Dresden 2011 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 37: Quantum Chaos II

DY 37.3: Talk

Thursday, March 17, 2011, 16:30–16:45, ZEU 118

GOE-GUE transition catastrophe in many body systems — •Quirin Hummel, Juan Diego Urbina, Jack Kuipers, and Klaus Richter — Institute of Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany

The quantum spectral fluctuations of classically chaotic systems undergo a transition between the orthogonal (GOE) and unitary (GUE) universality classes when a weak magnetic field is applied. In the context of Random Matrix Theory, closed analytical expressions for measures of spectral fluctuations (as the spectral form factor) are known for the full transition, and a semiclassical understanding of such results for single particle systems has emerged during the last years. We study how the semiclassical analysis is affected by going from single particle dynamics to a many body system of identical particles. We report here the apparent existence of a catastrophe in the GOE to GUE regime, in the sense that the mathematical limit where the number of particles tends to infinity produces a transition which is either infinitely slow or infinitely fast with respect to the magnitude of the applied magnetic field. We investigate to what extent interactions play a role in the corresponding analysis.