Characteristic Polynomials of Complex Random Matrices and Painlevé Transcendents
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DOI: 10.1093/imrn/rnaa111
Abstract: We study expectations of powers and correlation functions for characteristic polynomials of N×N non-Hermitian random matrices. For the 1-point and 2-point correlation function, we obtain several characterizations in terms of Painleve transcendents, both at finite-N… read more here.
Keywords: ginibre ensemble; characteristic polynomials; random matrices; polynomials complex ... See more keywords
Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble.
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DOI: 10.1103/physrevlett.130.010401
Abstract: Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians… read more here.
Keywords: entanglement entropy; ginibre ensemble; non hermitian; many body ... See more keywords
Many-Body Quantum Chaos and Emergence of Ginibre Ensemble.
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DOI: 10.1103/physrevlett.130.140403
Abstract: We show that non-Hermitian Ginibre random matrix behaviors emerge in spatially extended many-body quantum chaotic systems in the space direction, just as Hermitian random matrix behaviors emerge in chaotic systems in the time direction. Starting… read more here.
Keywords: body quantum; many body; spectral form; ginibre ensemble ... See more keywords