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

Physical Review A

Berry’s phase and effective action

Alex Kovner

Published Jul 1, 1989• 4 citations
Publisher

Abstract

It is shown that Berry's phase is equal to the integral of a symplectic 1-form of the effective action of a quantum theory along closed trajectory in the phase space, corresponding to configurations with cyclic evolution. In classical approximation this is just the Fp dq term in the classical action.
DOI
10.1103/physreva.40.545

Related papers

Berry’s phase and the symplectic character of quantum time evolution

John P. Ralston

General time-dependent, bilinear classical Lagrangian mechanics can be interpreted as a charged particle interacting with a gauge scalar and vector potential. For an arbitrary discrete number of degrees of freedom, there are enough symplectic symmetries in classical mechanics to make this system canonically identical to the most general discrete spectrum quantum system. It follows that the general invariance group of the Schr\"odinger system of equations is the symplectic group Sp(2N), not U(N). Several examples show the physical naturalness of the classical coordinates. In the adiabatic limit Berry's phase is identified as the cumulative change of the angle of action-angle coordinates of a normal mode. A generalization of Berry's phase, the time component of the adiabatic connection and its associated electric curvature, is shown to be on an equal footing with the usual Berry phase.

Physical Review A•Nov 1, 1989•14 citations

Berry phase in homogeneous Kähler manifolds with linear Hamiltonians

Luis J. Boya, A. M. Perelomov, Mariano Sant

We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X = G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of classical objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states. I.

•Sep 14, 2013•13 citations

Berry phase in homogeneous Kähler manifolds with linear Hamiltonians

Luis J. Boya, Askold M. Perelomov, Mariano Santander

We study the total [dynamical plus geometrical (Berry)] phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of classical objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.

arXiv:math-ph/0111022•Journal of Mathematical Physics•Nov 1, 2001•17 citations

Integrability of the quantum adiabatic evolution and geometric phases

Gianni Cassinelli, Ernesto De Vito, Alberto Levrero

We show that the cyclic adiabatic evolution of a quantum system is completely integrable as a classical Hamiltonian system. In this context the Berry phases arise naturally as cohomology of the invariant tori.

Journal of Mathematical Physics•Dec 1, 1997•2 citations

TOPOLOGICAL ACTION RELATING TO BERRY'S PHASE AND NON-ADIABATIC EFFECTS

Chen Sun

In non-adiabatic cases the topological action associated with Berry's phase and the corresponding effective Hamiltonian are obtained by path-integral method. We also give the non-adiabatic transition probability amplitude in the first-order approximation. It is thereby shown that the Berry's phase and the induced gauge structure have universality of existence. As an example, dynamics of induced monople relating to the Bitter-Dubber's experiment is analysed in terms of induced gauge field.

Chinese Physics C•Jan 1, 1990•0 citations

Quantum particle trajectories and geometric phase

Mihai Octavian Dima

Particle trajectories are defined as integrable dx μ dp μ =0 paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalize in ( x, p ) projection, the phase associated with the trajectories related to the geometric (Berry) phase and the classical mechanics action. Properties at high energies of the states evolving on particle trajectories are discussed.

arXiv:quant-ph/9912045•Journal of Experimental and Theoretical Physics Letters•Dec 1, 2000•3 citations
General time-dependent, bilinear classical Lagrangian mechanics can be interpreted as a charged particle interacting with a gauge scalar and vector potential. For an arbitrary discrete number of degrees of freedom, there are enough symplectic symmetries in classical mechanics to make this system canonically identical to the most general discrete spectrum quantum system. It follows that the general invariance group of the Schr\"odinger system of equations is the symplectic group Sp(2N), not U(N). Several examples show the physical naturalness of the classical coordinates. In the adiabatic limit Berry's phase is identified as the cumulative change of the angle of action-angle coordinates of a normal mode. A generalization of Berry's phase, the time component of the adiabatic connection and its associated electric curvature, is shown to be on an equal footing with the usual Berry phase.
We study the total (dynamical plus geometrical (Berry)) phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X = G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of classical objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states. I.
We study the total [dynamical plus geometrical (Berry)] phase of cyclic quantum motion for coherent states over homogeneous Kähler manifolds X=G/H, which can be considered as the phase spaces of classical systems and which are, in particular cases, coadjoint orbits of some Lie groups G. When the Hamiltonian is linear in the generators of a Lie group, both phases can be calculated exactly in terms of classical objects. In particular, the geometric phase is given by the symplectic area enclosed by the (purely classical) motion in the space of coherent states.
In non-adiabatic cases the topological action associated with Berry's phase and the corresponding effective Hamiltonian are obtained by path-integral method. We also give the non-adiabatic transition probability amplitude in the first-order approximation. It is thereby shown that the Berry's phase and the induced gauge structure have universality of existence. As an example, dynamics of induced monople relating to the Bitter-Dubber's experiment is analysed in terms of induced gauge field.