Quantum hydrodynamics of vorticity

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.

Transport signature of the magnetic Berezinskii-Kosterlitz-Thouless transition

“…We first review the qualitative derivation of the transport near the BKT transition in the superconducting films using the dual d = 2 + 1 EM theory [32][33][34][35]. We start with the Lagrangian density,…”

“…In this work, we examine the possibility of the long-distance spin transport in proximity to the magnetic BKT transition using the duality mapping from the 2D easy-plane magnetism to the electromagnetism (EM) in the d = 2 + 1 spacetime [32][33][34][35]. This allows us to both pursue close analogy to the current transport and pinpoint the difference that arises when the phenomenological finite spin lifetime is inserted.…”

Energy storage in magnetic textures driven by vorticity flow

“…by Stokes theorem, is also the total winding number at the boundary ∂Ω. Here n is the easy-plane projection of the order parameter n. We remark that this construction is true not only at the low-temperature regime, where N is integer-valued, but also applicable at high temperatures and the paramagnetic regime (even in the lattice limit [23]), where the vortex number is not quantized.…”

Explaining Ginzburg Landau Equations from First Principles

“…We had speculated then that tiny droplets may be formed which would tend to grow as we believe to be the case with electrons both behaving the same way in a turbulent environment. In both two of the phenomena we had found a vorticity field [2,5,6].…”