aqora

27p-ED-1 Berry's Phase and Fractional Quantization of Adiabatic Motion

晋司飯田, 比呂志倉辻

年会講演予稿集Mar 27, 19870 citations

Hannay's Angle and Berry's Phase in the Classical Adiabatic Motion of Charged Particlesa

Robert G. Littlejohn

Annals of the New York Academy of SciencesAug 1, 19880 citations

On the Extra Phase Accompanying Berry's Phase in Terms of Coherent State Path Integral

Takahiro Fukui

In the WKB approximation for coupled channel equations, it has been pointed out by Yabana and Horiuchi that the semi-classical quantization condition should be modified by Berry's phase and another extra phase. Recently Littlejohn and Flynn have rederived them in a quite elegant way. We concentrate on this extra phase in this paper, and derive it for a simple model by means of the path integral method in the generalized coherent state representation. It is shown that it appears as a quantum fluctuation around classical orbits.In the WKB approximation for coupled channel equations, it has been pointed out by Yabana and Horiuchi that the semi-classical quantization condition should be modified by Berry's phase and another extra phase. Recently Littlejohn and Flynn have rederived them in a quite elegant way. We concentrate on this extra phase in this paper, and derive it for a simple model by means of the path integral method in the generalized coherent state representation. It is shown that it appears as a quantum fluctuation around classical orbits.

Progress of Theoretical PhysicsApr 1, 19927 citations

Non-adiabatic Berry's phase in many-body and high-dimensional system

Zhi-Ming Bai, Guangzhou Chen, Mo‐Lin Ge

Physics Letters ANov 1, 19992 citations

Berry's Phase in the Presence of a Non-adiabatic Environment with an Application to Magnetic Resonance

Frank Gaitan

Journal of Magnetic ResonanceJul 1, 199916 citations

A quasi-static treatment of multiple phase jumps

R. Englman, Tamás Vértesi

A quasi-static, WKB-type treatment accounts well for the surprising phase jumps that are odd multiples of π, (1 + 2 n )π, found as a molecular system journeys adiabatically in a configuration coordinate plane that contains several points of degeneracies. We show that the number n in the phase jump is an integer close to | n '| that appears in the expression for the complex wavefunction amplitude valid (approximately) for times close to when the phase jump occurs: (δ T is a shifted and rescaled trajectory-time parameter and θ is a numerical fraction (<1) which depends on the adiabaticity of the motion.) The central quantity n ' is local, i.e., depends on the values of the parameters in the Hamiltonian only at the beginning of the trajectory and at the instant of the phase jump.A quasi-static, WKB-type treatment accounts well for the surprising phase jumps that are odd multiples of π, (1 + 2 n )π, found as a molecular system journeys adiabatically in a configuration coordinate plane that contains several points of degeneracies. We show that the number n in the phase jump is an integer close to | n '| that appears in the expression for the complex wavefunction amplitude valid (approximately) for times close to when the phase jump occurs: (δ T is a shifted and rescaled trajectory-time parameter and θ is a numerical fraction (<1) which depends on the adiabaticity of the motion.) The central quantity n ' is local, i.e., depends on the values of the parameters in the Hamiltonian only at the beginning of the trajectory and at the instant of the phase jump.

Journal of Physics B Atomic Molecular and Optical PhysicsJun 27, 200510 citations

Adiabatic Viewpoint for the WKB Treatment of Coupled Channel System: Appearance of the Berry Phase and Another Extra Phase Accompanying the Adiabatic Motion

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Adiabatic Viewpoint for the WKB Treatment of Coupled Channel System: Appearance of the Berry Phase and Another Extra Phase Accompanying the Adiabatic Motion

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