SKM 2023 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 48: Dynamics and Chaos in Many-Body Systems I (joint session DY/TT)

DY 48.7: Talk

Thursday, March 30, 2023, 16:45–17:00, MOL 213

Universal Eigenvalue Distribution for Locally Interacting Quantum Systems — •Tobias Helbig, Tobias Hofmann, Ronny Thomale, and Martin Greiter — Institut für Theoretische Physik und Astrophysik, Universität Würzburg, D-97074 Würzburg, Germany

Wigner has shown [1] that the eigenvalue distribution of a Gaussian orthogonal or unitary ensemble of random matrices approaches a semicircle in the thermodynamic limit. Here, we show that the joint eigenvalue distribution of locally interacting quantum systems, that is, ensembles of finite dimensional subsystems with local interactions between them, approaches a Gaussian distribution as the number of subsystems is taken to infinity [2]. In the talk, we present our analytical results supported by numerical data and discuss possible implications of a Gaussian density of states for physical problems.

[1] E. P. Wigner. On the statistical distribution of the widths and spacings of nuclear resonance levels. Mathematical Proceedings of the Cambridge Philosophical Society, 47(4): 790-798 (1951).

[2] T. Hofmann, T. Helbig, R. Thomale, and M. Greiter. In preparation.