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

Journal of Sichuan University

Study on the relation between two types of gauge solutions of a spin clusterin a time-dependent magnetic field

Song Yuan

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

The coordinate rotation method is applied to investigate the relation between two types of gauge analytical solutions for a su(2) algebraically symmetric spin cluster.We consider an annular 3- spin -r- chain with partially anisotropic coupling.It is found that the analytical solutions related to single -gauge transformation can be obtained from those related to double-gauge transformation.The geometric phase of the every basic analytical solution from single-gauge transformation is calculated,and the geometric phaseπis found.Ifλ=(π/2) in double-gauge transformation,the value of geometric phase obtained here is the same as that of every basic analytical solution from double-gauge transformation.

Related papers

Geometric phase of a Heisenberg-chain in a rotating magnetic field

Song Yuan

The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain in a rotating magnetic field.It is a su(2) algebraically symmetric 3-spin12 system with partially anisotropic coupling.The exact analytical solution of the time dependent Schrdinger equation and the geometric phases of this system are obtained in terms of gauge transformation and algebriaic dynamics.The partially anisotropic coupling is then extended to a more general coupling and the adiabatic geometric phases of the extended system are calculated.We find that the coupling strengths have no impact on the adiabatic geometric phases of the system.

Journal of Sichuan University•Jan 1, 2008•0 citations

Geometric Phase of a Heisenberg-chain

Xiaoyan Deng

Objective The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain,in order to find out how the coulping strengths between spins influence the geometric phase of this system.Method An interacting anisotropic 3-spin 1/2 system,which is driven by a rotating magnetic field,is considered.The system has a su(2) algebraic structure.By an unitary gauge transformation,this nonautonomous system becomes an autonomous system.The Schrodinger equation of the autonomous system is solved.By virtue of the inverse transformation of the original gauge transformation,the exact analytical solution to the time dependent Schrodinger equation is obtained in total spin 1/2 subspace.Resutlt The geometric phases in this subspace are calculated.Conclusion The result shows that(i)Coulping strengths don't influence the geometric phases of this system;(ii) The geometric phases of the system is the same as that of one spin 1/2 system in a rotating magnetic field.

Journal of Hebei North University•Jan 1, 2008•0 citations

Algebraic dynamic study of geometric phase for a homonuclear linear spincluster

X -X Chen, J Xue

A homonuclear linear [Formula: see text] coupling spin cluster with the middle particle driven by an external time-dependent magnetic field is investigated by using the method of algebraic dynamics. The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the external magnetic-field parameter θ (the angle between the magnetic field and the Z axis) and the effective coupling strength Jn. Based on the relation, how the geometric phase depends on the coupling strength Jn in different reducible subspace is discussed.PACS Nos.: 33.20.Wr, 03.65.Fd, 03.65.Vf

Canadian Journal of Physics•Jul 1, 2007•0 citations

Single qubit and its universal logic gate made of an annular spin cluster with anisotropic Heisenberg-chain

Xiao-Bo Yan, Shun-Jin Wang, (1)四川大学物理系,成都 610064; (2)四川大学物理系,成都 610064;兰州重离子加速器国家实验室,兰州 730000

We investigate an annular spin cluster made of three particles with anisotropic Heisenberg-chain controlled by a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, we have obtained the exact analytical solution to the time dependent Schrdinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and consequently six special single qubit logic gates can be realized.

Acta Physica Sinica•Jan 1, 2006•11 citations

The non-relativistic problem for a spin 3/2 particle in magnetic field, and tetrad gauge transformations

A. M. Kuzmich, A. V. Ivashkevich, Viktor M. Red'kov

In the present paper, we will focus on the non-relativistic problem for a spin 3/2 particle in magnetic field, applying cylindrical coordinates and two tetrads: Cartesian and cylindrical. Here appear six different presentations for 4-component wave functions: three Cartesian ones L cart Ψ cart ,Ψ cart and provided by using the relevant gauge transformation L cyl = S (φ) L cart three different presentations in cylindrical tetrad L cyl Ψ cyl ,Ψ cyl First, we specify the non-relativistic equation for a spin 3/2 particle in magnetic field for Cartesian tetrad in bases with non-diagonal and diagonal matrix of the third spin projection. Solutions of two types are found: the first one is associated with the operator of the orbital angular momentum; the second solution relates to the third projection of the total angular momentum. Equations arising here are solved in terms of the confluent hypergeometric functions, and the corresponding energy spectra are found. The gauge transformation is introduced which relates two tetrads: Cartesian and cylindrical; it permits us to transform the system of equations in polar coordinate from Cartesian tetrad to cylindrical one. The rules for gauge transformations of diagonalized operators of the total angular and orbital momentums are found.

