Publications

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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 | · 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
Enstrophy from symmetry

Raja Marjieh, Natalia Pinzani-Fokeeva, Amos Yarom

SciPost Phys. 12, 085 (2022) · published 9 March 2022 | · 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
The friction of tilted skates on ice

J. M. J. van Leeuwen

SciPost Phys. 8, 059 (2020) · published 16 April 2020 | · pdf

The friction felt by a speed skater is calculated as function of the velocity and tilt angle of the skate. This calculation is an extension of the more common theory of friction of upright skates. Not only in rounding a curve the skate has to be tilted, but also in straightforward skating small tilt angles occur, which turn out to be of noticeable influence on the friction. As for the upright skate the friction remains fairly insensitive of the velocities occurring in speed skating.

3 citations
On quantum melting of superfluid vortex crystals: From Lifshitz scalar to dual gravity

Dung Xuan Nguyen, Sergej Moroz

SciPost Phys. 17, 164 (2024) · published 11 December 2024 | · pdf

Despite a long history of studies of vortex crystals in rotating superfluids, their melting due to quantum fluctuations is poorly understood. Here we develop a fracton-elasticity duality to investigate a two-dimensional vortex lattice within the fast rotation regime, where the Lifshitz model of the collective Tkachenko mode serves as the leading-order low-energy effective theory. We incorporate topological defects and discuss several quantum melting scenarios triggered by their proliferation. Furthermore, we lay the groundwork for a dual non-linear emergent gravity description of the superfluid vortex crystals.

3 citations
Enstrophy without boost symmetry

Natalia Pinzani-Fokeeva, Amos Yarom

SciPost Phys. 12, 136 (2022) · published 21 April 2022 | · 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
The functional generalization of the Boltzmann-Vlasov equation and its gauge-like symmetry

Giorgio Torrieri

SciPost Phys. 16, 070 (2024) · published 11 March 2024 | · pdf

We argue that one can model deviations from the ensemble average in non-equilibrium statistical mechanics by promoting the Boltzmann equation to an equation in terms of functionals , representing possible candidates for phase space distributions inferred from a finite observed number of degrees of freedom. We find that, provided the collision term and the Vlasov drift term are both included, a gauge-like redundancy arises which does not go away even if the functional is narrow. We argue that this effect is linked to the gauge-like symmetry found in relativistic hydrodynamics [Ann. Phys. 442, 168902 (2022)] and that it could be part of the explanation for the apparent fluid-like behavior in small systems in hadronic collisions and other strongly-coupled small systems [Annu. Rev. Nucl. Part. Sci. 68, 211 (2018)]. When causality and Lorentz invariance are omitted this problem can be look at via random matrix theory show, and we show that in such a case thermalization happens much more quickly than the Boltzmann equation would infer. We also sketch an algorithm to study this problem numerically.

3 citations
Identifying diffusive length scales in one-dimensional Bose gases

Frederik Møller, Federica Cataldini, Jörg Schmiedmayer

SciPost Phys. Core 7, 025 (2024) · published 7 May 2024 | · pdf

In the hydrodynamics of integrable models, diffusion is a subleading correction to ballistic propagation. Here we quantify the diffusive contribution for one-dimensional Bose gases and find it most influential in the crossover between the main thermodynamic regimes of the gas. Analysing the experimentally measured dynamics of a single density mode, we find diffusion to be relevant only for high wavelength excitations. Instead, the observed relaxation is solely caused by a ballistically driven dephasing process, whose time scale is related to the phonon lifetime of the system and is thus useful to evaluate the applicability of the phonon bases typically used in quantum field simulators.

3 citations
Python-JAX-based fast Stokesian dynamics

Kim William Torre, Raoul D. Schram, Joost de Graaf

SciPost Phys. Codebases 56 (2025) · published 30 June 2025 | · pdf

Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on the inversion of large mobility matrices to determine hydrodynamic interactions. Recently, however, the simulation of thermalized systems with large numbers of particles has become feasible [Fiore and Swan, J. Fluid Mech. 878, 544 (2019)]. Their "fast Stokesian dynamics" (FSD) method leverages a saddle-point formulation to ensure overall scaling of the algorithm that is linear in the number of particles $\mathcal{O}(N)$; performance relies on dedicated graphics-processing-unit computing. Here, we present a different route toward implementing FSD, which instead leverages the Just-in-Time (JIT) compilation capabilities of Google JAX. We refer to this implementation as JFSD and perform benchmarks on it to verify that it has the right scaling and is sufficiently fast by the standards of modern computational physics. In addition, we provide a series of physical test cases that help ensure accuracy and robustness, as the code undergoes further development. Thus, JFSD is ready to facilitate the study of hydrodynamic effects in particle suspensions across the domains of soft, active, and granular matter.

2 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 | · 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
Codebase release 0.2 for JFSD

Kim William Torre, Raoul D. Schram, Joost de Graaf

SciPost Phys. Codebases 56-r0.2 (2025) · published 30 June 2025 | · src

Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on the inversion of large mobility matrices to determine hydrodynamic interactions. Recently, however, the simulation of thermalized systems with large numbers of particles has become feasible [Fiore and Swan, J. Fluid Mech. 878, 544 (2019)]. Their "fast Stokesian dynamics" (FSD) method leverages a saddle-point formulation to ensure overall scaling of the algorithm that is linear in the number of particles $\mathcal{O}(N)$; performance relies on dedicated graphics-processing-unit computing. Here, we present a different route toward implementing FSD, which instead leverages the Just-in-Time (JIT) compilation capabilities of Google JAX. We refer to this implementation as JFSD and perform benchmarks on it to verify that it has the right scaling and is sufficiently fast by the standards of modern computational physics. In addition, we provide a series of physical test cases that help ensure accuracy and robustness, as the code undergoes further development. Thus, JFSD is ready to facilitate the study of hydrodynamic effects in particle suspensions across the domains of soft, active, and granular matter.

1 citation

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