logo Periodic quantum integrable systems with delta-interactions
and double affine Hecke algebras.
Jasper V. Stokman,
Korteweg-de Vries Institute for Mathematics,

University of Amsterdam, The Netherlands

The one-dimensional quantum Bose gas with delta-function interactions is a particularly well studied integrable quantum many-particle system. It is directly linked to the integrable quantum field theory governed by the non-linear Schroedinger equation. In the present talk I aim to clarify the parallels of such types of systems with one-dimensional integrable quantum many-particle systems with long range interactions (Calogero-Moser systems).
Concretely, we discuss root system generalizations of quantum spin-particles on the circle with pair-wise delta-function interactions.
We show that these quantum integrable systems naturally arise from a basic representation of a suitable degeneration of the double affine Hecke algebra in terms of vector-valued Dunkl-type operators. The associated Bethe ansatz equations and Bethe ansatz eigenfunctions are discussed in detail.
This talk is based on joint work with Eric M. Opdam and Erdal Emsiz.