

author = "Mario Feingold",

year = "1997",

month = may,

day = "21",

doi = "10.1088/0305-4470/30/10/032",

language = "English",

volume = "30",

pages = "3603--3612",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "10",

}

TY - JOUR

T1 - Localization in strongly chaotic systems

AU - Feingold, Mario

PY - 1997/5/21

Y1 - 1997/5/21

N2 - We discuss the differences and similarities in structure between Hamiltonian matrices of strongly chaotic time-independent systems and the evolution operator matrix for the kicked-rotor model. Since the eigenvectors of the latter are exponentially localized, we study the influence of the differences between the two systems on this property. In particular, the Wigner ensemble is used to show that, for ℏ → 0, the effect of the slow variation of the diagonal matrix elements in the Hamiltonian matrices is restricted to the tails of the eigenvectors.

AB - We discuss the differences and similarities in structure between Hamiltonian matrices of strongly chaotic time-independent systems and the evolution operator matrix for the kicked-rotor model. Since the eigenvectors of the latter are exponentially localized, we study the influence of the differences between the two systems on this property. In particular, the Wigner ensemble is used to show that, for ℏ → 0, the effect of the slow variation of the diagonal matrix elements in the Hamiltonian matrices is restricted to the tails of the eigenvectors.

UR - http://www.scopus.com/inward/record.url?scp=0031582350&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/30/10/032

DO - 10.1088/0305-4470/30/10/032

M3 - Article

AN - SCOPUS:0031582350

SN - 1751-8113

VL - 30

SP - 3603

EP - 3612

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 10

ER -

Localization in strongly chaotic systems

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this