# LPTMS Publications

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## Archive ouverte HAL – Actin modulates shape and mechanics of tubular membranes

### A. Allard

^{1}M. Bouzid^{2}T. Betz^{3}C. SimonM. Abou-GhaliJ. Lemiere^{4}F. Valentino^{5}J. Manzi^{4}F. Brochard-Wyart^{6}K. Guevorkian^{6}J. Plastino^{6}M. Lenz^{2}C. Campillo^{7}C. Sykes^{6}#### A. Allard, M. Bouzid, T. Betz, C. Simon, M. Abou-Ghali, et al.. Actin modulates shape and mechanics of tubular membranes.

*Science Advances*, American Association for the Advancement of Science (AAAS), 2020, 6 (17), pp.eaaz3050. ⟨10.1126/sciadv.aaz3050⟩. ⟨hal-02565199⟩- 1. LNE - Laboratoire National de Métrologie et d'Essais [Trappes]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Atominstitut
- 4. PCC - Physico-Chimie-Curie
- 5. DTU Space - National Space Institute [Lyngby]
- 6. PCC - Physico-Chimie-Curie
- 7. inconnu

## Archive ouverte HAL – Asymptotic behavior of the length of the longest increasing subsequences of random walks

### J. Ricardo G. Mendonça

^{1}Hendrik Schawe^{2}Alexander K. Hartmann^{3}Alexander Hartmann#### J. Ricardo G. Mendonça, Hendrik Schawe, Alexander K. Hartmann, Alexander Hartmann. Asymptotic behavior of the length of the longest increasing subsequences of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032102⟩. ⟨hal-02512208⟩We numerically estimate the leading asymptotic behavior of the length $L_{n}$ of the longest increasing subsequence of random walks with step increments following Student's $t$-distribution with parameter in the range $1/2 \leq \nu \leq 5$. We find that the expected value $\mathbb{E}(L_{n}) \sim n^{\theta}\ln{n}$ with $\theta$ decreasing from $\theta(\nu=1/2) \approx 0.70$ to $\theta(\nu \geq 5/2) \approx 0.50$. For random walks with distribution of step increments of finite variance ($\nu > 2$), this confirms previous observation of $\mathbb{E}(L_{n}) \sim \sqrt{n}\ln{n}$ to leading order. We note that this asymptotic behavior (including the subleading term) resembles that of the largest part of random integer partitions under the uniform measure and that, curiously, both random variables seem to follow Gumbel statistics. We also provide more refined estimates for the asymptotic behavior of $\mathbb{E}(L_{n})$ for random walks with step increments of finite variance.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg
- 3. Institut für Physik

## Archive ouverte HAL – Collective excitations of a one-dimensional quantum droplet

### Marek TylutkiGrigori E. AstrakharchikBoris A. Malomed

^{1}Dmitry S. Petrov^{2}Grigori Astrakharchik^{3}Boris Malomed^{4}Dmitry Petrov#### Marek Tylutki, Grigori E. Astrakharchik, Boris A. Malomed, Dmitry S. Petrov, Grigori Astrakharchik, et al.. Collective excitations of a one-dimensional quantum droplet.

*Physical Review A*, American Physical Society 2020, 101 (5), ⟨10.1103/PhysRevA.101.051601⟩. ⟨hal-02881226⟩We calculate the excitation spectrum of a one-dimensional self-bound quantum droplet in a two-component bosonic mixture described by the Gross-Pitaevskii equation (GPE) with cubic and quadratic nonlinearities. The cubic term originates from the mean-field energy of the mixture proportional to the effective coupling constant $\delta g$, whereas the quadratic nonlinearity corresponds to the attractive beyond-mean-field contribution. The droplet properties are governed by a control parameter $\gamma\propto \delta g N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet features the flat-top shape with the discrete part of its spectrum consisting of plane-wave Bogoliubov phonons propagating through the flat-density bulk and reflected by edges of the droplet. With decreasing $\gamma$ these modes cross into the continuum, sequentially crossing the particle-emission threshold at specific critical values. A notable exception is the breathing mode which we find to be always bound. The balance point $\gamma = 0$ provides implementation of a system governed by the GPE with an unusual quadratic nonlinearity. This case is characterized by the ratio of the breathing-mode frequency to the particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$ this ratio tends to 1 and the droplet transforms into the soliton solution of the integrable cubic GPE.

- 1. Tel Aviv University [Tel Aviv]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. UPC - Universitat Politècnica de Catalunya [BarcelonaTech]
- 4. Department of Interdisciplinary Studies

## Archive ouverte HAL – Comment on “Effective Confining Potential of Quantum States in Disordered Media”

### Alain Comtet

^{1}Christophe Texier^{1}#### Alain Comtet, Christophe Texier. Comment on “Effective Confining Potential of Quantum States in Disordered Media”.

