Hydrodynamics at all length scales:

from high-energy to hard and soft matter

DIEP Workshop | 18th - 22nd November 2019 | @ Lorentz Centre | Snellius | Leiden, Netherlands

Hong Liu

John Toner

Andrei Starinets

Jorge Casalderrey Solana

Akash Jain

Johanna Erdmenger

Jan Zaanen

Jan de Boer

Anna Frishman

Natalia Pinzani-Fokeeva

Martine Ben Amar

Denis Bartolo

Federico Toschi

Nigel Hussey

Andrea Amoretti

Daniel Pearce

Blaise Gouteraux

Organizers: Jácome Armas, Luca Giomi, Erik van Heumen and Amos Yarom

Dirk van der Marel

Koenraad Schalm

Morten Brøns

Paolo Glorioso

Alberto Fernandez-Nieves

Napat Poovuttikul

Piermarco Fonda

Grégoire Mathys

An invitation to hydrodynamics at all length scales

The purpose of the workshop is to bring together theoretical and experimental physicists from high-energy, hard and soft condensed matter physics who work on different aspects of hydrodynamics. We aim at creating an interesting dialogue between these different communities and to identify tools and methods that can be adapted from one community to the other for solving problems in fluid dynamics. The topics will include turbulence, flows on curved spaces, active matter, fluid effective actions, defects and interfaces, effective field theories for hydrodynamics, symmetry-organising principles as well as experimental techniques and challenges

Invited participants (confirmed)

Hong Liu

(MIT)

Jan Zaanen

(University of Leiden)

Akash Jain

(University of Victoria)

Daniel Pearce

(U. Geneva)

John Toner

(University of Oregon)

Martine Ben Amar

(Ecole Normal Supérieure)

Jan de Boer

(University of Amsterdam)

Denis Bartolo

(ENS de Lyon)

Andrei Starinets

(University of Oxford)

Anna Frishman

(Technion)

Federico Toschi

(TU Eindhoven)

Johanna Erdmenger

(Universitat Würzburg)

Nigel Hussey

(Radboud University)

Andrea Amoretti

(INFN, University of Genoa)

Napat Poovuttikul

(University of Iceland)

Blaise Goutéraux

(CPHT Paris)

Morten Brøns

(Danish Technical University)

Dirk van der Marel

(Université de Genève)

Paolo Glorioso

(University of Chicago)

Koenraad Schalm

(University of Leiden)

Piermarco Fonda

(University of Leiden)

Grégoire Mathys

(U. Amsterdam)

Organisers

Corentin Coulais

(University of Amsterdam)

Jasper Van Wezel

(University of Amsterdam)

Jácome Armas

(University of Amsterdam)

