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

Communications in Theoretical Physics

Non-Abelian Induced Topological Action for Slowly Changing Quantum System and Non-Adiabatic Corrections

Chang-Pu Sun, Lei Wang

Published Jun 1, 1991• 1 citation
Publisher

Abstract

The induced topological action relevant to the non-Abelian Berry's phase factor (NABPF) is derived by combining the high-order adiabatic approximation (HOAA) method with Kuratsuji and Iida's adiabatic path integral formulation. The non-adiabatic corrections for the transition amplitude are thereby obtained and the corresponding graphic representations are defined for convenience in the calculation. The gauge invariant properties and the dynamical implications of the non-Abelian induced topological action are also analyzed in detail. Finally, some explicit calculations for a model of physics are carried out as examples.

DOI
10.1088/0253-6102/15/4/427

Related papers

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

High-order adiabatic approximations related to non-Abelian Berry's phase factors and nuclear quadrupole resonance

Chang-Pu Sun

A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 15, 1990•35 citations

HIGH-ORDER ADIABATIC APPROXIMATIONS FOR EVOLUTION OF DEGENERATE QUANTUM MECHANICAL SYSTEM AND NON-ABELIAN INDUCED GAUGE STRUCTURE

Chen Sun

In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry. We not only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure, but also point out the non-adiabatic corrections resulting from higher-order approximations. With nuclear quadrupole resonance as an explicit example, we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.

Chinese Physics C•Jan 1, 1990•0 citations

High-order adiabatic approximation for non-Hermitian quantum system and complexification of Berry's phase

Chang-Pu Sun

In this paper the evolution of a quantum system driven by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation (HOAA) method with Berry's phase, which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized force harmonic oscillator is discussed as an illustrative example.

arXiv:hep-th/9304165•Physica Scripta•Oct 1, 1993•47 citations

High-order quantum berry's adiabatic phase and its observable effect

Sun Changpu

New high-order adiabatic approximate method is proposed for the study of non-adiabatic evolution of a quantum system with slowly-changing Hamiltonian. The corresponding high-order Berry's adiabatic phases are used to describe the transition from a state to another, and their observable effects in quantum interference experiment are pointed out.

Chinese Physics Letters•Mar 1, 1989•5 citations

Adiabatic Approximation for Path Integrals and Geometrical Potentials

Takashi Ohnishi, Naoto Nagaosa

Geometrical concepts have played an important role in quantum mechanics. In the Schrodinger representation, the Berry–Simon connection and the quantum geometric tensor appear as gauge potentials in the effective Hamiltonian for a heavy system under the Born–Oppenheimer approximation. On the other hand, the Berry phase should arise as the amplitude of each path in the pathintegral formalism. In their pioneering work, Kuratsuji and Iida have developed the treatment of the Born– Oppenheimer approximation in the path integral quantization, where the Berry phase of the light system naturally appears in the effective action for the heavy system. However, they did not derive the gauge potentials themselves in the effective Hamiltonian. In this short note, we show that the gauge potentials which relate to the geometry of the Hilbert space of the light system are also derived in the adiabatic scheme of path integrals. Our result presents the path-integral formalism to consider the effective dynamics of the heavy system under the adiabatic approximation. Let us consider the following Hamiltonian:

Journal of the Physical Society of Japan•Dec 25, 2006•2 citations
The induced topological action relevant to the non-Abelian Berry's phase factor (NABPF) is derived by combining the high-order adiabatic approximation (HOAA) method with Kuratsuji and Iida's adiabatic path integral formulation. The non-adiabatic corrections for the transition amplitude are thereby obtained and the corresponding graphic representations are defined for convenience in the calculation. The gauge invariant properties and the dynamical implications of the non-Abelian induced topological action are also analyzed in detail. Finally, some explicit calculations for a model of physics are carried out as examples.
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.
A high-order adiabatic-approximation method is proposed to study the time evolution of degenerate quantum-mechanical systems with slowly changing Hamiltonians. We not only discuss the quantum adiabatic theorem, induced gauge structure, and non-Abelian Berry's phase factors in the first-order approximation, but we also give nonadiabatic corrections for problems in the second-order approximation. With the nuclear quadrupole resonance as an explicit example, we analyze the above-mentioned questions in detail and point out the observable effects of non-Abelian Berry's phase factors for nonadiabatic transitions between two instantaneous states in an improvement of Tycko's experiment.
In this paper high-order adiabatic approximate method is proposed to study the evolution of degenerate quantum systums with slowly-changing parameters and varying symmetry. We not only prove the quantum adiabatic theorem for degenerate cases and discuss the corresponding non-abelian induced gauge structure, but also point out the non-adiabatic corrections resulting from higher-order approximations. With nuclear quadrupole resonance as an explicit example, we use this method to analyse observable effects of non-abelian Berry's phases in adiabatic and non-adiabatic experimental process.
In this paper the evolution of a quantum system driven by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation (HOAA) method with Berry's phase, which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized force harmonic oscillator is discussed as an illustrative example.
Geometrical concepts have played an important role in quantum mechanics. In the Schrodinger representation, the Berry–Simon connection and the quantum geometric tensor appear as gauge potentials in the effective Hamiltonian for a heavy system under the Born–Oppenheimer approximation. On the other hand, the Berry phase should arise as the amplitude of each path in the pathintegral formalism. In their pioneering work, Kuratsuji and Iida have developed the treatment of the Born– Oppenheimer approximation in the path integral quantization, where the Berry phase of the light system naturally appears in the effective action for the heavy system. However, they did not derive the gauge potentials themselves in the effective Hamiltonian. In this short note, we show that the gauge potentials which relate to the geometry of the Hilbert space of the light system are also derived in the adiabatic scheme of path integrals. Our result presents the path-integral formalism to consider the effective dynamics of the heavy system under the adiabatic approximation. Let us consider the following Hamiltonian: