Publications

Order by: publication date number of citations

• Functional renormalisation group approach to shell models of turbulence

  Côme Fontaine, Malo Tarpin, Freddy Bouchet, Léonie Canet

  SciPost Phys. 15, 212 (2023) · published 28 November 2023 | Toggle abstract · pdf

  Shell models are simplified models of hydrodynamic turbulence, retaining only some essential features of the original equations, such as the non-linearity, symmetries and quadratic invariants. Yet, they were shown to reproduce the most salient properties of developed turbulence, in particular universal statistics and multi-scaling. We set up the functional renormalisation group (FRG) formalism to study generic shell models. In particular, we formulate an inverse RG flow, which consists in integrating out fluctuation modes from the large scales (small wavenumbers) to the small scales (large wavenumbers), which is physically grounded and has long been advocated in the context of turbulence. Focusing on the Sabra shell model, we study the effect of both a large-scale forcing, and a power-law forcing exerted at all scales. We show that these two types of forcing yield different fixed points, and thus correspond to distinct universality classes, characterised by different scaling exponents. We find that the power-law forcing leads to dimensional (K41-like) scaling, while the large-scale forcing entails anomalous scaling.

  4 citations

• Hamiltonian structure of 2D fluid dynamics with broken parity

  Gustavo Machado Monteiro, Alexander G. Abanov, Sriram Ganeshan

  SciPost Phys. 14, 103 (2023) · published 10 May 2023 | Toggle abstract · pdf

  Isotropic fluids in two spatial dimensions can break parity symmetry and sustain transverse stresses which do not lead to dissipation. Corresponding transport coefficients include odd viscosity, odd torque, and odd pressure. We consider an isotropic Galilean invariant fluid dynamics in the adiabatic regime with momentum and particle density conservation. We find conditions on transport coefficients that correspond to dissipationless and separately to Hamiltonian fluid dynamics. The restriction on the transport coefficients will help identify what kind of hydrodynamics can be obtained by coarse-graining a microscopic Hamiltonian system. Interestingly, not all parity-breaking transport coefficients lead to energy conservation and, generally, the fluid dynamics is energy conserving but not Hamiltonian. We show how this dynamics can be realized by imposing a nonholonomic constraint on the Hamiltonian system.

  7 citations

• A gauge theory for shallow water

  David Tong

  SciPost Phys. 14, 102 (2023) · published 9 May 2023 | Toggle abstract · pdf

  The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a $d=2+1$ dimensional Abelian gauge theory. The magnetic field corresponds to the conserved height of the fluid, while the electric charge corresponds to the conserved vorticity. In a certain linearised approximation, the shallow water equations reduce to relativistic Maxwell-Chern-Simons theory. This describes Poincaré waves. The chiral edge modes of the theory are identified as coastal Kelvin waves.

  16 citations

• Anti-holomorphic modes in vortex lattices

  Brook J. Hocking, Thomas Machon

  SciPost Phys. 14, 080 (2023) · published 24 April 2023 | Toggle abstract · pdf

  A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedure, secondly by taking the long-wavelength limit of Tkachenko's exact solution for a triangular vortex lattice. Solutions to the continuum theory are found, described by arbitrary anti-holomorphic functions, and give power-law localized edge modes. Numerical results for finite lattices show excellent agreement to the theory.

• From ray tracing to waves of topological origin in continuous media

  Antoine Venaille, Yohei Onuki, Nicolas Perez, Armand Leclerc

  SciPost Phys. 14, 062 (2023) · published 5 April 2023 | Toggle abstract · pdf

  Continuous media commonly support a discrete number of wave modes that are trapped along interfaces defined by spatially varying parameters. In the case of multicomponent wave problems, those trapped modes fill a frequency gap between different wave bands. When they are robust against continuous deformations of parameters, such waves are said to be of topological origin. It has been realized over the last decades that waves of topological origin can be predicted by computing a single topological invariant, the first Chern number, in a dual bulk wave problem that is much simpler to solve than the original wave equation involving spatially varying coefficients. The correspondence between the simple bulk problem and the more complicated interface problem is usually justified by invoking an abstract index theorem. Here, by applying ray tracing machinery to the paradigmatic example of equatorial shallow water waves, we propose a physical interpretation of this correspondence. We first compute ray trajectories in the phase space given by position and wavenumber of the wave packet, using Wigner-Weyl transforms. We then apply a quantization condition to describe the spectral properties of the original wave operator. This bridges the gap between previous work by Littlejohn and Flynn showing manifestation of Berry curvature in ray tracing equations, and more recent studies that computed the Chern number of flow models by integrating the Berry curvature over a closed surface in parameter space. We find that an integral of Berry curvature over this closed surface emerges naturally from the quantization condition, which allows us to recover the bulk-interface correspondence.