*Physical Review Letters*, American Physical Society, 2020, 124 (21), ⟨10.1103/PhysRevLett.124.219701⟩. ⟨hal-02881221⟩We provide some analytical tests of the density of states estimation from the "localization landscape" approach of Ref. [Phys. Rev. Lett. 116, 056602 (2016)]. We consider two different solvable models for which we obtain the distribution of the landscape function and argue that the precise spectral singularities are not reproduced by the estimation of the landscape approach.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Current fluctuations in noninteracting run-and-tumble particles in one dimension

### Tirthankar Banerjee

^{1}Satya N. Majumdar^{1}Alberto Rosso^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Tirthankar Banerjee, Satya N. Majumdar, Alberto Rosso, Satya Majumdar, Gregory Schehr. Current fluctuations in noninteracting run-and-tumble particles in one dimension.

*Physical Review E*, American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052101⟩. ⟨hal-02565189⟩We present a general framework to study the distribution of the flux through the origin up to time $t$, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density $\rho$ of particles to the left of the origin. We focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean $\mu(t)$ that we compute exactly in terms of the Green's function of the single particle dynamics. For the quenched case, we show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times $P_{\rm qu}(Q,t) \sim \exp\left[-\rho\, v_0\, \gamma \, t^2 \psi_{\rm RTP}\left(\frac{Q}{\rho v_0\,t} \right) \right]$, where $\gamma$ is the rate of tumbling and $v_0$ is the ballistic speed between two successive tumblings. In this paper, we compute the rate function $\psi_{\rm RTP}(q)$ and show that it is nontrivial. Our method also gives access to the probability of the rare event that, at time $t$, there is no particle to the right of the origin. For diffusive and run-and-tumble dynamics, we find that this probability decays with time as a stretched exponential, $\sim \exp(-c\, \sqrt{t})$ where the constant $c$ can be computed exactly. We verify our results for these large deviations by using an importance sampling Monte-Carlo method.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate

### M. Isoard

^{1}N. Pavloff^{1}#### M. Isoard, N. Pavloff. Departing from thermality of analogue Hawking radiation in a Bose-Einstein condensate.

*Phys.Rev.Lett.*, 2020, 124 (6), pp.060401. ⟨10.1103/PhysRevLett.124.060401⟩. ⟨hal-02317273⟩We study the quantum fluctuations in a one-dimensional Bose-Einstein condensate realizing an analogous acoustic black hole. The taking into account of evanescent channels and of zero modes makes it possible to accurately reproduce recent experimental measurements of the density correlation function. We discuss the determination of Hawking temperature and show that in our model the analogous radiation presents some significant departure from thermality.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Dispersionless evolution of inviscid nonlinear pulses

### M. Isoard

^{1}N. Pavloff^{1}A. M. Kamchatnov^{2}#### M. Isoard, N. Pavloff, A. M. Kamchatnov. Dispersionless evolution of inviscid nonlinear pulses.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020. ⟨hal-02565206⟩We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson equation which is valid for any kind of nonlinearity. The approach is exact for monoatomic classical gas and agrees very well with exact results and numerical simulations for other systems. We also provide a simple and accurate determination of the wave breaking time for typical initial conditions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Institute of Spectroscopy

## Archive ouverte HAL – Distribution of the time between maximum and minimum of random walks

### Francesco Mori

^{1}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Distribution of the time between maximum and minimum of random walks.

*Physical Review E*, American Physical Society (APS), 2020, 101 (5), ⟨10.1103/PhysRevE.101.052111⟩. ⟨hal-02881215⟩We consider a one-dimensional Brownian motion of fixed duration $T$. Using a path-integral technique, we compute exactly the probability distribution of the difference $\tau=t_{\min}-t_{\max}$ between the time $t_{\min}$ of the global minimum and the time $t_{\max}$ of the global maximum. We extend this result to a Brownian bridge, i.e. a periodic Brownian motion of period $T$. In both cases, we compute analytically the first few moments of $\tau$, as well as the covariance of $t_{\max}$ and $t_{\min}$, showing that these times are anti-correlated. We demonstrate that the distribution of $\tau$ for Brownian motion is valid for discrete-time random walks with $n$ steps and with a finite jump variance, in the limit $n\to \infty$. In the case of L\'evy flights, which have a divergent jump variance, we numerically verify that the distribution of $\tau$ differs from the Brownian case. For random walks with continuous and symmetric jumps we numerically verify that the probability of the event "$\tau = n$" is exactly $1/(2n)$ for any finite $n$, independently of the jump distribution. Our results can be also applied to describe the distance between the maximal and minimal height of $(1+1)$-dimensional stationary-state Kardar-Parisi-Zhang interfaces growing over a substrate of finite size $L$. Our findings are confirmed by numerical simulations. Some of these results have been announced in a recent Letter [Phys. Rev. Lett. 123, 200201 (2019)].

