Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems

Abstract

We present a non-chiral version of the Intermediate Long Wave (ILW) equation that can model nonlinear waves propagating on two opposite edges of a quantum Hall system, taking into account inter-edge interactions. We obtain exact soliton solutions governed by the hyperbolic Calogero-Moser-Sutherland (CMS) model, and we give a Lax pair, a Hirota form, and conservation laws for this new equation. We also present a periodic non-chiral ILW equation, together with its soliton solutions governed by the elliptic CMS model.

arXiv comment15 pages, 4 figures

References in corpus (27)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Fractional Quantum Hall States and Jack Polynomials
• Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra
• Quantum Hydrodynamics, Quantum Benjamin-Ono Equation, and Calogero Model
• Generalised hydrodynamics of the classical Toda system
• Quantum Shock Waves - the case for non-linear effects in dynamics of electronic liquids
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model
• Integrable hydrodynamics of Calogero-Sutherland model: Bidirectional Benjamin-Ono equation
• Generalized Gibbs Ensembles of the classical Toda chain
• Non-Linear hydrodynamics and Fractionally Quantized Solitons at Fractional Quantum Hall Edge
• Anyon Basis of c=1 Conformal Field Theory
• Steady states and universal conductance in a quenched Luttinger model
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Anyons and the elliptic Calogero-Sutherland model
• Quasi-particles in Fractional Quantum Hall Effect Edge Theories
• Loop groups, anyons and the Calogero-Sutherland model
• Construction by bosonization of a fermion-phonon model
• The classical hydrodynamics of the Calogero-Sutherland model
• Emergence of Calogero family of models in external potentials: Duality, Solitons and Hydrodynamics
• Deformed Calogero-Sutherland model and fractional Quantum Hall effect
• Second quantization of the elliptic Calogero-Sutherland model
• Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian
• The Quantum Hydrodynamics of the Sutherland Model
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation

Cited by in corpus (10)

• Multi-solitons of the half-wave maps equation and Calogero-Moser spin-pole dynamics
• Spin generalizations of the Benjamin-Ono equation
• On the non-chiral intermediate long wave equation II: periodic case
• Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
• The non-chiral intermediate Heisenberg ferromagnet equation
• Deep-water and shallow-water limits of the intermediate long wave equation
• Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation
• Generalized Calogero-Moser system and supergroup gauge origami
• Conformal field theory, solitons, and elliptic Calogero--Sutherland models
• Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics