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

International Journal of Theoretical Physics

Geometric Phases for Wave Packets of the Landau Problem

Mohamed Nazih Rhimi, R. El-Bahi

Published Sep 18, 2007• 4 citations
Publisher
DOI
10.1007/s10773-007-9538-4

Related papers

Geometric phases for wave packets in a uniform magnetic field

Qiong-Gui Lin

arXiv:quant-ph/0206036•Physics Letters A•Jun 1, 2002•5 citations

Geometric Phase Effects for Wave-Packet Revivals

Christopher Jarzynski

The study of wave-packet revivals is extended to the case of Hamiltonians which are made time dependent through the adiabatic cycling of some parameters. It is shown that the quantal geometric phase (Berry's phase) causes the revived packet to be displaced along the classical trajectory by an amount equal to the classical geometric phase (Hannay's angle), in one degree of freedom. A physical example illustrating this effect in three degrees of freedom is mentioned.

arXiv:solv-int/9501009•Physical Review Letters•Feb 20, 1995•16 citations

On Geometric Phases for Quantum Trajectories

Erik Sjöqvist

arXiv:quant-ph/0608237•Acta Physica Hungarica A) Heavy Ion Physics•Nov 1, 2006•11 citations

All-optical imprinting of geometric phases onto matter waves

Qi Zhang, Jiangbin Gong, C. H. Oh

Traditional optical phase imprinting of matter waves is of a dynamical nature. Here we show that both Abelian and non-Abelian geometric phases can be optically imprinted onto matter waves, yielding a number of interesting phenomena such as wave-packet redirecting and wave-packet splitting. In addition to their fundamental interest, our results open up opportunities for robust optical control of matter waves.

arXiv:0904.0310•Physical Review A•Apr 28, 2009•5 citations

Symplectic semiclassical wave packet dynamics

Tomoki Ohsawa, Melvin Boon-tiong Leok

The paper gives a symplectic-geometric account of semiclassical Gaussian wave packet dynamics. We employ geometric techniques to ‘strip away’ the symplectic structure behind the time-dependent Schrödinger equation and incorporate it into semiclassical wave packet dynamics. We show that the Gaussian wave packet dynamics is a Hamiltonian system with respect to the symplectic structure, apply the theory of symplectic reduction and reconstruction to the dynamics, and discuss dynamic and geometric phases in semiclassical mechanics. A simple harmonic oscillator example is worked out to illustrate the results. We show that the reduced semiclassical harmonic oscillator dynamics is completely integrable by finding the action–angle coordinates for the system, and calculate the associated dynamic and geometric phases explicitly. We also propose an asymptotic approximation of the potential term that provides a practical semiclassical correction term to the approximation by Heller. Numerical results for a simple one-dimensional example show that the semiclassical correction term realizes a semiclassical tunneling.

arXiv:1302.1139•Journal of Physics A Mathematical and Theoretical•Sep 19, 2013•31 citations

A resolution of the classical wave-particle problem

James Paul Wesley

Foundations of Physics•Feb 1, 1984•11 citations
The paper gives a symplectic-geometric account of semiclassical Gaussian wave packet dynamics. We employ geometric techniques to ‘strip away’ the symplectic structure behind the time-dependent Schrödinger equation and incorporate it into semiclassical wave packet dynamics. We show that the Gaussian wave packet dynamics is a Hamiltonian system with respect to the symplectic structure, apply the theory of symplectic reduction and reconstruction to the dynamics, and discuss dynamic and geometric phases in semiclassical mechanics. A simple harmonic oscillator example is worked out to illustrate the results. We show that the reduced semiclassical harmonic oscillator dynamics is completely integrable by finding the action–angle coordinates for the system, and calculate the associated dynamic and geometric phases explicitly. We also propose an asymptotic approximation of the potential term that provides a practical semiclassical correction term to the approximation by Heller. Numerical results for a simple one-dimensional example show that the semiclassical correction term realizes a semiclassical tunneling.