# Emergent Non-Eulerian Hydrodynamics of Quantum Vortices in Two Dimensions

## TL;DR

This paper introduces a coarse-grained model of quantum vortices in two dimensions, revealing a non-Eulerian fluid behavior with anomalous stresses and compressibility, supported by analytical and numerical results.

## Contribution

It develops a novel large-scale description of quantum vortices as a non-Eulerian fluid with unique stress properties, extending classical vortex models.

## Key findings

- Emergent vortex fluid exhibits non-Eulerian, compressible behavior.
- Analytic vortex shear flow solution matches numerical simulations.
- Identifies anomalous stresses caused by quantum vortex singularities.

## Abstract

We develop a coarse-grained description of the point-vortex model, finding that a large number of planar vortices and antivortices behave as an inviscid non-Eulerian fluid at large scales. The emergent binary vortex fluid is subject to anomalous stresses absent from Euler's equation, caused by the singular nature of quantum vortices. The binary vortex fluid is compressible, and has an asymmetric Cauchy stress tensor allowing orbital angular momentum exchange with the vorticity and vortex density. An analytic solution for vortex shear flow driven by anomalous stresses is in excellent agreement with numerical simulations of the point-vortex model.