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Extreme value statistics of correlated random variables: a pedagogical review

### Satya N. Majumdar

^{1}Arnab PalGregory Schehr^{1}#### Satya N. Majumdar, Arnab Pal, Gregory Schehr. Extreme value statistics of correlated random variables: a pedagogical review.

*Physics Reports*, Elsevier, 2020, ⟨10.10667⟩. ⟨hal-02512248⟩Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applications in climate, finance, sports, all the way to physics of disordered systems where one is interested in the statistics of the ground state energy. While the EVS of `uncorrelated' variables are well understood, little is known for strongly correlated random variables. Only recently this subject has gained much importance both in statistical physics and in probability theory. In this review, we will first recall the classical EVS for uncorrelated variables and discuss the three universality classes of extreme value limiting distribution, known as the Gumbel, Fr\'echet and Weibull distribution. We then show that, for weakly correlated random variables with a finite correlation length/time, the limiting extreme value distribution can still be inferred from that of the uncorrelated variables using a renormalisation group-like argument. Finally, we consider the most interesting examples of strongly correlated variables for which there are very few exact results for the EVS. We discuss few examples of such strongly correlated systems (such as the Brownian motion and the eigenvalues of a random matrix) where some analytical progress can be made. We also discuss other observables related to extremes, such as the density of near-extreme events, time at which an extreme value occurs, order and record statistics, etc.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Few-body bound states of two-dimensional bosons

### G. Guijarro

^{1}G. E. Astrakharchik^{1}J. Boronat^{1}B. BazakD. S. Petrov^{2}#### G. Guijarro, G. E. Astrakharchik, J. Boronat, B. Bazak, D. S. Petrov. Few-body bound states of two-dimensional bosons.

*Physical Review A*, American Physical Society 2020, ⟨10.1103/PhysRevA.101.041602⟩. ⟨hal-02537195⟩We study clusters of the type A$_N$B$_M$ with $N\leq M\leq 3$ in a two-dimensional mixture of A and B bosons, with attractive AB and equally repulsive AA and BB interactions. In order to check universal aspects of the problem, we choose two very different models: dipolar bosons in a bilayer geometry and particles interacting via separable Gaussian potentials. We find that all the considered clusters are bound and that their energies are universal functions of the scattering lengths $a_{AB}$ and $a_{AA}=a_{BB}$, for sufficiently large attraction-to-repulsion ratios $a_{AB}/a_{BB}$. When $a_{AB}/a_{BB}$ decreases below $\approx 10$, the dimer-dimer interaction changes from attractive to repulsive and the population-balanced AABB and AAABBB clusters break into AB dimers. Calculating the AAABBB hexamer energy just below this threshold, we find an effective three-dimer repulsion which may have important implications for the many-body problem, particularly for observing liquid and supersolid states of dipolar dimers in the bilayer geometry. The population-imbalanced ABB trimer, ABBB tetramer, and AABBB pentamer remain bound beyond the dimer-dimer threshold. In the dipolar model, they break up at $a_{AB}\approx 2 a_{BB}$ where the atom-dimer interaction switches to repulsion.

- 1. UPC - Universitat Politècnica de Catalunya [Barcelona]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Finite-time adiabatic processes: Derivation and speed limit

### Carlos Plata

^{1}David Guéry-Odelin^{2}Emmanuel Trizac^{3}Antonio Prados^{4}#### Carlos Plata, David Guéry-Odelin, Emmanuel Trizac, Antonio Prados. Finite-time adiabatic processes: Derivation and speed limit.

*Physical Review E*, American Physical Society (APS), 2020, 101 (3), ⟨10.1103/PhysRevE.101.032129⟩. ⟨hal-02535447⟩Obtaining adiabatic processes that connect equilibrium states in a given time represents a challenge for mesoscopic systems. In this paper, we explicitly show how to build these finite-time adiabatic processes for an overdamped Brownian particle in an arbitrary potential, a system that is relevant both at the conceptual and the practical level. This is achieved by jointly engineering the time evolutions of the binding potential and the fluid temperature. Moreover, we prove that the second principle imposes a speed limit for such adiabatic transformations: there appears a minimum time to connect the initial and final states. This minimum time can be explicitly calculated for a general compression/decompression situation.

- 1. Padova University
- 2. Atomes Froids (LCAR)
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 4. Universidad de Sevilla

## Archive ouverte HAL – Locally quasi-stationary states in noninteracting spin chains

### Maurizio Fagotti

^{1}#### Maurizio Fagotti. Locally quasi-stationary states in noninteracting spin chains.

*SciPost Phys.*, 2020, 8, pp.048. ⟨10.21468/SciPostPhys.8.3.048⟩. ⟨hal-02423699⟩Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including "quantum corrections").