Proceedings of the National Academy of Sciences of Belarus Physics and Mathematics Series•Mar 31, 2026•0 citations

The geometric phase of the quantum systems with slow but finite rate of the external time-dependent field

Jia Xin-Yan, Weidong Li, Liang Jiu-Qing

With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.

Chinese Physics•Oct 1, 2007•1 citation
The coordinate rotation method is applied to investigate the relation between two types of gauge analytical solutions for a su(2) algebraically symmetric spin cluster.We consider an annular 3- spin -r- chain with partially anisotropic coupling.It is found that the analytical solutions related to single -gauge transformation can be obtained from those related to double-gauge transformation.The geometric phase of the every basic analytical solution from single-gauge transformation is calculated,and the geometric phaseπis found.Ifλ=(π/2) in double-gauge transformation,the value of geometric phase obtained here is the same as that of every basic analytical solution from double-gauge transformation.
The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain in a rotating magnetic field.It is a su(2) algebraically symmetric 3-spin12 system with partially anisotropic coupling.The exact analytical solution of the time dependent Schrdinger equation and the geometric phases of this system are obtained in terms of gauge transformation and algebriaic dynamics.The partially anisotropic coupling is then extended to a more general coupling and the adiabatic geometric phases of the extended system are calculated.We find that the coupling strengths have no impact on the adiabatic geometric phases of the system.
Objective The algebriaic dynamics is applied to investigate the geometric phase of a Heisenberg-chain,in order to find out how the coulping strengths between spins influence the geometric phase of this system.Method An interacting anisotropic 3-spin 1/2 system,which is driven by a rotating magnetic field,is considered.The system has a su(2) algebraic structure.By an unitary gauge transformation,this nonautonomous system becomes an autonomous system.The Schrodinger equation of the autonomous system is solved.By virtue of the inverse transformation of the original gauge transformation,the exact analytical solution to the time dependent Schrodinger equation is obtained in total spin 1/2 subspace.Resutlt The geometric phases in this subspace are calculated.Conclusion The result shows that(i)Coulping strengths don't influence the geometric phases of this system;(ii) The geometric phases of the system is the same as that of one spin 1/2 system in a rotating magnetic field.
A homonuclear linear [Formula: see text] coupling spin cluster with the middle particle driven by an external time-dependent magnetic field is investigated by using the method of algebraic dynamics. The exact analytical solutions of the time-dependent Schrodinger equation of the spin cluster system are derived and employed to study the geometric phase. An alternative expression of the geometric phase in each eigenstate is obtained. It is shown that the geometric phase is related to the external magnetic-field parameter θ (the angle between the magnetic field and the Z axis) and the effective coupling strength Jn. Based on the relation, how the geometric phase depends on the coupling strength Jn in different reducible subspace is discussed.PACS Nos.: 33.20.Wr, 03.65.Fd, 03.65.Vf
We investigate an annular spin cluster made of three particles with anisotropic Heisenberg-chain controlled by a time-dependent magnetic field. The system has an SU(2) algebraic structure. Using algebraic dynamical method, we have obtained the exact analytical solution to the time dependent Schrdinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and consequently six special single qubit logic gates can be realized.
In the present paper, we will focus on the non-relativistic problem for a spin 3/2 particle in magnetic field, applying cylindrical coordinates and two tetrads: Cartesian and cylindrical. Here appear six different presentations for 4-component wave functions: three Cartesian ones L cart Ψ cart ,Ψ cart and provided by using the relevant gauge transformation L cyl = S (φ) L cart three different presentations in cylindrical tetrad L cyl Ψ cyl ,Ψ cyl First, we specify the non-relativistic equation for a spin 3/2 particle in magnetic field for Cartesian tetrad in bases with non-diagonal and diagonal matrix of the third spin projection. Solutions of two types are found: the first one is associated with the operator of the orbital angular momentum; the second solution relates to the third projection of the total angular momentum. Equations arising here are solved in terms of the confluent hypergeometric functions, and the corresponding energy spectra are found. The gauge transformation is introduced which relates two tetrads: Cartesian and cylindrical; it permits us to transform the system of equations in polar coordinate from Cartesian tetrad to cylindrical one. The rules for gauge transformations of diagonalized operators of the total angular and orbital momentums are found.
With the help of the time-dependent gauge transformation technique, we have studied the geometric phase of a spin-half particle in a rotating magnetic field. We have found that the slow but finite frequency of the rotating magnetic field will make the difference between the adiabatic geometric phase and the exact geometric phase. When the frequency is much smaller than the energy space and the adiabatic condition is perfectly guaranteed, the adiabatic approximation geometric phase is exactly consistent with the adiabatic geometric phase. A simple relation for the accuracy of the adiabatic approximation is given in terms of the changing rate of the frequency of the rotating magnetic field and the energy level space.