Emergent Spectral Form Factors in Sonic Systems

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.