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes

### Guillaume Lamour

^{1}Antoine Allard^{1, 2}Juan Pelta^{1}Sid Labdi^{1}Martin Lenz^{3}Clément Campillo^{1}#### Guillaume Lamour, Antoine Allard, Juan Pelta, Sid Labdi, Martin Lenz, et al.. Mapping and Modeling the Nanomechanics of Bare and Protein-Coated Lipid Nanotubes.

*Physical Review X*, American Physical Society, 2020, 10 (1), pp.011031. ⟨10.1103/PhysRevX.10.011031⟩. ⟨hal-02512272⟩Membrane nanotubes are continuously assembled and disassembled by the cell to generate and dispatch transport vesicles, for instance, in endocytosis. While these processes crucially involve the ill-understood local mechanics of the nanotube, existing micromanipulation assays only give access to its global mechanical properties. Here we develop a new platform to study this local mechanics using atomic force microscopy (AFM). On a single coverslip we quickly generate millions of substrate-bound nanotubes, out of which dozens can be imaged by AFM in a single experiment. A full theoretical description of the AFM tip-membrane interaction allows us to accurately relate AFM measurements of the nanotube heights, widths, and rigidities to the membrane bending rigidity and tension, thus demonstrating our assay as an accurate probe of nanotube mechanics. We reveal a universal relationship between nanotube height and rigidity, which is unaffected by the specific conditions of attachment to the substrate. Moreover, we show that the parabolic shape of force-displacement curves results from thermal fluctuations of the membrane that collides intermittently with the AFM tip. We also show that membrane nanotubes can exhibit high resilience against extreme lateral compression. Finally, we mimic in vivo actin polymerization on nanotubes and use AFM to assess the induced changes in nanotube physical properties. Our assay may help unravel the local mechanics of membrane-protein interactions, including membrane remodeling in nanotube scission and vesicle formation.

- 1. LAMBE - UMR 8587 - Laboratoire Analyse, Modélisation et Matériaux pour la Biologie et l'Environnement
- 2. PCC - Physico-Chimie-Curie
- 3. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Multi-component colloidal gels: interplay between structure and mechanical properties

### Claudia Ferreiro-CordovaMehdi Bouzid

^{1}Emanuela del GadoGiuseppe Foffi^{2}Claudia Ferreiro-Córdova#### Claudia Ferreiro-Cordova, Mehdi Bouzid, Emanuela del Gado, Giuseppe Foffi, Claudia Ferreiro-Córdova. Multi-component colloidal gels: interplay between structure and mechanical properties.

*Soft Matter*, Royal Society of Chemistry, 2020, 16 (18), pp.4414-4421. ⟨10.1039/C9SM02410G⟩. ⟨hal-02881157⟩We present a detailed numerical study of multi-component colloidal gels interacting sterically and obtained by arrested phase separation. Under deformation, we found that the interplay between the different intertwined networks is key. Increasing the number of component leads to softer solids that can accomodate progressively larger strain before yielding. The simulations highlight how this is the direct consequence of the purely repulsive interactions between the different components, which end up enhancing the linear response of the material. Our work {provides new insight into mechanisms at play for controlling the material properties and open the road to new design principles for} soft composite solids

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPS - Laboratoire de Physique des Solides

## Archive ouverte HAL – Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel

### Naftali R. Smith

^{1}David S. Dean^{2}Pierre Le Doussal^{3}Satya N. Majumdar^{1}Grégory Schehr^{1}#### Naftali R. Smith, David S. Dean, Pierre Le Doussal, Satya N. Majumdar, Grégory Schehr. Noninteracting trapped Fermions in double-well potentials: inverted parabola kernel.

*Phys.Rev.A*, 2020, 101 (5), pp.053602. ⟨10.1103/PhysRevA.101.053602⟩. ⟨hal-02484003⟩We study a system of N noninteracting spinless fermions in a confining double-well potential in one dimension. We show that when the Fermi energy is close to the value of the potential at its local maximum, physical properties, such as the average density and the fermion position correlation functions, display a universal behavior that depends only on the local properties of the potential near its maximum. This behavior describes the merging of two Fermi gases, which are disjoint at sufficiently low Fermi energies. We describe this behavior in terms of a correlation kernel that we compute analytically and we call it the inverted parabola kernel. As an application, we calculate the mean and variance of the number of particles in an interval of size 2L centered around the position of the local maximum, for sufficiently small L. We discuss the possibility of observing our results in experiments, as well as extensions to nonzero temperature and to higher space dimensions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LOMA - Laboratoire Ondes et Matière d'Aquitaine
- 3. LPTENS - Laboratoire de Physique Théorique de l'ENS

## Archive ouverte HAL – Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

### Alessandro Manacorda

^{1}Gregory Schehr^{2}Francesco Zamponi^{1}#### Alessandro Manacorda, Gregory Schehr, Francesco Zamponi. Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids.

