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

Operator disentanglement

G. Dattoli, M. Richetta, A. Torre

Published Mar 1, 1988• 31 citations
Publisher

Abstract

We obtain the time-ordered form of the evolution operator for Hamiltonian linear combinations of the generators of the SU(1,1), SU(2), and h(4) groups. The relevance of the obtained results to physics problems such as the generation of non-Poissonian statistics in laser-plasma scattering and the pulse propagation in free-electron lasers is also briefly discussed.

DOI
10.1103/physreva.37.2007

Related papers

Evolution of quantum systems driven by a Hamiltonian written in terms of the SU(1,1) group generators

G. Dattoli, A. Torre, R. Caloi

In this paper we exploit the Wei-Norman algebraic disentangling procedure to study the evolution of quantum states driven by a time-dependent Hamiltonian linear combination of the generators of the SU(1,1) group.

Physical Review A•Apr 1, 1986•22 citations

Time evolution of quantum systems with time-dependent non-Hermitian Hamiltonian and the pseudo Hermitian invariant operator

Mustapha Maamache, Oum Kaltoum Djeghiour, Walid Koussa +1 more

We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the pseudo-Hermitian invariant operator.

arXiv:1705.08298•May 21, 2017•2 citations

Time-dependent quantum systems and the invariant Hermitian operator

Y. Lai, J.-Q. Liang, Harald J W Müller-Kirsten +1 more

We study the time evolution of quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators. The invariant Hermitian operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. With the help of the invariant Hermitian operator we obtain not only the exact solutions of the Schr\"odinger equation but also the time-evolution operator. The adiabatic and nonadiabatic Berry phases are calculated with the exact solutions. \textcopyright{} 1996 The American Physical Society.

Physical Review A•May 1, 1996•93 citations

TIME EVOLUTION OF A QUANTUM SYSTEM WITH HAMILTONIAN CONSISTING OF TIME-DEPENDENT LINEAR COMBINATION OF SU(l, 1)AND SU(2) GENERATORS AND THE HERMITIAN INVARIANT OPERATOR

LAI YUN-ZHONG, Liang Jiu-Qing, (1)山西大学物理系,太原030006; (2)太原重型机械学院基础部,太原030024

We study the time evolution of a quantum system with Hamiltonian consisting of time-dependent linear combination of SU(1,1) and SU(2) generators. A proper hermitian invariant operator has been found to obtain not only closed formulas for the time evolution of quantum states but also the time evolution operators for both the SU(1, 1) and SU(2) systems. The time evolution operators have been used to investigate the time-dependent two photons and SU(2) squeezing states and squeezing properties of the time-dependent SU(1,1) coherent states.

Acta Physica Sinica•Jan 1, 1996•3 citations

The evolution operator technique in solving the Schrodinger equation, and its application to disentangling exponential operators and solving the problem of a mass-varying harmonic oscillator

C M Cheng, P. C. W. Fung

The authors present a method for finding the evolution operator for the Schrodinger equation for the Hamiltonian expressible as H(t)=a 1 (t)J 4 +a 2 (t)J 0 +a 3 (t) J - where J + , J 0 and J - are the SU(2) group generators. Such a method is applied to the disentangling technique for exponential operators which are not necessarily unitary. As a demonstration of our general approach, they solved the problem of a harmonic oscillator with a varying mass.

Journal of Physics A Mathematical and General•Nov 21, 1988•97 citations

SU(2) and SU(1,1) time-ordering theorems and Bloch-type equations

G. Dattoli, A. Torre

Algebraic time-ordering techniques for SU (2) and SU (1,1) coherence preserving Hamiltonians are reviewed. The link with Bloch-type equations is pointed out and the extension of the method to higher groups is briefly discussed.

Journal of Mathematical Physics•Mar 1, 1987•17 citations
We obtain the time-ordered form of the evolution operator for Hamiltonian linear combinations of the generators of the SU(1,1), SU(2), and h(4) groups. The relevance of the obtained results to physics problems such as the generation of non-Poissonian statistics in laser-plasma scattering and the pulse propagation in free-electron lasers is also briefly discussed.
We study the time evolution of quantum systems with a time-dependent Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators. The invariant Hermitian operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. With the help of the invariant Hermitian operator we obtain not only the exact solutions of the Schr\"odinger equation but also the time-evolution operator. The adiabatic and nonadiabatic Berry phases are calculated with the exact solutions. \textcopyright{} 1996 The American Physical Society.
We study the time evolution of a quantum system with Hamiltonian consisting of time-dependent linear combination of SU(1,1) and SU(2) generators. A proper hermitian invariant operator has been found to obtain not only closed formulas for the time evolution of quantum states but also the time evolution operators for both the SU(1, 1) and SU(2) systems. The time evolution operators have been used to investigate the time-dependent two photons and SU(2) squeezing states and squeezing properties of the time-dependent SU(1,1) coherent states.