Quantum Hydrodynamics of Vorticity

TL;DR

This paper develops a quantum theory of vorticity on a 2D bosonic lattice, connecting classical vortex dynamics with quantum effects, and proposes measurable predictions for vorticity conductivity.

Contribution

It introduces a quantum framework for vorticity dynamics on lattices, linking topological properties with boundary conditions and deriving a Kubo formula for vorticity conductivity.

Findings

Classical vortex-antivortex dynamics emerge in the condensate limit.

Bulk-edge correspondence reflects the topological nature of vorticity flows.

A practical device for measuring vorticity conductivity is proposed.

Abstract

We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal topological character of the vorticity flows is reflected in the bulk-edge correspondence dictated by the Stokes theorem. This is exploited to establish physical boundary conditions that realize, in the coarse-grained thermodynamic limit, an effective chemical-potential bias of vorticity. A Kubo formula is derived for the vorticity conductivity|which could be measured in a suggested practical device|in terms of quantum vorticity-flux correlators of the original lattice model. As an illustrative example, we discuss the superfluidity of vorticity, exploiting the particle-vortex duality at a bosonic superfluid-insulator transition.