Programme (slides below):
Monday, 18th of November
09:30-10:00  Registration & Coffee 
10:00-10:15  Opening Remarks by the Lorentz centre
10:15-10:30  Welcome by the organisers and who's in room?
10:30-11:30  John Toner (abstract)(slides)
11:30-12:00  Coffee & discussions
12:00-12:45  Andrei Starinets (abstract)(slides)
12:45-14:45  Lunch & discussions
14:45-15:30  Jan de Boer (abstract)(blackboard talk)
15:30-16:15  Akash Jain (abstract)(slides)
16:15-16:45  Coffee & discussions
16:45-17:30  Jorge Casalderrey-Solana (abstract)(slides) 
17:30-19:00  Welcoming snacks & drinks & discussions
Tuesday, 19th of November
09:00-09:15  Explanation programme of the day | recap of previous day
09:15-10:15  Dirk van der Marel (abstract)(slides)
10:15-11:00  Johanna Erdmenger (abstract)(slides)
11:00-11:30  Coffee & discussions
11:30-12:15  Koenraad Schalm (abstract)(slides)
12:15-14:15  Lunch & discussions
14:15-15:00  Blaise Gouteraux (abstract)(slides)
15:00-15:45  Andrea Amoretti (abstract)(slides)
15:45-16:15  Coffee & discussions
16:15-17:15  Panel discussion | Moderator: Jan Zaanen
Wednesday, 20th of November
09:00-09:15  Explanation programme of the day | recap of previous day
09:15-10:15  Denis Bartolo (abstract)(no slides)
10:15-11:00  Morten Brøns (abstract)(slides)
11:00-11:30  Coffee & discussions
11:30-12:15  Martine Ben Amar (abstract)(slides)
12:15-14:15  Lunch & discussions
14:15-15:00  Daniel Pearce (abstract)(slides)
15:00-15:45  Piermarco Fonda (abstract)(slides)
15:45-16:15  Coffee & discussions
16:15-17:15  Panel discussion | Moderator: Denis Bartolo
17:15-........  Dinner activities
Thursday, 21st of November
09:00-09:15  Explanation programme of the day | recap of previous day
09:15-10:15  Hong Liu (abstract)(slides)
10:15-11:00  Natalia Pinzani-Fokeeva (abstract)(slides)
11:00-11:30  Coffee & discussions
11:30-12:15  Paolo Glorioso (abstract)(slides)
12:15-14:15  Lunch & discussions
14:15-15:00  Napat Poovuttikul (abstract)(slides)
15:00-15:45  Grégoire Mathys (abstract)(slides)
15:45-16:15  Coffee & discussions
16:15-17:15  Panel discussion | Moderator: Amos Yarom
Friday, 22nd of November
09:00-09:15  Explanation programme of the day | recap of previous day
09:15-10:15  Anna Frishman (abstract)(slides)
10:15-11:00  Federico Toschi (abstract) 
11:00-11:30  Coffee & discussions
11:30-12:15  Alberto Fernandez-Nieves (abstract)(slides)
12:15-14:15  Lunch & discussions
14:15-15:00  Jan Zaanen (abstract)(slides)
15:00-15:45  Goodbye & Coffee
Abstract (John Toner): Birth, Death, and Flight: the hydrodynamics of Malthusian flocks
I'll present the hydrodynamic theory of ``Malthusian Flocks": moving aggregates of self-propelled entities (e.g., organisms, cytoskeletal actin, microtubules in mitotic spindles) that reproduce and die. Long-ranged order (i.e., the existence of  a non-zero average velocity <v (r, t)>=! 0) is possible in these systems, even in spatial dimension d=2. Their spatiotemporal scaling structure can be determined exactly in d=2;  furthermore, they  lack both  the longitudinal sound waves and the giant number fluctuations found in immortal flocks. Number fluctuations are very persistent, and propagate along the direction of flock motion, but at a different speed. I'll also present recent results for the three dimensional version of this problem, which required the first full blown dynamical renormalization treatment of a flocking system in its ordered phase.
Abstract (Johanna Erdmenger): New materials for holographic hydrodynamics
We teamed up with some condensed matter theorists in our department to suggest a new material in which holographic hydrodynamics is expected to be realized even better than in graphene.
Abstract (Denis Bartolo): Hydrodynamics of Flocks and Crowds: a Guliver travel
TBA
Abstract (Jan Zaanen): Dense entanglement and the hydrodynamical nature of the cuprate strange metal state
Presently the subject of hydrodynamical flows of electrons in condensed matter systems is a booming affair. This revolves around conventional Fermi-liquids realized in extremely clean materials such as graphene where the disorder length scale becomes even larger than the large electron-electron collision length. However, perhaps the most promising application of generic holographic wisdom for the condensed matter laboratory is in the prediction that despite their dirty nature hydro may apply to the cuprate metallic state as well (J. Zaanen, SciPost Phys. 6, 061 (2019); arXiv:1807.10951). The line of reasoning is that these strange metals are supposedly densely many-body entangled and according to holography such substances should be characterized by the minimal viscosity principle. Given the very small entropy density of the strange metals their viscosity should in fact be extremely small giving room for hydro flows even in the presence of microscopic disorder.  I will review some very recent, serendipitous experimental developments that appear to give a stunning support for this outrageous hypothesis.
Abstract (Morten Brøns): Bifurcations of vortex structures in two-dimensional flows
Vortices are coherent structures of rotating fluid elements. They are ubiquitous in flows in nature and technology, and occur at all length scales. While vortices are easy to identify in specific flow by visual inspection, for example by locating regions of concentrated vorticity, a formal mathematical definition is difficult to obtain. While no generally accepted definition exists, many attempts are available. I will discuss two vortex definitions, one based on the topology of the vorticity field, and one based on an invariant of the velocity gradient tensor, the Q-criterion. The talk focuses on how to develop a bifurcation theory for vortices from these definitions, with the purpose of rigorously describing vortex creation and merging. The theory is illustrated with computational studies of the creation of the von K·rm·n vortex street behind a cylinder, and eruption of vortices from a boundary layer.
Abstract (Napat Poovuttikul): Breakdown of first order hydrodynamics and almost conserved currents 

One explanation for an almost universal application of hydrodynamic is that it is a gradient expansion of Noether currents. 
However, there is a big caveat, well-known in the relativistic fluid context, that there is an ambiguity in choosing macroscopic variables and that choosing the "wrong" one results in a theory with linear instability. I want to show that such ambiguity is not unique to relativistic fluids but can happen in generic first order hydrodynamics. 