*Journal of Chemical Physics*, American Institute of Physics, 2020, 152 (16), pp.164506. ⟨10.1063/5.0007036⟩. ⟨hal-02554137⟩- 1. Systèmes Désordonnés et Applications
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States

### John MartinStefan WeigertOlivier Giraud

^{1}#### John Martin, Stefan Weigert, Olivier Giraud. Optimal Detection of Rotations about Unknown Axes by Coherent and Anticoherent States.

*Quantum*, Verein, 2020. ⟨hal-02881098⟩Coherent and anticoherent states of spin systems up to spin j=2 are known to be optimal in order to detect rotations by a known angle but unknown rotation axis. These optimal quantum rotosensors are characterized by minimal fidelity, given by the overlap of a state before and after a rotation, averaged over all directions in space. We calculate a closed-form expression for the average fidelity in terms of anticoherent measures, valid for arbitrary values of the quantum number j. We identify optimal rotosensors (i) for arbitrary rotation angles in the case of spin quantum numbers up to j=7/2 and (ii) for small rotation angles in the case of spin quantum numbers up to j=5. The closed-form expression we derive allows us to explain the central role of anticoherence measures in the problem of optimal detection of rotation angles for arbitrary values of j.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Optimizing Brownian escape rates by potential shaping

### Marie Chupeau

^{1}Jannes GladrowAlexei Chepelianskii^{2}Ulrich F. KeyserEmmanuel Trizac^{1}Ulrich Keyser#### Marie Chupeau, Jannes Gladrow, Alexei Chepelianskii, Ulrich F. Keyser, Emmanuel Trizac, et al.. Optimizing Brownian escape rates by potential shaping.

*Proceedings of the National Academy of Sciences of the United States of America*, National Academy of Sciences, 2020, 117 (3), pp.1383-1388. ⟨10.1073/pnas.1910677116⟩. ⟨hal-02512216⟩Brownian escape is key to a wealth of physico-chemical processes, including polymer folding, and information storage. The frequency of thermally activated energy barrier crossings is assumed to generally decrease exponentially with increasing barrier height. Here, we show experimentally that higher, fine-tuned barrier profiles result in significantly enhanced escape rates in breach of the intuition relying on the above scaling law, and address in theory the corresponding conditions for maximum speed-up. Importantly, our barriers end on the same energy on which they start. For overdamped dynamics, the achievable boost of escape rates is, in principle, unbounded so that the barrier optimization has to be regularized. We derive optimal profiles under two different regularizations, and uncover the efficiency of N-shaped barriers. We then demonstrate the viability of such a potential in automated microfluidic Brownian dynamics experiments using holographic optical tweezers and achieve a doubling of escape rates compared to unhindered Brownian motion. Finally, we show that this escape rate boost extends into the low-friction inertial regime.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPCT - Laboratoire de Physico-Chimie Théorique

## Archive ouverte HAL – Reversal of contractility as a signature of self-organization in cytoskeletal bundles

### Martin Lenz

^{1}#### Martin Lenz. Reversal of contractility as a signature of self-organization in cytoskeletal bundles.

*eLife*, eLife Sciences Publication, 2020, 9, ⟨10.7554/eLife.51751⟩. ⟨hal-02518848⟩- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Scalable quantum computing with qudits on a graph

### E. O. Kiktenko

^{1}A. S. NikolaevaPeng XuG. V. Shlyapnikov^{2}A. K. Fedorov^{3}#### E. O. Kiktenko, A. S. Nikolaeva, Peng Xu, G. V. Shlyapnikov, A. K. Fedorov. Scalable quantum computing with qudits on a graph.

*Physical Review A*, American Physical Society 2020, 101 (2), ⟨10.1103/PhysRevA.101.022304⟩. ⟨hal-02512218⟩We show a significant reduction of the number of quantum operations and the improvement of the circuit depth for the realization of the Toffoli gate by using qudits. This is done by establishing a general relation between the dimensionality of qudits and their topology of connections for a scalable multi-qudit processor, where higher qudit levels are used for substituting ancillas. The suggested model is of importance for the realization of quantum algorithms and as a method of quantum error correction codes for single-qubit operations.

- 1. IPE - Schmidt United Institute of Physics of the Earth [Moscow]
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. Russian Quantum Center

## Archive ouverte HAL – Statistics of first-passage Brownian functionals

### Satya N. Majumdar

^{1}Baruch Meerson#### Satya N. Majumdar, Baruch Meerson. Statistics of first-passage Brownian functionals.

