## LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE

### Attention : désormais les séminaires ont lieu tous les lundis à 10h45 en salle  523 du LPTMC - Tour 12-13

Satya Majumdar

LPTMS, Orsay

We study a simple model of search where the searcher undergoes normal diffusion, but once in a while resets to its initial starting point stochastically with rate $r$. The effect of a finite resetting rate r turns out to be rather drastic. First, the position of the walker approaches a nonequilibrium stationary state at long times. The approach to the stationary state is accompanied by an interesting `dynamical' phase transition. For searching an immobile target, resetting leads to finite mean search time which, as a function of r, has a minimum at an optimal resetting rate $r^*$. This makes the search process efficient. We then consider various generalizations of this simple resetting model: to Levy flights, to multiple walkers and also to spatially extended system such as fluctuating interfaces.

Benjamin Canals (Institut Néel, Grenoble)

Artificial magnets as model systems : from the fragmentation of magnetization to the square ice model

Complex architectures of nanostructures are routinely elaborated using bottom-up or nanofabrication processes. This technological capability allows scientists to engineer materials with properties that do not exist in nature, but also to manufacture model systems to explore fundamental issues which appeared in condensed matter physics. One- and two-dimensional frustrated arrays of magnetic nanostructures are one class of systems for which theoretical predictions can now be tested and challenged experimentally. These systems have been the subject of intense research in the last few years and have allowed the investigation of a rich physics and fascinating phenomena, such as the exploration of the extensively degenerate ground-state manifolds of spin ice systems, the evidence of new magnetic phases in purely two-dimensional lattices, and the observation of pseudo-excitations involving classical analogues of magnetic charges. This talk aims at providing two examples of two-dimensional artificial magnets which allow to probe the low energy manifolds of two exotic Ising systems.

The first one is related to the seminal 6-vertex model and shows that it is possible to perform a scan through the 6-vertex model phase diagram with an appropriately designed artificial magnet [1]. In particular, the symmetric point of the (Lieb) square ice is recovered, providing with the opportunity to study the signatures of an algebraic Coulomb spin liquid. Because of the experimental procedure used to reach the low energy manifold, quasi-particles are trapped in this disordered manifold, pointing to the need of thermal systems, but also emphasizing that these systems may be well suited to study out of equilibrium relaxation of monopole-(anti)monopole pairs in a near future.

The second one refers to a recent proposal, the fragmentation of magnetisation [2], in an Ising Kagomé model. Here, we show it is possible to observe this intriguing phenomena, which corresponds to the splitting of the local degree of freedom into two channels, one ordering at low effective temperatures, in an AF all-in all-out ordering despite the ferromagnetic nature of the system, the other, building a Coulomb-like low energy manifold, inside which the magnetic equivalent of the Kirchhoff law at each node of the Kagomé lattice is fulfilled [3].

[1] Y. Perrin, B. Canals, N. Rougemaille, Nature 540, 410–413 (2016).
[2] M. E. Brooks-Bartlett, S. T. Banks, L. D. C. Jaubert, A. Harman-Clarke, and P. C. W. Holdsworth, Phys. Rev. X, 4, 011007 (2014).
[3] B. Canals, I. A. Chioar, V.-D. Nguyen, M. Hehn, D. Lacour, F. Montaigne, A. Locatelli, T. O. Mentes, B. S. Burgos and N. Rougemaille, Nat. Comm. 7, 11446 (2016).

Thomas Franosch

Institut fÜr Theoretische Physik, Universität Innsbruck

Non-equilibrium dynamics of active agents and driven particles in microrheology

The paradigm of virtually all transport processes  in  soft matter or biophysics systems is Brownian motion. However, often the constituents are highly anisotropic resulting in a non-trivial coupling between orientational and translational degrees of freedom.

In this talk I will introduce an exact solution of the Smoluchowski-Perrin equation for anisotropic diffusion exploiting a mathematical analogy to the quantum pendulum. Then the single-particle dynamics can be obtained as a superposition of suitable eigenfunctions of the Smoluchowski operator.
We discuss  features emerging due to the interplay of particle anisotropy and translational motion and how they manifest themselves in the directly measurable intermediate scattering functions.

Next, we investigate the dynamics of a single active particle, i.e. an agent that undergoes self-propelled motion along an axis of orientation which slowly and randomly changes. Again the intermediate function can be elaborated analytically and reveals oscillatory behavior for intermediate wave numbers, in striking contrast to passive overdamped systems. We compare our results with recent dynamic differential microscopy measurements and demonstrate that our solution allows  reliably extracting motility parameters.

Last we address the driven dynamics of tracer particle in a colloidal suspension of hard spheres upon switching on an external force. The force drives the system far from equilibrium and we monitor the time-dependent velocity response. Within a low-density expansion and computer
simulations we show that linear response as encoded in the fluctuation-dissipation theorem becomes qualitatively wrong.

16h - Bibliothèque du LPTHE (couloir 13-14, 4ème étage)

Shamik Gupta
Max Planck Institute for the Physics of Complex Systems,

Synchronization in coupled oscillator systems

Collective synchronization involves a large population of coupled oscillators of diverse frequencies spontaneously synchronizing to oscillate at a common frequency. Common examples are synchronized firings of heart cells, phase synchronization in electrical power networks, rhythmic applause in concert halls, etc. The Kuramoto model serves as a prototype to study collective synchronization. The model comprises oscillators with distributed natural frequencies interacting through a mean-field coupling. Interpreting the dynamics as that of a long-range interacting system driven out of equilibrium by quench disordered external torques, I will discuss the rich out-of-equilibrium phenomena the model exhibits, and in particular, its complete phase diagram for unimodal frequency distributions.

François Crépin
LPTMC

Appariement impair en fréquence d'électrons dans les canaux de bord d'isolants topologiques.

Les liquides hélicaux sont des gaz uni-dimensionnels d'électrons ayant la particularité d'une forte corrélation entre la valeur du spin et le sens de propagation. Ils émergent naturellement aux bords de certains semi-conducteurs communément appelés isolants topologiques [1]. En plus d'une certaine robustesse face aux impuretés non-magnétiques, ces nouveaux états électroniques présentent de nombreuses propriétés remarquables, notamment lorsqu'on les place à proximité d'un supraconducteur [2]. Dans ce séminaire, je propose tout d'abord de passer en revue plusieurs phénomènes directement causés par l'hélicité et caractéristiques d'une supraconductivité non-conventionnelle, comme des effets Josephson fractionnaires ou l'apparition d'états-liés exotiques. Dans une deuxième partie, je présenterai une analyse détaillée des symétries d'appariement dans des jonctions hybrides supraconducteur/isolant topologique [3]. En particulier, nous discuterons d'un appariement exotique, dit impair en fréquence, et de ses signatures possibles dans des mesures non-locales de la conductance de ces jonctions.

[1] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010)
[2] Liang Fu and C. L. Kane, Phys. Rev. Lett. 100, 096407 (2008)
[3] François Crépin, Pablo Burset, and Björn Trauzettel, Phys. Rev. B 92, 100507(R) (2015)