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

Chinese Physics C

A CLASSICAL MODLE OF QUANTUM BERRY'S PHASE FACTOR

Chen Sun

Published Jan 1, 1989• 0 citations
OpenAlex

Abstract

Considering that the classical evolution equations are similar to the Schrodinger eqaution, we point out that there is the structure of the Berry's Phase in the solution of a classical evolution eqaution with adiabatic changing parameters. Thus, we can use a classical evolution process to imitate the quantum adiabatic process. As an example, the motion of a charged particle in slowly-changing magnetic field is studied and the corresponding phase factor can be interpreted as a holomony of the fiber bundle on the sphare s~2 in the parameter space.

Related papers

Classical analogues of quantum berry's phase

Sun Changpu

With the classical generalized harmonic oscillator as an example, we show that the analogues of the quantum Berry's phase can appear in the classical mechanic systems with adiabatically-changing parameters, which have the Schrödinger-type evolution equations. The corresponding guage structures are naturally induced in these systems.

Chinese Physics Letters•Nov 1, 1989•5 citations

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

High-order quantum adiabatic approximation and Berry's phase factor

Chang-Pu Sun

In this paper high-order adiabatic approximate solutions of the Schrodinger equation for a quantum system with a slowly changing Hamiltonian are presented. The author not only obtains Berry's phase factor and strictly proves the quantum adiabatic theorem in the first-order approximation, but also discusses an observable effect of the second adiabatic approximation.

Journal of Physics A Mathematical and General•Apr 7, 1988•85 citations

QUASI-ADIABATIC APPROXIMATION FOR THE SLOWLYCHANGING QUANTUM PROCCESS AND BERRY PHASE FACTOR

Chen Sun

By using group representation theory, th quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper. We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation, but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated. It is pointed out that this universal Berry phase factor has observable effects.

Chinese Physics C•Jan 1, 1988•0 citations

Simulating two-level quantum systems via classical orbit motion: Adiabatic cyclic evolution and Berry phase

Shao-Wu Yao, Bo You, Li-Xiang Cen

We propose a method to simulate adiabatically driven two-level quantum systems and detect the Berry phase induced in the cyclic evolution by observing the classical orbit motion of a charged particle under a time-varying magnetic field. Analogy between the dynamics of these two species of systems is revealed and the correspondence relationship is established by virtue of their equations of motion, i.e., the von Neumman equation of the quantum binary system and the Newton-Lorentz equation of the charged particle. In particular, we show how the complex phase information of the quantum system, say, the Berry phase shift acquired by its wave function during the loop evolution, can be visually captured by examining the spatial motion of the classical particle.

Physical Review A•Feb 12, 2024•1 citation

Magnetic translation and Berry's phase factor through adiabatically rotating a magnetic field

J. Chee

For a spin subjected to an adiabatically changing magnetic field, the solid angle result as embodied by a rotation operator is the only path-dependent factor in the quantum evolution operator. For a charged particle, the infinite degeneracy calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a magnetic translation operator that is the path-dependent factor in the quantum evolution operator. This result agrees with the fact that the instantaneous hamiltonian is invariant under magnetic translation as well as rotation. Simple experimental verification is proposed.

•Jan 1, 2000•4 citations
Considering that the classical evolution equations are similar to the Schrodinger eqaution, we point out that there is the structure of the Berry's Phase in the solution of a classical evolution eqaution with adiabatic changing parameters. Thus, we can use a classical evolution process to imitate the quantum adiabatic process. As an example, the motion of a charged particle in slowly-changing magnetic field is studied and the corresponding phase factor can be interpreted as a holomony of the fiber bundle on the sphare s~2 in the parameter space.
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.
By using group representation theory, th quasi-adiabatic approximation solution of the schrodinger equation of a quantum system with slowly-changing Hamiltonian are presented in this paper. We not only obtained the Berry phase factor and strictly proved the quantum adiabatic theorem as the zeroth-order approximation, but also studied the universal Berry phase factor and its geometrical interpretation when the adiabatic condition is violated. It is pointed out that this universal Berry phase factor has observable effects.
We propose a method to simulate adiabatically driven two-level quantum systems and detect the Berry phase induced in the cyclic evolution by observing the classical orbit motion of a charged particle under a time-varying magnetic field. Analogy between the dynamics of these two species of systems is revealed and the correspondence relationship is established by virtue of their equations of motion, i.e., the von Neumman equation of the quantum binary system and the Newton-Lorentz equation of the charged particle. In particular, we show how the complex phase information of the quantum system, say, the Berry phase shift acquired by its wave function during the loop evolution, can be visually captured by examining the spatial motion of the classical particle.
For a spin subjected to an adiabatically changing magnetic field, the solid angle result as embodied by a rotation operator is the only path-dependent factor in the quantum evolution operator. For a charged particle, the infinite degeneracy calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a magnetic translation operator that is the path-dependent factor in the quantum evolution operator. This result agrees with the fact that the instantaneous hamiltonian is invariant under magnetic translation as well as rotation. Simple experimental verification is proposed.