*J.Stat.Mech.*, 2020, 2002 (2), pp.023202. ⟨10.1088/1742-5468/ab6844⟩. ⟨hal-02497830⟩We study the distribution of first-passage functionals of the type where represents a Brownian motion (with or without drift) with diffusion constant D, starting at x 0 > 0, and t f is the first-passage time to the origin. In the driftless case, we compute exactly, for all n > −2, the probability density . We show that has an essential singular tail as and a power-law tail as . The leading essential singular behavior for small A can be obtained using the optimal fluctuation method (OFM), which also predicts the optimal paths of the conditioned process in this limit. For the case with a drift toward the origin, where no exact solution is known for general n > −1, we show that the OFM successfully predicts the tails of the distribution. For it predicts the same essential singular tail as in the driftless case. For it predicts a stretched exponential tail for all n > 0. In the limit of large Péclet number , where is the drift velocity toward the origin, the OFM predicts an exact large-deviation scaling behavior, valid for all A: , where is the mean value of in this limit. We compute the rate function analytically for all n > −1. We show that, while for n > 0 the rate function is analytic for all z, it has a non-analytic behavior at z = 1 for −1 < n < 0 which can be interpreted as a dynamical phase transition. The order of this transition is 2 for −1/2 < n < 0, while for −1 < n < −1/2 the order of transition is ; it changes continuously with n. We also provide an illuminating alternative derivation of the OFM result by using a WKB-type asymptotic perturbation theory for large . Finally, we employ the OFM to study the case of (drift away from the origin). We show that, when the process is conditioned on reaching the origin, the distribution of coincides with the distribution of for with the same .

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Stochastic growth in time-dependent environments

### Guillaume Barraquand

^{1}Pierre Le Doussal^{1}Alberto Rosso^{2}#### Guillaume Barraquand, Pierre Le Doussal, Alberto Rosso. Stochastic growth in time-dependent environments.

*Physical Review E*, American Physical Society (APS), 2020, 101 (4), ⟨10.1103/PhysRevE.101.040101⟩. ⟨hal-02565202⟩We study the Kardar-Parisi-Zhang (KPZ) growth equation in one dimension with a noise variance $c(t)$ depending on time. We find that for $c(t)\propto t^{-\alpha}$ there is a transition at $\alpha=1/2$. When $\alpha>1/2$, the solution saturates at large times towards a non-universal limiting distribution. When $\alpha<1/2$ the fluctuation field is governed by scaling exponents depending on $\alpha$ and the limiting statistics are similar to the case when $c(t)$ is constant. We investigate this problem using different methods: (1) Elementary changes of variables mapping the time dependent case to variants of the KPZ equation with constant variance of the noise but in a deformed potential (2) An exactly solvable discretization, the log-gamma polymer model (3) Numerical simulations.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order

### Ananyo Maitra

^{1, 2}Pragya SrivastavaM. Cristina MarchettiSriram RamaswamyMartin Lenz^{2, 3}#### Ananyo Maitra, Pragya Srivastava, M. Cristina Marchetti, Sriram Ramaswamy, Martin Lenz. Swimmer Suspensions on Substrates: Anomalous Stability and Long-Range Order.

*Phys.Rev.Lett.*, 2020, 124 (2), pp.028002. ⟨10.1103/PhysRevLett.124.028002⟩. ⟨hal-02475283⟩We present a comprehensive theory of the dynamics and fluctuations of a two-dimensional suspension of polar active particles in an incompressible fluid confined to a substrate. We show that, depending on the sign of a single parameter, a state with polar orientational order is anomalously stable (or anomalously unstable), with a nonzero relaxation (or growth) rate for angular fluctuations, not parallel to the ordering direction, at zero wave number. This screening of the broken-symmetry mode in the stable state does lead to conventional rather than giant number fluctuations as argued by Bricard et al., Nature 503, 95 (2013), but their bend instability in a splay-stable flock does not exist and the polar phase has long-range order in two dimensions. Our theory also describes confined three-dimensional thin-film suspensions of active polar particles as well as dense compressible active polar rods, and predicts a flocking transition without a banding instability.

- 1. LJP - Laboratoire Jean Perrin
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 3. ESPCI ParisTech

## Archive ouverte HAL – Symmetries in $B \to D^* \ell \nu$ angular observables

### Marcel AlgueróSébastien Descotes-Genon

^{1}Joaquim MatiasMartín Novoa-Brunet^{2}#### Marcel Algueró, Sébastien Descotes-Genon, Joaquim Matias, Martín Novoa-Brunet. Symmetries in $B \to D^* \ell \nu$ angular observables.

