相关论文: N-points correlator for the Gaudin's model realiza…
After review the quantum Hall effect on the fuzzy two-sphere $S^2$ and Zhang and Hu's 4-sphere $S^4$, the incompressible quantum Hall fluid on $S^2$, $S^4$ and torus are discussed respectively. Next, the corresponding Laughlin wavefunctions…
The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the graded osp(1|2) vertex model we find the…
We briefly review a theoretical picture of the quantum Hall effect in which gauge symmetry of non-relativistic quantum mechanics, the representation theory of U(1)-current algebra, and the study of odd, positive integral quadratic forms on…
We show that a charged fluid endowed with an internal spin degree of freedom naturally satisfies the Pauli equation for a nonrelativistic spin-1/2 particle, and that a collection of n such interacting fluids can be reformulated as an Euler…
The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$…
We study the connection between N = 2 supersymmetric gauge theories, quantum cohomology and quantum integrable systems of hydrodynamic type. We consider gauge theories on ALE spaces of A and D-type and discuss how they describe the quantum…
We prove that the wave vectors of the off-shell Bethe Ansatz equation for the inhomogeneous SU(2) lattice vertex model render in the quasiclassical limit the solution of the Knizhnik-Zamolodchikov equation.
We review our recent work on the algebraic characterization of quantum Hall fluids. Specifically, we explain how the incompressible quantum fluid ground states can be classified by effective edge field theories with the W-infinity dynamical…
We generalize the previously established connection between the off-shell Bethe ansatz equation for inhomogeneous SU(2) lattice vertex models in the quasiclassical limit and the solutions of the SU(2) Knizhnik-Zamolodchikov equations to the…
Based on Haldane's spherical geometrical formalism of two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of $S^2$ and the two-dimensional quantum Hall fluids is exhibited. If the number of particles $N$ is…
In this note we demonstrate that vortices in a non-relativistic Chern-Simons theory form a quantum Hall fluid. We show that the vortex dynamics is controlled by the matrix mechanics previously proposed by Polychronakos as a description of…
The semiclassical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models for the $sl(2|1)^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$ independents Gaudin Hamiltonians. We also use the…
Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium transfer rates of the boundary sine-Gordon and the…
We study a nonlinear fluid-structure interaction problem in which the fluid is described by the three-dimensional incompressible Navier-Stokes equations, and the elastic structure is modeled by the nonlinear plate equation which includes a…
Using branes in massive Type IIA string theory, and a novel decoupling limit, we provide an explicit correspondence between non-commutative Chern-Simons theory and the fractional quantum Hall fluid. The role of the electrons is played by…
We argue that a system of interacting D-branes, generalizing a recent proposal, can be modelled as a Quantum Hall fluid. We show that tachyon condensation in such a system is equivalent to one particle tunnelling. In a conformal field…
We develop a microscopic theory for the dynamics of quantum fluids of light, deriving an effective kinetic equation in momentum space that takes the form of the convection-diffusion equation. In the particular case of two-dimensional…
This paper explores the quantum-fluid correspondence in a charged relativistic fluid with intrinsic spin. We begin by examining the nonrelativistic case, showing that the inclusion of spin introduces a quantum correction to the classical…
The topological physics of quantum Hall states is efficiently encoded in purely topological quantum field theories of the Chern-Simons type. The reliable inclusion of low-energy dynamical properties in a continuum description however…
The elliptic Gaudin model describes completely anisotropic spin systems with long range interactions. The model was proven to be quantum integrable by Gaudin and latter the exact solution was found by means of the algebraic Bethe ansatz. In…