  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.
