Abstract

The complex behavior of interacting many-body quantum systems continues to challenge contemporary researchers. In particular, inferring edge dynamics from bulk properties, which typically relies on a bulk-boundary correspondence, remains an unsolved problem in many condensed matter systems. Most edge theories are derived by integrating out bulk matter fields, leaving behind a theory that describes only the edge degrees of freedom. Alternatively, when a suitable hydrodynamic theory for the system is developed, the relationship between bulk matter fields and edge dynamics naturally follows from “classical” hydrodynamic boundary conditions, such as no-penetration and no-stress.

If a system admits an effective theory in terms of a single complex scalar, such as an order parameter or wavefunction, constructing a hydrodynamic theory becomes straightforward, with boundary conditions arising directly from conservation laws. In this talk I will outline this general process and apply the formalism to three illustrative examples. Fractional Quantum Hall fluids offer insights into hydrodynamic Chern-Simons theories, while polariton fluids motivate the introduction of dissipative effects. Integer quantum Hall states of bosons, representing a type of symmetry-protected topological phase, are effectively described by a two-fluid model which leads to a broader class of boundary conditions and edge modes. Time permitting, I will discuss how this framework may also shed light on turbulence in both quantum and classical systems.