# Publications

## Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers.

Nat Mater (2021)

Actomyosin machinery endows cells with contractility at a single-cell level. However, within a monolayer, cells can be contractile or extensile based on the direction of pushing or pulling forces exerted by their neighbours or on the substrate. It has been shown that a monolayer of fibroblasts behaves as a contractile system while epithelial or neural progentior monolayers behave as an extensile system. Through a combination of cell culture experiments and in silico modelling, we reveal the mechanism behind this switch in extensile to contractile as the weakening of intercellular contacts. This switch promotes the build-up of tension at the cell-substrate interface through an increase in actin stress fibres and traction forces. This is accompanied by mechanotransductive changes in vinculin and YAP activation. We further show that contractile and extensile differences in cell activity sort cells in mixtures, uncovering a generic mechanism for pattern formation during cell competition, and morphogenesis.

## Bacteria solve the problem of crowding by moving slowly (Nov, 10.1038/s41567-020-01070-6, 2020)

NATURE PHYSICS (2021)

## Roadmap on emerging concepts in the physical biology of bacterial biofilms: from surface sensing to community formation.

Physical biology (2021)

Bacterial biofilms are communities of bacteria that exist as aggregates that can adhere to surfaces or be free-standing. This complex, social mode of cellular organization is fundamental to the physiology of microbes and often exhibits surprising behaviour. Bacterial biofilms are more than the sum of their parts: Single cell behaviour has a complex relation to collective community behaviour, in a manner perhaps cognate to the complex relation between atomic physics and condensed matter physics. Biofilm microbiology is a relatively young field by biology standards, but it has already attracted intense attention from physicists. Sometimes, this attention takes the form of seeing biofilms as inspiration for new physics. In this roadmap, we highlight the work of those who have taken the opposite strategy: We highlight work of physicists and physical scientists who use physics to engage fundamental concepts in bacterial biofilm microbiology, including adhesion, sensing, motility, signalling, memory, energy flow, community formation and cooperativity. These contributions are juxtaposed with microbiologists who have made recent important discoveries on bacterial biofilms using state-of-the-art physical methods. The contributions to this roadmap exemplify how well physics and biology can be combined to achieve a new synthesis, rather than just a division of labour.

## Local measures enable COVID-19 containment with fewer restrictions due to cooperative effects

EClinicalMedicine (2021)

© 2020 The Authors Background: Many countries worldwide are faced with the choice between the (re)surgence of COVID-19 and endangering the economic and mental well-being of their citizens. While infection numbers are monitored and measures adjusted, a systematic strategy for balancing contact restrictions and socioeconomic life in the absence of a vaccine is currently lacking. Methods: In a mathematical model, we determine the efficacy of regional containment strategies, where contact restrictions are triggered locally in individual regions upon crossing critical infection number thresholds. Our stochastic meta-population model distinguishes between contacts within a region and cross-regional contacts. We use current data on the spread of COVID-19 in Germany, Italy, England, New York State and Florida, including the effects of their individual national lockdowns, and county population sizes obtained from census data to define individual regions. As a performance measure, we determine the number of days citizens will experience contact restrictions over the next 5 years (‘restriction time’) and compare it to an equivalent national lockdown strategy. To extract crucial parameters, we vary the proportion of cross-regional contacts (between 0% and 100%), the thresholds for initiating local measures (between 5 and 20 active infections per 100,000 inhabitants) as well as their duration after infection numbers have returned below the threshold (between 7 and 28 days). We compare performance across the five different countries and test how further subdivision of large counties into independently controlled regions of up to 100,000 or 200,000 inhabitants affects the results. Findings: Our numerical simulations show a substantially reduced restriction time for regional containment, if the effective reproduction number of SARS-CoV-2 without restrictions, R0, is only slightly larger than 1 and the proportion of cross-regional contacts (the so-called leakiness) is low. In Germany, specifically, for R0=1.14, a leakiness of 1% is sufficiently low to reduce the mean restriction time from 468 days (s.d. 3 days) for the national containment strategy to 43 days (s.d. 3 days across simulations) for the regional strategy, when local measures are initiated at 10 infections per 100,000 inhabitants in the past 7 days. For R0=1.28, the allowed leakiness for minimal restriction time reduces to approximately 0.3%. The dependence of the restriction time on the leakiness is threshold-like only for regional containment, due to cooperative effects. It rises to levels similar to the national containment strategy for a leakiness > 10% (517 days national vs. 486 days regional for leakiness 32% and R0=1.14). We find a strong correlation between the population size of each region and the experienced restriction time. For countries with large counties, this can result in only a mild reduction in restriction time for regional containment, which can only be partly compensated by lower thresholds for initiating local measures and increasing their duration. In contrast, further subdividing large counties into smaller units can ensure a strong reduction of the restriction time for the regional strategy. Interpretation: The leakiness, i.e. the proportion of cross-regional contacts, and the regional structure itself were crucial parameters for the performance of the regional strategy. Therefore, regional strategies could offer an adaptive way to contain the epidemic with fewer overall restrictions, if cross-regional infections can be kept below the critical level, which could be achieved without affecting local socioeconomic freedom. Maintaining general hygiene and contact tracing, testing should be intensified to ensure regional measures can be initiated at low infection thresholds, preventing the spread of the disease to other regions before local elimination. While such tight control could lead to more restrictions in the short run, restrictions necessary for long-term containment could be reduced by up to a factor of 10. Our open-source simulation code is freely available and can be readily adapted to other countries. Funding: This work was supported by the Max Planck Society.

