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DY: Fachverband Dynamik und Statistische Physik

DY 32: Quantum Chaos

DY 32.7: Vortrag

Mittwoch, 22. März 2017, 12:00–12:15, HÜL 186

Berry-Tabor Trace Formula for the Lieb-Liniger Model — •Christian Scharf, Juan-Diego Urbina, and Klaus Richter — Universität Regensburg

We report our progress in constructing a trace formula for the semiclassical density of states of the Lieb-Liniger model, describing a gas of one-dimensional bosons interacting via a repulsive δ-potential.

We combine the methods of Berry and Tabor used in [1] for any integrable Hamiltonian and apply them to this system by making use of the Bethe-Ansatz equations expressing the quantization of the momenta. Further, using Poisson summation and applying a stationary phase approximation we get perfect agreement between semiclassical and numerical calculation for the oscillatory part of the density of states for the two-particle case while extending the results to arbitrary number of particles is work in progress. We show how this method can be used to obtain a trace formula for other systems like the Fermi- or the Bose-Hubbard models.

[1] Berry, M. V.,Tabor, M., Proc. R. Soc. Lond. A. 349, 101-123 (1976)