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

• URL: http://arxiv.org/abs/2306.16262v3
• Date: Fri, 4 Aug 2023 18:24:37 GMT
• Title: The Dissipative Spectral Form Factor for I.I.D. Matrices
• Authors: Giorgio Cipolloni and Nicolo Grometto
• Abstract summary: The Dissipative Spectral Form Factor (DSFF) is a key tool to study universal properties of dissipative quantum systems. 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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