## Bacteria solve the problem of crowding by moving slowly

Nature Physics Springer Nature (2020)

Bacteria commonly live attached to surfaces in dense collectives containing billions of cells1. While it is known that motility allows these groups to expand en masse into new territory2,3,4,5, how bacteria collectively move across surfaces under such tightly packed conditions remains poorly understood. Here we combine experiments, cell tracking and individual-based modelling to study the pathogen Pseudomonas aeruginosa as it collectively migrates across surfaces using grappling-hook-like pili3,6,7. We show that the fast-moving cells of a hyperpilated mutant are overtaken and outcompeted by the slower-moving wild type at high cell densities. Using theory developed to study liquid crystals8,9,10,11,12,13, we demonstrate that this effect is mediated by the physics of topological defects, points where cells with different orientations meet one another. Our analyses reveal that when defects with topological charge +1/2 collide with one another, the fast-moving mutant cells rotate to point vertically and become trapped. By moving more slowly, wild-type cells avoid this trapping mechanism and generate collective behaviour that results in faster migration. In this way, the physics of liquid crystals explains how slow bacteria can outcompete faster cells in the race for new territory.

## Contrasting lattice geometry dependent versus independent quantities: Ramifications for Berry curvature, energy gaps, and dynamics

Physical Review B: Condensed Matter and Materials Physics American Physical Society **102** (2020) 165148

In the tight-binding description of electronic, photonic, or cold atomic dynamics in a periodic lattice potential, particle motion is described in terms of hopping amplitudes and potentials on an abstract network of discrete sites corresponding to physical orbitals in the lattice. The physical attributes of the orbitals, including their locations in three-dimensional space, are independent pieces of information. In this paper we identify a notion of geometry-independence: any physical quantity or observable that depends only on the tight-binding parameters (and not on the explicit information about the orbital geometry) is said to be “geometry-independent.” The band structure itself, and for example the Chern numbers of the bands in a two-dimensional system, are geometryindependent, while the Bloch-band Berry curvature is geometry-dependent. Careful identification of geometry-dependent versus independent quantities can be used as a novel principle for constraining a variety of results. By extending the notion of geometry-independence to certain classes of interacting systems, where the many-body energy gap is evidently geometry-independent, we shed new light on a hypothesized relation between many-body energy gaps of fractional Chern insulators and the uniformity of Bloch band Berry curvature in the Brillouin zone. We furthermore explore the geometry-dependence of semiclassical wave packet dynamics, and use this principle to show how two different types of Hall response measurements may give markedly different results due to the fact that one is geometry-dependent, while the other is geometry-independent. Similar considerations apply for anomalous thermal Hall response, in both electronic and spin systems.

## Glide symmetry breaking and Ising criticality in the quasi-1D magnet CoNb2O6

Proceedings of the National Academy of Sciences National Academy of Sciences **117** (2020) 25219-25224

We construct a microscopic spin-exchange Hamiltonian for the quasi–one-dimensional (1D) Ising magnet CoNb2O6 that captures detailed and hitherto-unexplained aspects of its dynamic spin structure factor. We perform a symmetry analysis that recalls that an individual Ising chain in this material is buckled, with two sites in each unit cell related by a glide symmetry. Combining this with numerical simulations benchmarked against neutron scattering experiments, we argue that the single-chain Hamiltonian contains a staggered spin-exchange term. We further argue that the transverse-field–tuned quantum critical point in CoNb2O6 corresponds to breaking this glide symmetry, rather than an on-site Ising symmetry as previously believed. This gives a unified microscopic explanation of the dispersion of confined states in the ordered phase and quasiparticle breakdown in the polarized phase at high transverse field.

