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 Mathematical Physics

Construction of the eigenstates for the quantum nonlinear Schrödinger model with the most general supermatrices

Yu‐Kui Zhou, Guo-Hun Yun

Published Aug 1, 1989• 0 citations
Publisher

Abstract

A quantum nonlinear Schrödinger model with the most general supermatrices, having a structure (n−i, i)×(m−j, j), is studied by using the quantum inverse scattering method. The scattering states and bound states of the model are constructed.
DOI
10.1063/1.528596

Related papers

A STUDY ON THE EIGENSTATES OF QUANTUM NONLINEAR SCHR?DINGER MODEL WITH GENERAL SUPERMATRICES

ZHOU YU-KUI, Guohong Yun, (1)内蒙古大学物理系; (2)西北大学现代物理研究所

A quantum nonlinear Schr?dinger model with the most general supermatrices, having structure (n-k,k)(m-l,l), is studied by using the quantum inverse scattering method. The eigenstates of the Hamiltonian and the infinite number of the conserved quantities of the system are discussed, In particular, the N-particle bound states with the mixture of bosons and fermions are found. The energy of the N-particle eigenstate are ∑j=1Nλj2 and Np2-(c2/12)N(N2-1) for the scattering stateand the bound state respectively.

Acta Physica Sinica•Jan 1, 1989•0 citations

Quantum inverse scattering method for the nonlinear Schrodinger model of fermions with attractive interaction

Haitao Fan, Fu‐Cho Pu, Bao‐Heng Zhao

The quantum inverse scattering method is applied to the nonlinear Schrodinger model of fermions with attractive interactions. Both scattering and bound-state operators are constructed. Among state operators, there are generators of infinitely many conserved quantities and the creators of the eigenstates of these quantities. The commutation relations and the eigenvalues of physical interest are calculated. The quantum Gelfand-Levitan equations are established. The Fourier transform of the connected part of the 4-point Green function and the two body S matrix are calculated explicitly.

Journal of Physics A Mathematical and General•Nov 21, 1989•3 citations

The construction of the eigenstates for nonlinear Schrödinger model with supermatrices and attractive coupling

Yu-Sen Zhou

The European Physical Journal C•Jun 1, 1988•1 citation

Quantum inverse scattering method for a nonlinear N-wave resonance interaction system with both boson and fermion fields

Huan-Qiang Zhou, Jian Zhang, Lin-Jie Jiang

The nonlinear N-wave resonance interaction system with both boson and fermion fields is studied in the framework of the quantum inverse scattering method. The model Hamiltonian is diagonalised and the degeneracy of the eigenstates and the existence of the quantum bound states are analysed. Moreover, the classical limit is also discussed.

Journal of Physics A Mathematical and General•Nov 21, 1989•1 citation

Algebraic Bethe ansatz for the nonlinear Schrodinger model. I. Multicomponent fields

Yu-Sen Zhou

The generalisation of the quantum inverse scattering method is used to derive the Bethe ansatz equation of a system for a multicomponent nonlinear Schrodinger models with n species (or colours) of bosons or fermions. The matrix periodic boundary conditions for bosons and fermions are obtained and the relationship between them discussed. The eigenstates for the infinite conserved quantities of the system are constructed. Lastly, the author generalises these results to the non-linear Schrodinger model with the mirror-image delta potentials proposed by Schulz (1987).

Journal of Physics A Mathematical and General•May 21, 1988•10 citations

The Quantum Nonlinear Schrödinger Model; Gelfand-Levitan Equation and Classical Soliton

Miki Wadati, Atsuo Kuniba, Tetsuro Konishi

Through the quantum inverse scattering method the nonlinear Schrödinger model is studied for the attractive case. Making use of the bound state operators and the quantum Gelfand-Levitan equation, the matrix elements of the field operator φ( x ) and the density operator φ + ( x )φ( x ) are explicitly calculated. Each matrix element is found to be expressed in a product form. Based on the results, the connection between classical soliton and the quantum field theory is investigated. It is shown that the wave form of the classical soliton is related to the matrix element of the field operator in the limit n →∞, where n is the particle number making the bound state. The powerfulness of the quantum Gelfand-Levitan equation is stressed.

Journal of the Physical Society of Japan•May 15, 1985•24 citations
A quantum nonlinear Schr?dinger model with the most general supermatrices, having structure (n-k,k)(m-l,l), is studied by using the quantum inverse scattering method. The eigenstates of the Hamiltonian and the infinite number of the conserved quantities of the system are discussed, In particular, the N-particle bound states with the mixture of bosons and fermions are found. The energy of the N-particle eigenstate are ∑j=1Nλj2 and Np2-(c2/12)N(N2-1) for the scattering stateand the bound state respectively.
The quantum inverse scattering method is applied to the nonlinear Schrodinger model of fermions with attractive interactions. Both scattering and bound-state operators are constructed. Among state operators, there are generators of infinitely many conserved quantities and the creators of the eigenstates of these quantities. The commutation relations and the eigenvalues of physical interest are calculated. The quantum Gelfand-Levitan equations are established. The Fourier transform of the connected part of the 4-point Green function and the two body S matrix are calculated explicitly.
The generalisation of the quantum inverse scattering method is used to derive the Bethe ansatz equation of a system for a multicomponent nonlinear Schrodinger models with n species (or colours) of bosons or fermions. The matrix periodic boundary conditions for bosons and fermions are obtained and the relationship between them discussed. The eigenstates for the infinite conserved quantities of the system are constructed. Lastly, the author generalises these results to the non-linear Schrodinger model with the mirror-image delta potentials proposed by Schulz (1987).
Through the quantum inverse scattering method the nonlinear Schrödinger model is studied for the attractive case. Making use of the bound state operators and the quantum Gelfand-Levitan equation, the matrix elements of the field operator φ( x ) and the density operator φ + ( x )φ( x ) are explicitly calculated. Each matrix element is found to be expressed in a product form. Based on the results, the connection between classical soliton and the quantum field theory is investigated. It is shown that the wave form of the classical soliton is related to the matrix element of the field operator in the limit n →∞, where n is the particle number making the bound state. The powerfulness of the quantum Gelfand-Levitan equation is stressed.