Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physica D Nonlinear Phenomena

Comparison of quantal, classical, and semiclassical behavior at an isolated avoided crossing

D.W. Noid

Published Jun 1, 1985• 0 citations
Publisher
DOI
10.1016/0167-2789(85)90077-6

Related papers

Semiclassical study of avoided crossings

利也 高見

•Jan 1, 1995•0 citations

Comparison of quantal, classical, and semiclassical behavior at an isolated avoided crossing

D. W. Noid, Michael L. Koszykowski, R. A. Marcus

The quantal and classical/semiclassical behavior at an isloated avoided crossing are compared. While the quantum mechanical eigenvalue perturbation parameter plots exhibit the avoided crossing, the corresponding primitive semiclassical eigenvalue plots pass through the intersection. Otherwise, the eigenvalues agree well with the quantum mechanical values. The semiclassical splitting at the intersection is calculated from an appropriate Fourier transform. In the quasiperiodic regime, a quantum state near an avoided crossing is seen to exhibit typically more delocalization than the classical state. However, trajectories near the ‘‘separatrix’’ display a quasiperiodic ‘‘transition’’ between two zeroth order classical states.

The Journal of Chemical Physics•Mar 15, 1983•72 citations

Semiclassical Dynamics and Relaxation

Springer eBooks•Dec 19, 2007•1 citation

Semiclassical behavior at a quantum avoided crossing

Marc Joyeux

For a polynomial potential with resonant fundamental frequencies (1:2 and 1:3 resonances), quantum avoided crossings can occur when quantum eigenvalues are plotted versus a parameter in the Hamiltonian. In the present paper, primitive (EBK) semiclassical behavior at the quantum avoided crossing is reinvestigated, using the exact analytical calculation of the action integrals, which was devised recently [Chem. Phys. 185, 263 (1994)] for an approximate resonance Hamiltonian that can be deduced from the exact polynomial Hamiltonian by low order perturbation theory. The previously reported behavior, that is semiclassical levels passing through the intersection instead of avoiding each other, is shown to happen if there exist two superimposed branches in the plot of the second action integral ℐ2 as a function of the energy. These results are interpreted in terms of semiclassical diabatic basis and of quantum dynamical tunneling. In contrast, if the semiclassical system enters the (anti)crossing region with semiclassical quantum numbers ℐ2 which do not lie on superimposed branches of the plot, it is shown that at least one, and possibly two, level(s) must cross the separatrix, that is pass from the inside to the outside of the resonance region (or conversely) in order to adapt to the quantum avoided crossing. This causes (i) corresponding semiclassical quantum number ℐ2 to change (ii) the close correspondence between quantum and semiclassical mechanics to break down.

The Journal of Chemical Physics•Feb 15, 1995•7 citations

Classical behavior from a fully quantum mechanical description

Michael Brieger

•Jan 1, 2002•0 citations

Behavior of the Hamiltonian's Eigenstates Around the Avoided Level Crossing

Quan-Lin Jie, Gong-ou Xu, Wen-ge Wang

We numerically show the changing of eigenstates of the Hamiltonian as a function of a control parameter governing the strength of a non-integrable perturbation. The eigenstates change abruptly at avoided level crossing. After the avoided level crossing, they tend to restore their original form before the avoided level crossing, and exchange their distribution, especially for those which can he treated as isolated two-body collisions. But in general, the eigenstates have some changings after the avoided crossing, and the symmetries of the system are broken down locally at this kind of avoided level crossings.

Communications in Theoretical Physics•Jan 30, 1997•1 citation
The quantal and classical/semiclassical behavior at an isloated avoided crossing are compared. While the quantum mechanical eigenvalue perturbation parameter plots exhibit the avoided crossing, the corresponding primitive semiclassical eigenvalue plots pass through the intersection. Otherwise, the eigenvalues agree well with the quantum mechanical values. The semiclassical splitting at the intersection is calculated from an appropriate Fourier transform. In the quasiperiodic regime, a quantum state near an avoided crossing is seen to exhibit typically more delocalization than the classical state. However, trajectories near the ‘‘separatrix’’ display a quasiperiodic ‘‘transition’’ between two zeroth order classical states.
For a polynomial potential with resonant fundamental frequencies (1:2 and 1:3 resonances), quantum avoided crossings can occur when quantum eigenvalues are plotted versus a parameter in the Hamiltonian. In the present paper, primitive (EBK) semiclassical behavior at the quantum avoided crossing is reinvestigated, using the exact analytical calculation of the action integrals, which was devised recently [Chem. Phys. 185, 263 (1994)] for an approximate resonance Hamiltonian that can be deduced from the exact polynomial Hamiltonian by low order perturbation theory. The previously reported behavior, that is semiclassical levels passing through the intersection instead of avoiding each other, is shown to happen if there exist two superimposed branches in the plot of the second action integral ℐ2 as a function of the energy. These results are interpreted in terms of semiclassical diabatic basis and of quantum dynamical tunneling. In contrast, if the semiclassical system enters the (anti)crossing region with semiclassical quantum numbers ℐ2 which do not lie on superimposed branches of the plot, it is shown that at least one, and possibly two, level(s) must cross the separatrix, that is pass from the inside to the outside of the resonance region (or conversely) in order to adapt to the quantum avoided crossing. This causes (i) corresponding semiclassical quantum number ℐ2 to change (ii) the close correspondence between quantum and semiclassical mechanics to break down.
We numerically show the changing of eigenstates of the Hamiltonian as a function of a control parameter governing the strength of a non-integrable perturbation. The eigenstates change abruptly at avoided level crossing. After the avoided level crossing, they tend to restore their original form before the avoided level crossing, and exchange their distribution, especially for those which can he treated as isolated two-body collisions. But in general, the eigenstates have some changings after the avoided crossing, and the symmetries of the system are broken down locally at this kind of avoided level crossings.