EXACT RESULTS FOR THE ONE-DIMENSIONAL MANY-BODY PROBLEM WITH CONTACT INTERACTION: INCLUDING A TUNABLE IMPURITY

DOI10.1142/S0129055X07002973zbMath1118.81081arXivcond-mat/0501110OpenAlexW2117292440WikidataQ61834233 ScholiaQ61834233MaRDI QIDQ5292220

Nicolas Crampé, Vincent Caudrelier

Publication date: 20 June 2007

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/0501110

zbMATH Keywords

Bethe equationsimpuritycoordinate Bethe ansatzdelta interactionsone-dimensional bosons

Mathematics Subject Classification ID

Exactly solvable models; Bethe ansatz (82B23) Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items

Exact energy spectrum for models with equally spaced point potentials ⋮ Diagonalization of an integrable discretization of the repulsive delta Bose gas on the circle ⋮ Exactly solvable interacting two-particle quantum graphs ⋮ Many-Particle Quantum Graphs: A Review ⋮ The semi-infinite \(q\)-boson system with boundary interaction ⋮ Solvable models of interacting 𝑛-particle systems on quantum graphs

Cites Work

• Unnamed Item
• Factorizing particles on a half-line and root systems
• Symmetries of Schrödinger operators with point interactions
• Boundary exchange algebras and scattering on the half line
• Solving the quantum nonlinear Schrödinger equation with δ-type impurity
• IntegrableN-particle Hamiltonians with Yangian or reflection algebra symmetry
• The quantum nonlinear Schrödinger model with point-like defect
• Relationship between Systems of Impenetrable Bosons and Fermions in One Dimension
• Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line
• Reflection–transmission algebras
• Spontaneous symmetry breaking in the non-linear Schrödinger hierarchy with defect
• Reflection–transmission quantum Yang–Baxter equations
• The nonlinear Schrödinger equation on the half line
• Boundary conditions for integrable quantum systems
• Study of Exactly Soluble One-Dimensional N-Body Problems
• Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State
• Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
• Symmetry, duality, and anholonomy of point interactions in one dimension