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

TL;DR

This paper computes the Dissipative Spectral Form Factor for a broad class of non-Hermitian random matrices, confirming universal predictions and revealing non-universal corrections at short times, thus advancing understanding of dissipative quantum systems.

Contribution

It provides the first analytic formula for the DSFF of real non-Hermitian matrices and analyzes non-universal short-time corrections based on eigenvalue statistics.

Findings

Confirmed DSFF predictions for complex matrices up to intermediate times.

Derived the first analytic DSFF formula for real matrices.

Identified non-universal corrections depending on the fourth cumulant at short times.

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].