Berlin 2024 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 17: Focus Session: Quantum Interactive Dynamics II (joint session DY/TT)
TT 17.8: Vortrag
Montag, 18. März 2024, 17:30–17:45, A 151
Non-interacting limit of the many-body mean level density as an indicator of integrable vs. chaotic single particle dynamics — •Georg Maier1, Carolyn Echter1, Juan-Diego Urbina1, Caio Lewenkopf2, and Klaus Richter1 — 1Institut für Theoretische Physik, Universität Regensburg — 2Instituto de Física, Universidade Federal Fluminense
A celebrated result of semiclassical analysis states that two definitorial aspects of a system's classical dynamics, integrability and chaos, are universally reflected in the spectral fluctuations of its quantized version. According to this picture, therefore, the mean level density (that encodes the smooth, mean features of the spectrum) provides just a system-dependent background that is routinely removed to focus on fluctuations. I will present that, contrary to a naive application of this paradigm, the smooth part of the many-body level density is extremely sensitive to the nature of the single-particle phase space. Specifically, while the spectral fluctuations of many body systems in the mean field limit can be shown to be Poissonian for both chaotic and integrable single-particle dynamics, it is the average level density the one that reflects such distinction. Our results are based on the study of the mean level density obtained from averaging over ensembles of single-particle spectra with the characteristic fluctuations representing the integrable and chaotic dynamics of the weakly interacting (mean field) limit. We are then able to obtain closed analytical expressions for systems with N=2,3 bosons/fermions, while extensive numerical simulations support our claims for larger values.
Keywords: Many Body Density of States; Quantum Choas; Non interacting distingushale Particles