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

Modern Physics Letters B

GEOMETRIC PHASE IN A GENERALIZED TIME-DEPENDENT GIANT SPIN MODEL

Anling Wang, Fuping Liu, Zhao-Xian Yu, Zhi-Yong Jiao

Published Sep 20, 2009• 0 citations
Publisher

Abstract

By using of the invariant theory, we have studied the generalized time-dependent giant spin model. The dynamical and geometric phases are given, respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.
DOI
10.1142/s021798490902093x

Related papers

Aharonov-Anandan geometric phase for spin-1/2 periodic Hamiltonians

David J. Fernández C., Luis Miguel Nieto, M. A. del Olmo +1 more

The authors calculate exactly the Aharonov-Anandan phase for the evolution of a spin-1/2 in some periodic time-dependent magnetic fields, and give a discussion of the results versus the adiabatic ones. In particular, they analyse the existence of cyclic states and show explicit examples of systems with a prescribed value of the AA phase for all cyclic evolutions.

Journal of Physics A Mathematical and General•Oct 7, 1992•57 citations

Exact Solution of the Bloch Equation with Time-Dependent Coefficients and Aharonov-Anandan Phase

Jing‐Bo Xu, Lan Wang, Xiao-Chun Gao

In this letter, the matrix invariant of the Bloch equation with time-dependent coefficients is found, the time evolution of the system is discussed and the exact solution of the system is obtained. We then proceed to study the cyclic evolution of the system, obtaining the Aharonov-Anandan phase. Finally, it is shown that the study of noncyclic evolution of the system can be reduced to the cyclic evolution.

Chinese Physics Letters•Mar 1, 1993•0 citations

Dynamical and Geometric Phases of a Two Energy-Level Bose–Einstein Condensate Interacting with a Laser Field

Zhao-Xian Yu, Jiao Zhi-Yong, Shuo Jin +1 more

By using of the invariant theory, we study a two energy-level Bose–Einstein condensate interacting with a time-dependent laser field, the dynamical and geometric phases are given respectively. The Aharonov–Anandan phase is also obtained under the cyclical evolution.

Chinese Physics Letters•Jan 18, 2007•1 citation

Quantum Phases of Pancharatnam Type for a General Spin in a Time-Dependent Magnetic Field

Zhao Yue-gang, Bo‐Zang Li

Based on the quantum invariant theory, the quantum phases, including the total phase as well as its dynamical and geometric parts, of Pancharatnam type are derived for a general spin in a time-dependent magnetic field, without the constraint of adiabatic, cyclic or unitary condition. The geometric meaning of geometric phase is expounded.

Chinese Physics Letters•Nov 1, 1997•6 citations

Invariants and geometric phase for systems with non-Hermitian time-dependent Hamiltonians

Xiao-Chun Gao, Jing-Bo Xu, Tiezheng Qian

In this paper, the Lewis-Riesenfeld invariant theory is generalized for the study of systems with non-Hermitian time-dependent Hamiltonians. It is then used to study the nonadiabatic cyclic evolution and the Aharonov-Anandan phase. It is shown that the study of noncyclic evolution can be reduced to the study of cyclic evolution. The two-level dissipative system and the classical time-dependent harmonic oscillator are discussed as illustrative examples.

Physical Review A•Oct 1, 1992•46 citations

Classification of cyclic initial states and geometric phase for the spin-j system

Nikolai R. Skrynnikov, Jin-Jian Zhou, B. C. Sanctuary

Quantum states which evolve cyclically in their projective Hilbert space give rise to a geometric (or Aharonov-Anandan) phase. An aspect of primary interest is stable cyclic behaviour as realized under a periodic Hamiltonian. The problem has been handled by use of time-dependent transformations treated along the lines of Floquet's theory as well as in terms of exponential operators with a goal to examine the variety of initial states exhibiting cyclic behaviour. A particular case of special cyclic initial states is described which is shown to be important for nuclear magnetic resonance experiments aimed at the study of the effects of the geometric phase. An example of arbitrary spin j in a precessing magnetic field and spin j=1 subject to both axially symmetric quadrupolar interaction and a precessing magnetic field are presented. The invariant (Kobe's) geometric phase is calculated for special cyclic states.

Journal of Physics A Mathematical and General•Sep 21, 1994•8 citations
Quantum states which evolve cyclically in their projective Hilbert space give rise to a geometric (or Aharonov-Anandan) phase. An aspect of primary interest is stable cyclic behaviour as realized under a periodic Hamiltonian. The problem has been handled by use of time-dependent transformations treated along the lines of Floquet's theory as well as in terms of exponential operators with a goal to examine the variety of initial states exhibiting cyclic behaviour. A particular case of special cyclic initial states is described which is shown to be important for nuclear magnetic resonance experiments aimed at the study of the effects of the geometric phase. An example of arbitrary spin j in a precessing magnetic field and spin j=1 subject to both axially symmetric quadrupolar interaction and a precessing magnetic field are presented. The invariant (Kobe's) geometric phase is calculated for special cyclic states.