  13 citations

• Interplay of Kelvin-Helmholtz and superradiant instabilities of an array of quantized vortices in a two-dimensional Bose-Einstein condensate

  Luca Giacomelli, Iacopo Carusotto

  SciPost Phys. 14, 025 (2023) · published 28 February 2023 | Toggle abstract · pdf

  We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose–Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin–Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI can resonantly couple to acoustic excitations propagating away in the bulk fluid on both sides. This makes the KHI rate to be effectively suppressed and other mechanisms to dominate: For finite and relatively small systems along the transverse direction, the instability involves a repeated superradiant scattering of sound waves off the vortex lattice; for transversally unbound systems, a radiative instability dominates, leading to the simultaneous growth of a localized wave along the vortex lattice and of acoustic excitations propagating away in the bulk. Finally, for slow velocities, where the KHI rate is intrinsically slow, another instability associated to the rigid lateral displacement of the vortex lattice due to the vicinity of the system's boundary is found to dominate.

  7 citations

• Topological quantum computation using analog gravitational holonomy and time dilation

  Emil Génetay Johansen, Tapio Simula

  SciPost Phys. Core 6, 005 (2023) · published 1 February 2023 | Toggle abstract · pdf

  Non-universal topological quantum computation models, such as the Majorana fermion-based Ising anyon model, have to be supplemented with an additional non-topological noisy gate in order to achieve universality. Here we endeavour to remedy this using an Einstein­—Cartan analog gravity picture of scalar fields. Specifically, we show that the analog gravity picture enables unitary transformations to be realized in two distinct ways: (i) via space-time holonomy and (ii) as gravitational time dilation. The non-abelian geometric phases are enabled by gravitational interactions, which are mediated by the spin-connection. We analytically compute its matrix elements as a function of the scalar field density distribution. This density can be regarded as the gravitating distribution of matter in an analog universe. We show via explicit calculations that there exists an infinite set of asymptotically flat analog gravitational fields, each of which implements a unique unitary transformation, that render the interactions topological. We emphasise the generality of this result by asserting that such gravitational gates could potentially be implemented in a broad range of real systems modeled by scalar field with an acoustic metric.

  1 citation

• A splash in a one-dimensional cold gas

  Subhadip Chakraborti, Abhishek Dhar, P. L. Krapivsky

  SciPost Phys. 13, 074 (2022) · published 29 September 2022 | Toggle abstract · pdf

  We consider a set of hard point particles distributed uniformly with a specified density on the positive half-line and all initially at rest. The particle masses alternate between two values, $m$ and $M$. The particles interact via collisions that conserve energy and momentum. We study the cascade of activity that results when the left-most particle is given a positive velocity. At long times we find that this leads to two fascinating features in the observed dynamics. First, in the bulk of the gas, a shock front develops separating the cold gas from a thermalized region. The shock-front travels sub-ballistically, with the bulk described by self-similar solutions of Euler hydrodynamics. Second, there is a splash region formed by the recoiled particles which move ballistically with negative velocities. The splash region is completely non-hydrodynamic and we propose two conjectures for the long time particle dynamics in this region. We provide a detailed analytic understanding of these coexisting regimes. These are supported by the results of molecular dynamics simulations.

  5 citations

• Enstrophy without boost symmetry

  Natalia Pinzani-Fokeeva, Amos Yarom

  SciPost Phys. 12, 136 (2022) · published 21 April 2022 | Toggle abstract · pdf

  We construct an approximately conserved current for $2+1$ dimensional, Aristotelian (non boost invariant), fluid flow. When Aristotelian symmetry is enhanced to Galilean symmetry, this current matches the enstrophy current responsible for the inverse cascade in incompressible fluids. Other enhancements of Aristotelian symmetry discussed in this work include Lorentzian, Carrollian and Lifshitz scale symmetry.

  3 citations

• Enstrophy from symmetry

  Raja Marjieh, Natalia Pinzani-Fokeeva, Amos Yarom

  SciPost Phys. 12, 085 (2022) · published 9 March 2022 | Toggle abstract · pdf

  We study symmetry principles associated with the approximately conserved enstrophy current, responsible for the inverse energy cascade in non relativistic 2+1 dimensional turbulence. We do so by identifying the accidental symmetry associated with enstrophy current conservation in a recently realized effective action principle for hydrodynamics. Our analysis deals with both relativistic and non relativistic effective actions and their associated symmetries.

  3 citations