Universal spectral correlations in open Floquet systems with localized leaks

TL;DR

This paper demonstrates that localized leaks in Floquet systems induce universal spectral correlations described by a non-Hermitian symmetry class, with concrete evidence from the leaky quantum standard map and truncated circular orthogonal ensemble.

Contribution

It reveals that localized leaks lead to universal spectral correlations governed by the non-Hermitian class $ ext{AI}^ op$, supported by analytical and numerical analysis of specific models.

Findings

Bulk spectral properties match the TCOE model

Short-range correlations follow the $ ext{AI}^ op$ statistics

Global density of states approaches the Ginibre law with stronger leakage

Abstract

We show that introducing a localized leak in Floquet systems with time-reversal symmetry leads to universal spectral correlations governed by the non-Hermitian symmetry class $\mathrm{AI}^{\dagger}$, associated with complex-symmetric Ginibre random matrices, rather than by the unconstrained Ginibre ensemble. As a concrete example, we analyze the leaky quantum standard map (L-QSM) of the kicked rotor. Since the closed map exhibits circular orthogonal ensemble (COE) statistics, the open system is naturally compared with the truncated circular orthogonal ensemble (TCOE), which models localized leakage by removing columns from a COE matrix. We find excellent agreement between the bulk spectral properties of the L-QSM and the TCOE, and demonstrate that their short-range spectral correlations follow the universal statistics of the non-Hermitian symmetry class $\mathrm{AI}^{\dagger}$. This agreement holds for smaller leak sizes as the matrices increase, while the COE limit is recovered only when the truncation is smaller than one full column. In contrast to local properties, the global density of states of the L-QSM and the TCOE approaches the Ginibre circular law only when the leakage becomes sufficiently strong.