Abstract
The quantum eigenstates and eigenvalues on a toroidal two dimensional phase-space are studied. To each eigenfunction is associated an integer, the Chern index, which tests the localization of the eigenfunction as some periodicity conditions are changed. The Chern index is a topological invariant which can only change when a spectral degeneracy occurs. These topological numbers are computed for three different models: two having an underlying regular dynamics, the third-one having a chaotic dynamics. The role played by the separatrix-states, the effects of quantum tunneling (symmetry effects) and of a classically chaotic dynamics in the spectrum of the Chern indices are discussed. The values taken by those indices are interpreted in terms of a phase-space distribution function. (author) 13 refs.; 12 figs.
Citation Formats
Faure, F, and Leboeuf, P.
Structure of wave functions on the torus characterized by a topological Chern index.
France: N. p.,
1992.
Web.
Faure, F, & Leboeuf, P.
Structure of wave functions on the torus characterized by a topological Chern index.
France.
Faure, F, and Leboeuf, P.
1992.
"Structure of wave functions on the torus characterized by a topological Chern index."
France.
@misc{etde_10111434,
title = {Structure of wave functions on the torus characterized by a topological Chern index}
author = {Faure, F, and Leboeuf, P}
abstractNote = {The quantum eigenstates and eigenvalues on a toroidal two dimensional phase-space are studied. To each eigenfunction is associated an integer, the Chern index, which tests the localization of the eigenfunction as some periodicity conditions are changed. The Chern index is a topological invariant which can only change when a spectral degeneracy occurs. These topological numbers are computed for three different models: two having an underlying regular dynamics, the third-one having a chaotic dynamics. The role played by the separatrix-states, the effects of quantum tunneling (symmetry effects) and of a classically chaotic dynamics in the spectrum of the Chern indices are discussed. The values taken by those indices are interpreted in terms of a phase-space distribution function. (author) 13 refs.; 12 figs.}
place = {France}
year = {1992}
month = {Oct}
}
title = {Structure of wave functions on the torus characterized by a topological Chern index}
author = {Faure, F, and Leboeuf, P}
abstractNote = {The quantum eigenstates and eigenvalues on a toroidal two dimensional phase-space are studied. To each eigenfunction is associated an integer, the Chern index, which tests the localization of the eigenfunction as some periodicity conditions are changed. The Chern index is a topological invariant which can only change when a spectral degeneracy occurs. These topological numbers are computed for three different models: two having an underlying regular dynamics, the third-one having a chaotic dynamics. The role played by the separatrix-states, the effects of quantum tunneling (symmetry effects) and of a classically chaotic dynamics in the spectrum of the Chern indices are discussed. The values taken by those indices are interpreted in terms of a phase-space distribution function. (author) 13 refs.; 12 figs.}
place = {France}
year = {1992}
month = {Oct}
}