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arXiv · 1908.10474

Quantum Hydrodynamics of Vorticity

Yaroslav Tserkovnyak·Ji Zou
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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.

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Yaroslav Tserkovnyak, Ji Zou. 2019-08-27. Quantum Hydrodynamics of Vorticity. https://doi.org/10.1103/physrevresearch.1.033071

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