There are ways in which relativists got rid of this problem, inspired by kinetic theory, by phenomenologically introducing new macroscopic variables. I will discuss how these phenomenological models can be understood in terms of almost conserved currents in memory matrix formalism. If time allows, I will discuss how these almost conservation laws are encoded in the holographic dual. 

Abstract (Dirk van der Marel): Anomalous free charge carriers in Nd2Ir2O7 

An introduction will be given on the progress in experimental probes of hydrodynamics in solids. Particular attention will be given to early transport experiments on Poisseuil flow, and experiments on graphene as well as experimental probes of hydrodynamics at finite frequencies. I will then move to a recent study in Geneva on Nd2Ir2O7 a strongly correlated semimetal with the pyrochlore structure where spin-orbit coupling and electron-electron interactions compete. Among other things a time-reversal symmetry broken Weyl semi-metal (WSM) phase has been predicted, characterized by pairs of topologically protected Dirac points at the Fermi energy. We observe that below 40 K the free carrier spectral weight grows with temperature as  wp^2 = a T^2. On the one hand this is the expected behavior of free charge carriers having a massless Dirac dispersion. On the other hand we expect to find a corresponding T^3 contribution to the entropy, which however we don’t observe in the entropy calculated from the specific heat. For the same range of temperatures we observe that the interband optical conductivity below 20 meV is progressively suppressed. The anomalous transfer of spectral weight over at least 2 eV indicates that this breakdown is associated to « Mottness" e.g. a sensitivity to local interactions and proximity to a Mott insulating phase. The momentum relaxation time of the free carriers has a Planckian 1/T  temperature dependence below 40 K. These observations can not be reconciled within the framework of band theory of electron-like quasiparticles. Instead our observations point toward the collective nature of the low energy charge degrees of freedom in this system. 

Abstract (Martine Ben Amar): Clonal pattern dynamics in tumor: the concept of cancer stem cells  

In this talk, I will  present a multiphase model for solid tumor  initiation and progression focusing on the properties of cancer stem cells (CSC). CSCs are  a small and singular cell sub-population having outstanding capacities: high proliferation rate, self-renewal and extreme  therapy resistance. Our model  takes all these factors into account under a recent perspective: the possibility of phenotype switching of differentiated cancer cells (DC)  to the stem cell state, mediated by chemical activators.  This plasticity of cancerous cells  complicates the complete eradication of CSCs and  the tumor suppression. The model in itself requires a sophisticated treatment of  population dynamics driven by chemical factors. Three fixed points guide the dynamics, and  two of them may lead to an optimistic issue, predicting either a control of the cancerous cell population or a complete eradication. The space environment, critical  for the tumor outcome, is introduced via  a density formalism. Patterns will be presented and discussed.

 

Reference: F. Olmeda and M. Ben Amar,”Clonal pattern dynamics in tumor: the concept of cancer stem cells”, Nature: Scientific Reports, October 2019.

Abstract (Andrea Amoretti): A hydrodynamical description for transport in the strange metal phase of cuprates

High temperature superconductors are strongly coupled systems which present a complicated phase diagram with many coexisting phases. This makes it difficult to understand the mechanism which generates their singular transport properties. Hydrodynamics, which mostly relies on the symmetries of the system without referring to any specific microscopic mechanism, constitutes a promising framework to analyze these materials. In this talk I will show that in the strange metal phase of the cuprates, a whole set of transport coefficients are described by a universal hydrodynamic framework. We corroborate our theoretical prediction by measuring the DC transport properties of Bi-2201 close to optimal doping, proving the validity of our approach. Our argument can be used as a consistency check to understand the universality class governing the behavior of high temperature cuprate superconductors.

Abstract (Blaise Goutéraux): Universal relaxation of pinned density waves in Condensed Matter and Holography

Phases with spontaneously broken translations are characterized by the emergence of new gapless degrees of freedom, which are Goldstone bosons. In the presence of weak disorder, the Goldstones become massive and damped. The mass and the damping rate are determined by the microscopic details of the disorder distributions. I will discuss two class of examples, electronic Wigner solids in 2d electron gases at high magnetic fields and a holographic 'Q-lattice', where the relaxation of the Goldstones in the presence of disorder is universal, in the sense that their ratio is determined by a diffusivity of the clean system. 