## Scalar Active Mixtures: The Nonreciprocal Cahn-Hilliard Model

Physical Review X **10** (2020)

© 2020 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society. Pair interactions between active particles need not follow Newton's third law. In this work, we propose a continuum model of pattern formation due to nonreciprocal interaction between multiple species of scalar active matter. The classical Cahn-Hilliard model is minimally modified by supplementing the equilibrium Ginzburg-Landau dynamics with particle-number-conserving currents, which cannot be derived from a free energy, reflecting the microscopic departure from action-reaction symmetry. The strength of the asymmetry in the interaction determines whether the steady state exhibits a macroscopic phase separation or a traveling density wave displaying global polar order. The latter structure, which is equivalent to an active self-propelled smectic phase, coarsens via annihilation of defects, whereas the former structure undergoes Ostwald ripening. The emergence of traveling density waves, which is a clear signature of broken time-reversal symmetry in this active system, is a generic feature of any multicomponent mixture with microscopic nonreciprocal interactions.

## Flow states and transitions of an active nematic in a three-dimensional channel

Physical Review Letters American Physical Society **125** (2020) 148002

We use active nematohydrodynamics to study the flow of an active fluid in a 3D microchannel, finding a transition between active turbulence and regimes where there is a net flow along the channel. We show that the net flow is only possible if the active nematic is flow aligning and that, in agreement with experiments, the appearance of the net flow depends on the aspect ratio of the channel cross section. We explain our results in terms of when the hydrodynamic screening due to the channel walls allows the emergence of vortex rolls across the channel.

## Stochastic effects on the dynamics of an epidemic due to population subdivision.

Chaos (Woodbury, N.Y.) **30** (2020) 101102-

Using a stochastic susceptible-infected-removed meta-population model of disease transmission, we present analytical calculations and numerical simulations dissecting the interplay between stochasticity and the division of a population into mutually independent sub-populations. We show that subdivision activates two stochastic effects-extinction and desynchronization-diminishing the overall impact of the outbreak even when the total population has already left the stochastic regime and the basic reproduction number is not altered by the subdivision. Both effects are quantitatively captured by our theoretical estimates, allowing us to determine their individual contributions to the observed reduction of the peak of the epidemic.

## Spin crossovers and superdiffusion in the one-dimensional Hubbard model

Physical Review B American Physical Society **102** (2020) 115121

We use tools from integrability and generalized hydrodynamics to study finite-temperature dynamics in the one-dimensional Hubbard model. First, we examine charge, spin, and energy transport away from half-filling and zero magnetization, focusing on the strong coupling regime where we identify a rich interplay of temperature and energy scales, with crossovers between distinct dynamical regimes. We identify an intermediate-temperature regime analogous to the spin-incoherent Luttinger liquid, where spin degrees of freedom are hot but charge degrees of freedom are at low temperature. We demonstrate that the spin Drude weight exhibits sharp features at the crossover between this regime and the low-temperature Luttinger liquid regime, which are absent in the charge and energy response, and rationalize this behavior in terms of the properties of Bethe ansatz quasiparticles. We then turn to the dynamics along special lines in the phase diagram corresponding to half-filling and/or zero magnetization where on general grounds we anticipate that the transport is subballistic but superdiffusive. We provide analytical and numerical evidence for Kardar-Parisi-Zhang (KPZ) dynamical scaling (with length and time scales related via x ∼ t 2 / 3 ) along both lines and at the SO ( 4 ) -symmetric point where they intersect. Our results suggest that both spin-coherence crossovers and KPZ scaling may be accessed in near-term experiments with optical lattice Hubbard emulators.

## Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions

SciPost Physics **9** (2020)

© 2020 SciPost Foundation. All rights reserved. We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models.

## Measurement-induced steering of quantum systems

Phys. Rev. Research **2** (2020) 033347-033347

We set out a general protocol for steering the state of a quantum system from an arbitrary initial state towards a chosen target state by coupling it to auxiliary quantum degrees of freedom. The protocol requires multiple repetitions of an elementary step: during each step the system evolves for a fixed time while coupled to auxiliary degrees of freedom (which we term 'detector qubits') that have been prepared in a specified initial state. The detectors are discarded at the end of the step, or equivalently, their state is determined by a projective measurement with an unbiased average over all outcomes. The steering harnesses back-action of the detector qubits on the system, arising from entanglement generated during the coupled evolution. We establish principles for the design of the system-detector coupling that ensure steering of a desired form. We illustrate our general ideas using both few-body examples (including a pair of spins-1/2 steered to the singlet state) and a many-body example (a spin-1 chain steered to the Affleck-Kennedy-Lieb-Tasaki state). We study the continuous time limit in our approach and discuss similarities to (and differences from) drive-and-dissipation protocols for quantum state engineering. Our protocols are amenable to implementations using present-day technology. Obvious extensions of our analysis include engineering of other many-body phases in one and higher spatial dimensions, adiabatic manipulations of the target states, and the incorporation of active error correction steps.

