David Martin

Semiclassical trace formula for Lieb-Liniger

The Lieb-Liniger model (also known as Bose gas) plays an important role in modern physics. Originally it enables the authors to find the exact solution for the ground state and the energy spectrum via Bethe ansatz. It has gained a renewed interest since it can be realised in cold atom experiments. In this talk we are interested in establishing a well-known technique from quantum chaos, the trace formula, for this model. In particular there are strong connections with a billiard problem with unusual type of boundary conditions. We will present how we could derive an explicit approximation for the density of state of the Bose gas and compare to numerics.