Abstract (Koenraad Schalm): Detecting chaos in hydrodynamics 

Hydrodynamics assumes local equilibration and equilibration assumes ergodic mixing driven by chaos --- at least in semi-classical systems. For a generic such system the timescales of macroscopic thermalization and onset of microscopic chaos are very different. Nevertheless, it is a pillar of Boltzmann transport that long-time equilibration can be computed from microscopic dynamics. We show how in these systems the two timescales are in fact related. Moreover, we show that a similar connection between both scales surprisingly also exists in extremely strongly coupled systems through a phenomenon christened pole-skipping in hydrodynamic response.

Abstract (Alberto Fernandez-Nieves): Topological defects in active nematics

We will discuss recent results with active nematics confined to either toroidal or flat space. We will first describe how curvature affects defect arrangement on tori. We will show that despite the intrinsic activity and out-of-equilibrium character of the system, there are still remnants of the expected curvature-induced defect unbinding predicted for nematics in their ground state. Activity, however, augments the behavior leading to unexpected defect distributions. We will then focus on defect orientation and show that on flat space, there is short-range orientational correlations without long-range orientational order.

Abstract (Andrei Starinets): Fluid dynamics, quark-gluon plasma, and quasinormal spectra of black holes

Heavy ion collision programs at RHIC and LHC instigated  a renewal of theoretical interest in relativistic hydrodynamics as an effective theory. The collisions create hot and dense nuclear matter known as the strongly coupled quark-gluon plasma: the parameters of the plasma can be measured with remarkable precision but its theoretical study is hindered by the strong non-perturbative effects of thermal QCD. At the same time, strongly interacting gauge theories at finite temperature and density can be investigated via holographic duality, connecting them to classical black hole space-times in higher dimensions. In particular, spectra of quasiparticle excitations in the strongly coupled plasmas are mapped into the quasinormal spectra of black holes, whose dying whispers tell us about plasma's viscosity and other transport coefficients, and set the limits on the fluid dynamics description. In the talk, we review the current status of this line of research, and reflect on recent advances in our understanding of gauge theory plasmas in the regime of intermediate coupling provided by dual gravity with higher derivative terms. We also discuss the issue of the convergence of the series representing collective excitations of the strongly coupled fluid and the related phenomenon of quasinormal spectrum level-crossing.

Abstract (Akash Jain): Hydrodynamic Framework for Viscoelasticity

The theory of viscoelasticity describes near equilibrium thermal fluctuations in a crystalline solid. It can be setup within the hydrodynamic framework by including Goldstones for spontaneously broken translations. These goldstones model the spatial arrangement of lattice sites in the continuum limit. We setup a generic framework capable of describing low-energy fluctuations of (liquid) crystals in the hydrodynamic regime. We compare our formulation to the existing holographic models of viscoelasticity and comment on some discrepancies. We also present briefly a dual formulation for viscoelasticity in terms of generalised global symmetries. The talk is based on [arXiv:1908.01175].

Abstract (Hong Liu): Effective field theory approach to fluctuating hydrodynamics and an application to quantum many-body chaos

TBA

Abstract (Jorge Casalderrey Solana): Holographic Collisions and Hydrodynamics across a Phase Transition

We use holography to analyze relativistic collisions in a one-parameter family of strongly coupled gauge theories with thermal phase transitions. For a critical value of the parameter, the transition is second order, for subcritical values it is first order, and for supercritical values it a smooth crossover. We extract the gauge theory stress tensor from collisions of gravitational shock waves on the dual geometries. Regardless of the nature of the transition, for values of the parameter close to the critical value, almost all the energy of the projectiles is deposited into a long-lived, quasistatic blob of energy. This configuration is well described by the constitutive relations of second-order hydrodynamics that include all second-order gradients that are purely spatial in the local rest frame. In contrast, a Müller-Israel-Stewart-type formulation of hydrodynamics fails to provide a good description.

Abstract (Anna Frishman): How turbulence organizes itself---a story in two dimensions 

Turbulence is a state with many interacting degrees of freedom deviated far from equilibrium. It is thus not surprising that a first principles theory of turbulence remains elusive. I will first review basic concepts for homogeneous and isotropic turbulence, and then focus on a two dimensional system which breaks those symmetries---where I will show that a perturbative approach is possible. 

