The Nonlinear Schrodinger Equation on the Half Line

Abstract

The nonlinear Schrodinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov-Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag-Ruelle framework, suitably generalized to the case of broken translation invariance in space.

Tex file, no figures, 32 pages

References in corpus (1)

• Quantization of the Nonlinear Schrodinger Equation on the Half Line

Cited by in corpus (17)

• General boundary conditions for the sl(N) and sl(M|N) open spin chains
• Quantum Fields on Star Graphs
• Scattering in the Presence of a Reflecting and Transmitting Impurity
• Reflection-Transmission Algebras
• Spontaneous symmetry breaking in the gl(N)-NLS hierarchy on the half line
• The quantum non-linear Schrodinger model with point-like defect
• Boundary reduction formula
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Exact results for the one-dimensional many-body problem with contact interaction: Including a tunable impurity
• Solving the quantum non-linear Schrodinger equation with delta-type impurity
• Lax pair and super-Yangian symmetry of the non-linear super-Schrödinger equation
• The semi-infinite q-boson system with boundary interaction
• Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
• Spontaneous symmetry breaking in the non-linear Schrodinger hierarchy with defect
• Quantum resolution of the nonlinear super-Schrodinger equation
• Factorization in integrable systems with impurity
• On some aspects of the definition of scattering states in quantum field theory