The Dissipative Spectral Form Factor for I.I.D. Matrices

2023/06/28 by Cipolloni, Giorgio, Grometto, Nicolo · 2 citations
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2306.16262

Abstract

The Dissipative Spectral Form Factor (DSFF), recently introduced in [arXiv:2103.05001] for the Ginibre ensemble, is a key tool to study universal properties of dissipative quantum systems. In this work we compute the DSFF for a large class of random matrices with real or complex entries up to an intermediate time scale, confirming the predictions from [arXiv:2103.05001]. The analytic formula for the DSFF in the real case was previously unknown. Furthermore, we show that for short times the connected component of the DSFF exhibits a non-universal correction depending on the fourth cumulant of the entries. These results are based on the central limit theorem for linear eigenvalue statistics of non-Hermitian random matrices [arXiv:2002.02438, arXiv:1912.04100].

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• Higher-order spectral form factors of circular unitary ensemble
• Quenched properties of the Spectral Form Factor

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