Periodic integrable systems with delta-potentials

Abstract

In this paper we study root system generalizations of the quantum Bose-gas on the circle with pair-wise delta function interactions. The underlying symmetry structures are shown to be governed by the associated graded of Cherednik's (suitably filtered) degenerate double affine Hecke algebra, acting by Dunkl-type differential-reflection operators. We use Gutkin's generalization of the equivalence between the impenetrable Bose-gas and the free Fermi-gas to derive the Bethe ansatz equations and the Bethe ansatz eigenfunctions.

36 pages. The analysis of the propagation operator in Sections 5 and 6 is corrected and simplified. To appear in Comm. Math. Phys

References in corpus (2)

• Exchange Operator Formalism for Integrable Systems of Particles
• Inverse Harish-Chandra Transform and Difference Operators

Cited by in corpus (21)

• Higgs Bundles, Gauge Theories and Quantum Groups
• Trigonometric Cherednik algebra at critical level and quantum many-body problems
• Orthogonality of Bethe Ansatz eigenfunctions for the Laplacian on a hyperoctahedral Weyl alcove
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit
• Completeness of the Bethe Ansatz for an open $q$-boson system with integrable boundary interactions
• Traces of Integrability in Relaxation of One-Dimensional Two-Mass Mixtures
• Exactly solvable quantum few-body systems associated with the symmetries of the three-dimensional and four-dimensional icosahedra
• Discrete harmonic analysis on a Weyl alcove
• Unitary representations of affine Hecke algebras related to Macdonald spherical functions
• Creating Entanglement Using Integrals of Motion
• Traces of integrability in scattering of one-dimensional dimers on a barrier
• Discrete series characters for affine Hecke algebras and their formal degrees
• Spectral transfer morphisms for unipotent affine Hecke algebras
• A discrete analogue of periodic delta Bose gas and affine Hecke algebra
• Extended trigonometric Cherednik algebras and nonstationary Schrödinger equations with delta-potentials
• Affine Pieri rule for periodic Macdonald spherical functions and fusion rings
• A discrete Fourier transform associated with the affine Hecke algebra
• Quantum propagator and characteristic equation in the presence of a chain of $\delta$-potentials
• A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schrödinger Model
• Completeness of the Bethe ansatz on Weyl alcoves
• A non-symmetric Yang-Baxter algebra for the quantum nonlinear Schrödinger model (PhD Thesis)