 Apart from being a rich and beautiful fundamental system, 2D turbulence is relevant for the understanding of natural flows such as Jupiters Great Red Spot and its zonal winds, whose dynamics is approximately two dimensional and where persistent large scale flows coexist with turbulent fluctuations.

Indeed, in 2D, turbulence takes a counter-intuitive role: energy is transferred to progressively larger scales, which can terminate in the self organization of the turbulence into a large scale coherent structure, a so called condensate, on top of turbulent fluctuations. I will describe a recent theoretical framework within which the profile of this coherent mean flow can be obtained, along with the mean momentum flux and the main characteristics of the average energy.

Abstract (Grégoire Mathys): Superfluids as Higher-form Anomalies

We recast superfluid hydrodynamics as the hydrodynamic theory of a system with an emergent anomalous higher-form symmetry. The higher-form charge counts the winding planes of the superfluid – its constitutive relation replaces the Josephson relation of conventional superfluid hydrodynamics. This formulation puts all hydrodynamic equations on equal footing. The anomalous Ward identity can be used as an alternative starting point to prove the existence of a Goldstone boson, without reference to spontaneous symmetry breaking. This provides an alternative characterization of Landau phase transitions in terms of higher-form symmetries and their anomalies instead of how the symmetries are realized. As an application of this formalism we construct the hydrodynamic theories of conventional (0-form) and 1-form superfluids.

Abstract (Piermarco Fonda): On the thermodynamics of lipid mixtures on curved substrates

It has been known since long that thermodynamic stability of two-dimensional lipid mixtures is influenced by curvature. Inspired by recent experimental results on lipid membranes coated on colloidal scaffolds, we propose a simple and general framework for interpreting the phase diagram of inhomogeneous closed systems. When the critical behaviour of a system is affected by its shape, we further show how new thermodynamic states can arise in the phase diagram, where lipids are in a mixed phase yet exhibit strong lateral segregation. We prove how different types of inhomogeneous couplings must induce qualitatively different phenomena - such as a curvature dependent line tension - and thus provide a way to distinguish different types of curvature interactions. 

Abstract (Jan de Boer): Perfect fluids without boost symmetry

TBA

Abstract (Daniel Pearce): Defect driven flows in chiral active nematics

Collective cell migration, important in for instance fibrosarcoma-cell invasion and metastasis, can be controlled through confinement geometry. Here, we investigate the emergent  patterns of HT1080 cell assemblies under rectangular confinement using micro-patterning techniques. For a wide range of stripe's width, we observed that HT1080 collective flows exhibit irregular and heterogeneous flows in a domain near the geometric midline, but near the edges coherent net migration arises with a broken left-right mirror symmetry between both edges. Cell shape anisotropy patterns reveal a boundary-layer with increased cell ordering and a well-defined tilt in cell shape orientation with respect to the parallel configuration. A theoretical description of an active nematic fluid including active chiral stresses reproduces the above-mentioned experimental observations for varying stripe's width. We show that the interplay between edge ordering and active chiral stresses give rise to positive-defect orientation tilt, driving net coherent flows near the edges. 

Abstract (Natalia Pinzani-Fokeeva): Effective field theories for hydrodynamics from black holes

I will show how recently developed effective field theories for fluid dynamics can be derived from microscopic theories which admit gravitational holographic duals. The derivation involves a mixed signature bulk spacetime whereby an eternal asymptotically Anti-de Sitter black hole is glued to its Euclidean counterpart along an initial time slice in a way to match the desired double-time contour of the dual field theory. For concreteness I will focus on the example of charge diffusion.

Abstract (Paolo Glorioso): Infrared instability of chiral diffusion

In this talk I will apply the framework of effective field theory of hydrodynamics to the anomalous conservation of a U(1) current, with particular focus on 1+1 dimensions, which may be relevant to edge transport in quantum Hall systems. I will discuss an infrared instability caused by hydrodynamic fluctuations which, contrary to the usual instability of non-chiral hydrodynamics, persists even without momentum conservation. I will then discuss the fate of this instability.

Abstract (Federico Toschi): On the role of vorticity and helicity in turbulence

TBA

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Registration by invitation

Registration for the workshop is by invitation only. For more information, send an e-mail to info@d-iep.org.

Organisers

Jácome Armas

(University of Amsterdam)

Luca Giomi

(University of Leiden)

Erik van Heumen

(University of Amsterdam)

Amos Yarom

(Technion)

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