Localization of eigenfunctions in the stadium billiard
| Autor: | M. R. Haggerty, W. E. Bies, Lev Kaplan, Eric J. Heller |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Physics
Local density of states FOS: Physical sciences Eigenfunction Nonlinear Sciences - Chaotic Dynamics Space (mathematics) 01 natural sciences Quantum chaos 010305 fluids & plasmas Nonlinear Sciences::Chaotic Dynamics Classical mechanics Phase space Quantum mechanics 0103 physical sciences Homogeneous space Chaotic Dynamics (nlin.CD) Dynamical billiards 010306 general physics Random phase approximation |
| Zdroj: | Physical Review E. 63 |
| ISSN: | 1095-3787 1063-651X |
| DOI: | 10.1103/physreve.63.066214 |
| Popis: | We present a systematic survey of scarring and symmetry effects in the stadium billiard. The localization of individual eigenfunctions in Husimi phase space is studied first, and it is demonstrated that on average there is more localization than can be accounted for on the basis of random-matrix theory, even after removal of bouncing-ball states and visible scars. A major point of the paper is that symmetry considerations, including parity and time-reversal symmetries, enter to influence the total amount of localization. The properties of the local density of states spectrum are also investigated, as a function of phase space location. Aside from the bouncing-ball region of phase space, excess localization of the spectrum is found on short periodic orbits and along certain symmetry-related lines; the origin of all these sources of localization is discussed quantitatively and comparison is made with analytical predictions. Scarring is observed to be present in all the energy ranges considered. In light of these results the excess localization in individual eigenstates is interpreted as being primarily due to symmetry effects; another source of excess localization, scarring by multiple unstable periodic orbits, is smaller by a factor of $\sqrt{\hbar}$. Comment: 31 pages, including 10 figures |
| Databáze: | OpenAIRE |
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