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Quantum integrable multiple three-wave interaction models

Branislav Jurčo

Physics Letters AJan 1, 19905 citations

Quantum Three Wave Interaction Models

Kenji Ohkuma, Miki Wadati

The quantum three wave interaction models are introduced for three choices of statistics. The general Bethe states are constructed, and the existence of bound states is discussed for each model. It is concluded that the quantum three wave interaction models are completely integrable.

Journal of the Physical Society of JapanSep 15, 198414 citations

Integrable open-boundary conditions for the supersymmetric t-J model the quantum-group-invariant case

A. González-Ruiz

arXiv:hep-th/9401118Nuclear Physics BAug 1, 199491 citations

Spin excitations in the integrable open quantum group invariant supersymmetric t−J model

Yu-Sen Zhou, Murray T. Batchelor

arXiv:cond-mat/9611013Nuclear Physics BApr 1, 199713 citations

Quantum Integrability of a Supersymmetric Multiple Three-wave Interaction Model

管习文, 熊庄, 杨拉勋 +1 more

Recently, a considerable interest has been aroused in the study of completely integrable systems. As is well known, the dassical and quantum Yang-Baxter equations (CYBE and QYBE, respectively) play a central role in the theory of classical and quantum integrable systems. In 1973, Gaudin introduced a new class of completely integrable quantum

中国科学通报：英文版Jan 1, 19930 citations

Langevin dynamics, stochastic quantization and the supersymmetric systems

Alexander Punnoose, Rudolf A. Römer

We establish a novel correspondence between the spacetime correlators of one-dimensional (1D) N-particle classical stochastic models described by a Langevin equation with that of the ground-state dynamics of a class of integrable 1D interacting many-body quantum models of the supersymmetric elliptic type. We show that these seemingly different concepts of stochastic systems, supersymmetry and quantum integrability can be viewed in a unified framework. Starting with an Lax matrix, we show that row (column) sums driven by a Gaussian noise term may be interpreted as a set of forward (backward) Langevin equations. Then, following functional path integral methods of stochastic quantization, we straightforwardly find an associated supersymmetric 1D quantum Hamiltonian. If, further, the classical stochastic system consists of two-body interactions only and we also want the quantum interactions to be of two-body type, we find that the only class of interactions permissible for the quantum models corresponds to the elliptic models. The algebraic structure that emerges very naturally reproduces the proof of integrability and allows the identification of the ground-state wavefunction of these quantum models.We establish a novel correspondence between the spacetime correlators of one-dimensional (1D) N-particle classical stochastic models described by a Langevin equation with that of the ground-state dynamics of a class of integrable 1D interacting many-body quantum models of the supersymmetric elliptic type. We show that these seemingly different concepts of stochastic systems, supersymmetry and quantum integrability can be viewed in a unified framework. Starting with an Lax matrix, we show that row (column) sums driven by a Gaussian noise term may be interpreted as a set of forward (backward) Langevin equations. Then, following functional path integral methods of stochastic quantization, we straightforwardly find an associated supersymmetric 1D quantum Hamiltonian. If, further, the classical stochastic system consists of two-body interactions only and we also want the quantum interactions to be of two-body type, we find that the only class of interactions permissible for the quantum models corresponds to the elliptic models. The algebraic structure that emerges very naturally reproduces the proof of integrability and allows the identification of the ground-state wavefunction of these quantum models.

Journal of Physics A Mathematical and GeneralApr 21, 19961 citation

A quantum integrable supersymmetric multiple three-wave interaction model

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A quantum integrable supersymmetric multiple three-wave interaction model

Abstract

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