Emergent Spectral Form Factors in Sonic Systems

TL;DR

This paper investigates the spectral form factor in hydrodynamic systems with sound poles, revealing complex behaviors like resonances, emergent integrability, and large fluctuations, linked to quantum particle dynamics in finite cavities.

Contribution

It introduces a novel connection between hydrodynamic spectral form factors and quantum particle spectral properties in finite systems, highlighting emergent phenomena.

Findings

Spectral form factor linked to quantum particle in cavity

Emergent integrability observed in certain regimes

Large fluctuations and resonance phenomena identified

Abstract

We study the spectral form factor (SFF) for hydrodynamic systems with a sound pole, a large class including any fluid with momentum conservation and energy conservation, or any extended system with spontaneously broken continuous symmetry. We study such systems in a finite volume cavity and find that the logarithm of the hydrodynamic enhancement to the SFF is closely related to the spectral form factor of a quantum particle moving in the selfsame cavity. Depending upon the dimensionality and nature of the effective single-particle physics, these systems exhibit a range of behaviors including an intricate resonance phenomenon, emergent integrability in the SFF, and anomalously large fluctuations of the SFF.