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1. Anomalies in fluid dynamics: flows in a chiral background via variational principle

   https://doi.org/10.1088/1751-8121/ac9202  

   Abanov, A G; Wiegmann, P B (September 2022, Journal of Physics A: Mathematical and Theoretical)

   Abstract We study flows of barotropic perfect fluid under the simultaneous action of the electromagnetic field and the axial–vector potential, the external field conjugate to the fluid helicity. We obtain the deformation of the Euler equation by the axial–vector potential and the deformations of various currents by two external fields. We show that the divergence of the vector and axial currents are controlled by the chiral anomaly known in quantum field theories with Dirac fermions. We obtain these results by extending the variational principle for barotropic flows of a perfect fluid by coupling with the external axial–vector potential. 

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2. Chiral transport in curved spacetime via holography

   https://doi.org/10.1007/JHEP08(2021)007  

   Avdoshkin, Alexander; Sharipov, Rustem (August 2021, Journal of High Energy Physics)

   A bstract We consider a holographic model of strongly interacting plasma with a gravitational anomaly. In this model, we compute parity-odd responses of the system at finite temperature and chemical potential to external electromagnetic and gravitational fields. Working within the linearized fluid/gravity duality, we performed the calculation up to the third order in gradient expansion. Besides reproducing the chiral magnetic (CME) and vortical (CVE) effects we also obtain gradient corrections to the CME and CVE due to the gravitational anomaly. Additionally, we find energy-momentum and current responses to the gravitational field similarly determined by the gravitational anomaly. The energy-momentum response is the first purely gravitational transport effect that has been related to quantum anomalies in a holographic theory. 

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3. Vortex line entanglement in active Beltrami flows

   https://doi.org/10.1017/jfm.2024.115  

   Romeo, Nicolas; Słomka, Jonasz; Dunkel, Jörn; Burns, Keaton J (March 2024, Journal of Fluid Mechanics)

   Over the last decade, substantial progress has been made in understanding the topology of quasi-two-dimensional (2-D) non-equilibrium fluid flows driven by ATP-powered microtubules and microorganisms. By contrast, the topology of three-dimensional (3-D) active fluid flows still poses interesting open questions. Here, we study the topology of a spherically confined active flow using 3-D direct numerical simulations of generalized Navier–Stokes (GNS) equations at the scale of typical microfluidic experiments. Consistent with earlier results for unbounded periodic domains, our simulations confirm the formation of Beltrami-like bulk flows with spontaneously broken chiral symmetry in this model. Furthermore, by leveraging fast methods to compute linking numbers, we explicitly connect this chiral symmetry breaking to the entanglement statistics of vortex lines. We observe that the mean of linking number distribution converges to the global helicity, consistent with the asymptotic result by Arnold [InVladimir I. Arnold – Collected Works(ed. A.B. Givental, B.A. Khesin, A.N. Varchenko, V.A. Vassiliev & O.Y. Viro), pp. 357–375. Springer]. Additionally, we characterize the rate of convergence of this measure with respect to the number and length of observed vortex lines, and examine higher moments of the distribution. We find that the full distribution is well described by a k-Gamma distribution, in agreement with an entropic argument. Beyond active suspensions, the tools for the topological characterization of 3-D vector fields developed here are applicable to any solenoidal field whose curl is tangent to or cancels at the boundaries of a simply connected domain. 

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4. Incompressible active phases at an interface. Part 1. Formulation and axisymmetric odd flows

   https://doi.org/10.1017/jfm.2022.856  

   Jia, Leroy L.; Irvine, William T.M.; Shelley, Michael J. (November 2022, Journal of Fluid Mechanics)

   Inspired by the recent realization of a two-dimensional (2-D) chiral fluid as an active monolayer droplet moving atop a 3-D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2-D linear, incompressible and isotropic fluid, having a viscous shear stress, an active chiral driving stress and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3-D Stokes phase. We pose the dynamics as the solution to a singular integral–differential equation, over the droplet surface, using the mapping from surface stress to surface velocity for the 3-D Stokes equations. Specializing to the case of axisymmetric droplets, exact representations for the chiral surface flow are given in terms of solutions to a singular integral equation, solved using both analytical and numerical techniques. For a disc-shaped monolayer, we additionally employ a semi-analytical solution that hinges on an orthogonal basis of Bessel functions and allows for efficient computation of the monolayer velocity field, which ranges from a nearly solid-body rotation to a unidirectional edge current, depending on the subphase depth and the Saffman–Delbrück length. Except in the near-wall limit, these solutions have divergent surface shear stresses at droplet boundaries, a signature of systems with codimension-one domains embedded in a 3-D medium. We further investigate the effect of a Hall viscosity, which couples radial and transverse surface velocity components, on the dynamics of a closing cavity. Hall stresses are seen to drive inward radial motion, even in the absence of edge tension. 

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5. Anomalous normal fluid response in a chiral superconductor UTe2

   https://doi.org/10.1038/s41467-021-22906-6  

   Bae, Seokjin; Kim, Hyunsoo; Eo, Yun Suk; Ran, Sheng; Liu, I-lin; Fuhrman, Wesley T.; Paglione, Johnpierre; Butch, Nicholas P.; Anlage, Steven M. (May 2021, Nature Communications)

   Abstract Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe₂with surface normal fluid response. The microwave surface impedance of the UTe₂crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe₂can be a new platform to study exotic topological excitations in higher dimension. 

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