*JHEP*, 2020, 06, pp.156. ⟨10.1007/JHEP06(2020)156⟩. ⟨hal-02518081⟩We apply the formalism of amplitude symmetries to the angular distribution of the decays B → D$^{∗}$ℓν for ℓ = e, μ, τ . We show that the angular observables used to describe the distribution of this class of decays are not independent in absence of New Physics contributing to tensor operators. We derive sets of relations among the angular coefficients of the decay distribution for the massless and massive lepton cases which can be used to probe in a very general way the consistency among the angular observables and the underlying New Physics at work. We use these relations to access the longitudinal polarisation fraction of the D$^{∗}$ using different angular coefficients from the ones used by Belle experiment. This in the near future can provide an alternative strategy to measure $ {F}_L^{D\ast } $ in B → D$^{∗}$τν and to understand the relatively high value measured by the Belle experiment. Using the same symmetries, we identify three observables which may exhibit a tension if the experimental value of $ {F}_L^{D\ast } $ remains high. We discuss how these relations can be exploited for binned measurements. We also propose a new observable that could test for specific scenarios of New Physics generated by light right-handed neutrinos. Finally we study the prospects of testing these relations based on the projected experimental sensitivity of new experiments.

- 1. IJCLab - Laboratoire de Physique des 2 Infinis Irène Joliot-Curie
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – The convex hull of the run-and-tumble particle in a plane

### Alexander K HartmannSatya N Majumdar

^{1}Hendrik Schawe^{2}Gregory Schehr^{1}Alexander Hartmann^{2}Satya Majumdar^{1}#### Alexander K Hartmann, Satya N Majumdar, Hendrik Schawe, Gregory Schehr, Alexander Hartmann, et al.. The convex hull of the run-and-tumble particle in a plane.

*Journal of Statistical Mechanics: Theory and Experiment*, IOP Publishing, 2020, 2020 (5), pp.053401. ⟨10.1088/1742-5468/ab7c5f⟩. ⟨hal-02881103⟩We study the statistical properties of the convex hull of a planar run-and-tumble particle (RTP), also known as the "persistent random walk", where the particle/walker runs ballistically between tumble events at which it changes its direction randomly. We consider two different statistical ensembles where we either fix (i) the total number of tumblings $n$ or (ii) the total duration $t$ of the time interval. In both cases, we derive exact expressions for the average perimeter of the convex hull and then compare to numerical estimates finding excellent agreement. Further, we numerically compute the full distribution of the perimeter using Markov chain Monte Carlo techniques, in both ensembles, probing the far tails of the distribution, up to a precision smaller than $10^{-100}$. This also allows us to characterize the rare events that contribute to the tails of these distributions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. University of Oldenburg

## Archive ouverte HAL – Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus

### Nina Javerzat

^{1}Marco Picco^{2}Raoul Santachiara^{1}#### Nina Javerzat, Marco Picco, Raoul Santachiara. Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus.

*J.Stat.Mech.*, 2020, 2005, pp.053106. ⟨10.1088/1742-5468/ab7c5e⟩. ⟨hal-02416915⟩In a recent paper, we considered the effects of the torus lattice topology on the two-point connectivity of Q-Potts clusters. These effects are universal and probe non-trivial structure constants of the theory. We complete here this work by considering the torus corrections to the three- and four-point connectivities. These corrections, which depend on the scale invariant ratios of the triangle and quadrilateral formed by the three and four given points, test other non-trivial structure constants. We also present results of Monte Carlo simulations in good agreement with our predictions.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. LPTHE - Laboratoire de Physique Théorique et Hautes Energies

## Archive ouverte HAL – Two anyons on the sphere: nonlinear states and spectrum

### Alexios P. PolychronakosStéphane Ouvry

^{1}#### Alexios P. Polychronakos, Stéphane Ouvry. Two anyons on the sphere: nonlinear states and spectrum.

*Nucl.Phys.B*, 2020, 951, pp.114906. ⟨10.1016/j.nuclphysb.2019.114906⟩. ⟨hal-02340259⟩We study the energy spectrum of two anyons on the sphere in a constant magnetic field. Making use of rotational invariance we reduce the energy eigenvalue equation to a system of linear differential equations for functions of a single variable, a reduction analogous to separating center of mass and relative coordinates on the plane. We solve these equations by a generalization of the Frobenius method and derive numerical results for the energies of non-analytically derivable states.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Universal gap statistics for random walks for a class of jump densities

### Matteo Battilana

^{1}Satya N. Majumdar^{1}Gregory Schehr^{1}#### Matteo Battilana, Satya N. Majumdar, Gregory Schehr. Universal gap statistics for random walks for a class of jump densities.

