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DY: Fachverband Dynamik und Statistische Physik

DY 39: Quantum Chaos (joint session DY/TT)

DY 39.13: Vortrag

Mittwoch, 18. März 2020, 18:30–18:45, HÜL 186

The Conditioned Real Ginibre Ensemble and PT-Symmetric Quantum Chaos — •Simon Malzard¹, Steve Mudute-Ndumbe¹, Roman Riser², Joshua Feinburg², and Eva-Maria Graefe¹ — ¹Imperial College London, London, UK — ²University of Haifa, Haifa, Israel

In Hermitian systems the universality of spectral fluctuations described by the standard Gaussian ensembles is one of the most pronounced fingerprints of chaos in a quantum system. With the recent intense interest in non-Hermitian PT-symmetric systems, it is a natural question whether there are PT-symmetric random matrix ensembles yielding similar universality classes. One candidate for PT-symmetric systems with P^2=1 and T^2=1 which display quantum chaos is the real Ginibre ensemble. Eigenvalues of real Ginibre matrices are real or occur in complex conjugate pairs. The spectral properties of the real Ginibre matrices depend crucially on the number of real eigenvalues. Hence, when studying the eigenvalue distributions and level spacings of PT-symmetric quantum chaotic systems, one should make comparisons to an ensemble of real Ginibre matrices conditioned to have the corresponding number of real eigenvalues. Here we present a numerical method to produce samples of real Ginibre matrices conditioned to have a particular number of real eigenvalues.