Energy spectrum and eigenfunctions through the Quantum Section Method

Ortiz, J. S. Espinoza; Carvalho, R. Egydio de

doi:10.1590/s0103-97332001000400003

Cited by 3 publications

(2 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) is to perform a coordinate transformation through a Fourier expansion, following Refs. [14][15][16], changing the reference frame to the origin of the inner circle. Thus the even and the odd solutions of the two-dimensional wave equation in polar coordinates ͑r , ͒ referred to the origin O ( Fig.…”

Section: Quantizationmentioning

confidence: 99%

Fluctuations of doublet splittings using the annular billiard

Carvalho

Mijolaro

2004

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

We study the statistical distribution of quantum energy splittings due to a dynamical tunneling. The system, the annular billiard, has whispering quasimodes due to a discrete symmetry that exists even when chaos is present in the underlying classical dynamics. Symmetric and antisymmetric combinations of these quasimodes correspond to quantum doublet states whose degeneracies decrease as the circles become more eccentric. We construct numerical ensembles composed of splittings for two distinct regimes, one which we call semiclassical for high quantum numbers and high energies where the whispering regions are connected by chaos, and other which we call quantal for low quantum numbers, low energies, and near integrable where dynamical tunneling is not a dominant mechanism. In both cases we observe a variation on the fluctuation amplitudes, but their mean behaviors follow the formula of Leyvraz and Ullmo [J. Phys. A 29, 2529 (1996)]. A description of a three-level collision involving a doublet and a singlet is also provided through a numerical example.

show abstract

Section: Quantizationmentioning

confidence: 99%

Fluctuations of doublet splittings using the annular billiard

Carvalho

Mijolaro

2004

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…Hard-wall billiards are among the simplest and most studied systems in the field of classical and quantum chaos [1][2][3][4][5]. A two-dimensional quantum billiard is analogous to a vibrating membrane because of the mathematical equivalence of the stationary Schrödinger and Helmholtz equation with the same Dirichlet boundary conditions.…”

Section: Introductionmentioning

confidence: 99%