*Markov Processes And Related Fields*, Polymat Publishing Company, 2020. ⟨hal-02518812⟩We study the order statistics of a random walk (RW) of $n$ steps whose jumps are distributed according to symmetric Erlang densities $f_p(\eta)\sim |\eta|^p \,e^{-|\eta|}$, parametrized by a non-negative integer $p$. Our main focus is on the statistics of the gaps $d_{k,n}$ between two successive maxima $d_{k,n}=M_{k,n}-M_{k+1,n}$ where $M_{k,n}$ is the $k$-th maximum of the RW between step 1 and step $n$. In the limit of large $n$, we show that the probability density function of the gaps $P_{k,n}(\Delta) = \Pr(d_{k,n} = \Delta)$ reaches a stationary density $P_{k,n}(\Delta) \to p_k(\Delta)$. For large $k$, we demonstrate that the typical fluctuations of the gap, for $d_{k,n}= O(1/\sqrt{k})$ (and $n \to \infty$), are described by a non-trivial scaling function that is independent of $k$ and of the jump probability density function $f_p(\eta)$, thus corroborating our conjecture about the universality of the regime of typical fluctuations (see G. Schehr, S. N. Majumdar, Phys. Rev. Lett. 108, 040601 (2012)). We also investigate the large fluctuations of the gap, for $d_{k,n} = O(1)$ (and $n \to \infty$), and show that these two regimes of typical and large fluctuations of the gaps match smoothly.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques

## Archive ouverte HAL – Universal Scaling of the Velocity Field in Crack Front Propagation

### Clément Le Priol

^{1}Pierre Le Doussal^{2}Laurent Ponson^{3}Alberto Rosso^{4}Julien Chopin^{5}#### Clément Le Priol, Pierre Le Doussal, Laurent Ponson, Alberto Rosso, Julien Chopin. Universal Scaling of the Velocity Field in Crack Front Propagation.

*Physical Review Letters*, American Physical Society, 2020, 124 (6), ⟨10.1103/PhysRevLett.124.065501⟩. ⟨hal-02512228⟩The propagation of a crack front in disordered materials is jerky and characterized by bursts of activity, called avalanches. These phenomena are the manifestation of an out-of-equilibrium phase transition originated by the disorder. As a result avalanches display universal scalings which are however difficult to characterize in experiments at finite drive. Here we show that the correlation functions of the velocity field along the front allow to extract the critical exponents of the transition and to identify the universality class of the system. We employ these correlations to characterize the universal behavior of the transition in simulations and in an experiment of crack propagation. This analysis is robust, efficient and can be extended to all systems displaying avalanche dynamics.

- 1. LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
- 2. Champs Aléatoires et Systèmes hors d'Équilibre
- 3. DALEMBERT - Institut Jean Le Rond d'Alembert
- 4. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 5. IF-UFB - Instituto de Fisica, Universidade Federal da Bahia

## Archive ouverte HAL – Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle

### Francesco Mori

^{1}Pierre Le Doussal^{2}Satya N. Majumdar^{1}Satya Majumdar^{1}Gregory Schehr^{1}#### Francesco Mori, Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Universal Survival Probability for a d -Dimensional Run-and-Tumble Particle.

*Physical Review Letters*, American Physical Society, 2020, 124 (9), ⟨10.1103/PhysRevLett.124.090603⟩. ⟨hal-02512214⟩We consider an active run-and-tumble particle (RTP) in $d$ dimensions and compute exactly the probability $S(t)$ that the $x$-component of the position of the RTP does not change sign up to time $t$. When the tumblings occur at a constant rate, we show that $S(t)$ is independent of $d$ for any finite time $t$ (and not just for large $t$), as a consequence of the celebrated Sparre Andersen theorem for discrete-time random walks in one dimension. Moreover, we show that this universal result holds for a much wider class of RTP models in which the speed $v$ of the particle after each tumbling is random, drawn from an arbitrary probability distribution. We further demonstrate, as a consequence, the universality of the record statistics in the RTP problem.

- 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
- 2. Champs Aléatoires et Systèmes hors d'Équilibre

## Archive ouverte HAL – Velocity and diffusion constant of an active particle in a one-dimensional force field

### Pierre Le Doussal

^{1}Satya N. Majumdar^{2}Satya Majumdar^{2}Gregory Schehr^{2}#### Pierre Le Doussal, Satya N. Majumdar, Satya Majumdar, Gregory Schehr. Velocity and diffusion constant of an active particle in a one-dimensional force field.

*EPL - Europhysics Letters*, European Physical Society/EDP Sciences/Società Italiana di Fisica/IOP Publishing, 2020, 130 (4), pp.40002. ⟨10.1209/0295-5075/130/40002⟩. ⟨hal-02881224⟩We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of period $L$. They involve the "active potential" which allows to define a global bias. Upon varying parameters, such as an external force $F$, the dynamics undergoes transitions from non-ergodic trapped states, to various moving states, some with non analyticities in the $V_L$ versus $F$ curve. A random landscape in the presence of a bias leads, for large $L$, to anomalous diffusion $x \sim t^\mu$, $\mu<1$, or to a phase with a finite velocity that we calculate.

- 1. Champs Aléatoires et Systèmes hors d'Équilibre
- 2. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques