Quantum Hydrodynamics

by Dylan Reynolds (ICTS)

Wednesday 16 Jul 2025, 15:00 → 17:00 Europe/Rome

1/3-1 - Sala R (Dipartimento di Fisica e Astronomia - Edificio Marzolo)

The complex behavior of interacting many-body quantum systems continues
to challenge contemporary researchers. In particular, inferring edge
dynamics from bulk properties—typically relying 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.