|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
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
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.