### The semi-infinite q-boson system with boundary interaction

**van Diejen, JF ***(Ponticia Universidad Católica de Chile)*

Thursday 11 July 2013, 11:30-12:00

Seminar Room 1, Newton Institute

#### Abstract

The q-boson system is a lattice discretization of the one-dimensional quantum nonlinear
Schrödinger equation built of particle creation and annihilation operators representing the q-oscillator algebra. Its n-particle eigenfunctions are given by Hall-Littlewood functions. I will discuss a system of q-bosons on the semi-infinite lattice with boundary interactions arising from a quadratic deformation of the q-boson field algebra at the end point and show that the Bethe Ansatz eigenfunctions are given by Macdonald's three-parameter Hall-Littlewood functions with hyperoctahedral symmetry associated with the BC-type root system. From a stationary phase analysis, it then follows that the n-particle scattering matrix factorizes as a product of explicitly computed two-particle bulk and one-particle boundary scattering matrices.

#### Presentation

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