Erlangen 2018 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 27: Quantum Gases (Bosons) III

Q 27.2: Vortrag

Montag, 5. März 2018, 16:30–16:45, K 2.020

Finite size effects and scrambling at the quantum phase transition of a 1D Bose gas — •Benjamin Geiger, Quirin Hummel, Juan Diego Urbina, and Klaus Richter — Institut für theoretische Physik, Universität Regensburg, Germany

It is known from mean-field theory that a system of bosons with attractive contact interactions in one dimension exhibits a quantum phase transition at a certain critical coupling [1]. At this critical point the Bogoliubov spectrum collapses to a single point and thus mean-field theory fails to describe the characteristical finite level spacing. We investigate the situation for a large but finite number of particles in a momentum-truncated model and show that semiclassical many-body torus quantization allows to calculate the precursors of the quantum phase transition. We show that the phase transition is accompanied by a change in the topology of the available classical phase space, a fact that enables us to define a sharp critical coupling wherever the topology of a quantized torus changes, despite the fact that the spectrum is analytic in the interaction parameter. Our approach has a direct application to the description of scrambling times around criticality, a subject of large recent interest.
[1] R. Kanamoto, H. Saito, M. Ueda, Phys. Rev. A 67, 013608 (2003)