Mainz 2017 – wissenschaftliches Programm

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Q: Fachverband Quantenoptik und Photonik

Q 14: Quantum Gases: Bosons II

Q 14.5: Vortrag

Montag, 6. März 2017, 18:00–18:15, P 204

Understanding quantum phase transitions in the attractive Lieb-Liniger model by quantizing critical mean-field behaviour — •Quirin Hummel, Benjamin Geiger, Juan-Diego Urbina, and Klaus Richter — Institut für Theoretische Physik, Universität Regensburg, Germany

We consider a one-dimensional model of Bosons with attractive interactions which is known to display a quantum phase transition (QPT) at a critical value of the interaction strength α. A semiclassical quantization, where a large number of particles N plays the role of small ℏ, allows us to find the parameters of the QPT in terms of quantized orbits passing through a separatrix in classical phase space. Moreover it allows us to analytically quantify effects arising from the discreteness of the quantum mechanical spectrum like the scaling of the ground state gap with N right at the critical α (explaining the numerical findings in [1]), and the high-density spectrum around the excited state QPT for larger couplings. We extract the exact time-scale of the latter - also known as the scrambling time - and rigurously show that it is related to a stability exponent of the underlying classical dynamics. Finally, the universal applicability of our ideas whenever the QPT is related to similar classical behaviour, leads us to expect that this semiclassical picture can be applied to a broad class of QPT with effective one-dimensional descriptions (e.g. Dicke model, Lipkin-Meshkov-Glick model).

[1] R Kanamoto and H Saito and M Ueda, Phys. Rev. A 67, 013608 (2003)