## Collective chemotaxis of active nematic droplets

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics American Physical Society **102** (2020) 020601

Collective chemotaxis plays a key role in the navigation of cell clusters in e.g. embryogenesis and cancer metastasis. Using the active nematic continuum equations, coupled to a chemical field that regulates activity, we demonstrate and explain a physical mechanism that results in collective chemotaxis. The activity naturally leads to cell polarisation at the cluster interface which induces outwards flows. The chemical gradient then breaks the symmetry of the flow field, leading to a net motion. The velocity is independent of the cluster size in agreement with experiment.

## Active inter-cellular forces in collective cell motility.

Journal of the Royal Society, Interface **17** (2020) 20200312-20200312

The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion, and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We use a phase-field model to explore the interplay between these two contributions and compare the dynamics of a cell sheet when the polarity of the cells aligns to (i) their main axis of elongation, (ii) their velocity and (iii) when the polarity direction executes a persistent random walk. In all three cases, we observe a sharp transition from a jammed state (where cell rearrangements are strongly suppressed) to a liquid state (where the cells can move freely relative to each other) when either the polar or the inter-cellular forces are increased. In addition, for case (ii) only, we observe an additional dynamical state, flocking (solid or liquid), where the majority of the cells move in the same direction. The flocking state is seen for strong polar forces, but is destroyed as the strength of the inter-cellular activity is increased.

## Quantum Hall network models as Floquet topological insulators

Phys. Rev. Lett. **125** (2020) 086601-086601

Network models for equilibrium integer quantum Hall (IQH) transitions are described by unitary scattering matrices, that can also be viewed as representing non-equilibrium Floquet systems. The resulting Floquet bands have zero Chern number, and are instead characterized by a chiral Floquet (CF) winding number. This begs the question: How can a model without Chern number describe IQH systems? We resolve this apparent paradox by showing that non-zero Chern number is recovered from the network model via the energy dependence of network model scattering parameters. This relationship shows that, despite their topologically distinct origins, IQH and CF topology-changing transitions share identical universal scaling properties.

## Degenerate states, emergent dynamics and fluid mixing by magnetic rotors.

Soft matter **16** (2020) 6484-6492

We investigate the collective motion of magnetic rotors suspended in a viscous fluid under a uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a 3 × 3 array of magnets, we observe three characteristic dynamical patterns as the external field strength is varied: a synchronized pattern, an oscillating pattern, and a chessboard pattern. The relative stability of these depends on the competition between the energy due to the external magnetic field and the energy of the magnetic dipole-dipole interactions among the rotors. We argue that the chessboard pattern can be understood as an alternation in the stability of two degenerate states, characterized by striped and spin-ice configurations, as the applied magnetic field rotates. For larger arrays, we observe propagation of slip waves that are similar to metachronal waves. The rotor arrays have potential as microfluidic devices that can mix fluids and create vortices of different sizes.

## Transport properties of multilayer graphene

Physical Review B American Physical Society **101** (2020) 245438

We apply the semi-classical Boltzmann formalism for the computation of transport properties to multilayer graphene. We compute the electrical conductivity as well as the thermal conductivity and thermopower for Bernal-stacked multilayers with an even number of layers. We show that the window for hydrodynamic transport in multilayer graphene is similar to the case of bilayer graphene. We introduce a simple hydrodynamic model which we dub the multi-fluid model and which can be used to reproduce the results for the electrical conductivity and thermopower from the semi-classical Boltzmann equation.

## Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions

in *Fractional Quantum Hall Effects: New Developments*, World Scientific (2020)

## Cooperatively enhanced reactivity and "stabilitaxis" of dissociating oligomeric proteins.

Proceedings of the National Academy of Sciences of the United States of America **117** (2020) 11894-11900

Many functional units in biology, such as enzymes or molecular motors, are composed of several subunits that can reversibly assemble and disassemble. This includes oligomeric proteins composed of several smaller monomers, as well as protein complexes assembled from a few proteins. By studying the generic spatial transport properties of such proteins, we investigate here whether their ability to reversibly associate and dissociate may confer on them a functional advantage with respect to nondissociating proteins. In uniform environments with position-independent association-dissociation, we find that enhanced diffusion in the monomeric state coupled to reassociation into the functional oligomeric form leads to enhanced reactivity with localized targets. In nonuniform environments with position-dependent association-dissociation, caused by, for example, spatial gradients of an inhibiting chemical, we find that dissociating proteins generically tend to accumulate in regions where they are most stable, a process that we term "stabilitaxis."