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

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**Thomas Franosch (Institut für Theoretische Physik, Universität Innsbruck, Austria)**

### Gravitaxis of a single active particle

The active Brownian particle (ABP) model has become a paradigm for dynamics far from equilibrium and has attracted considerable attention in the statistical-physics/soft-matter community [1,2]. In this model particles undergo directed motion along their axis of orientation which is subject to orientational diffusion. While it is rather easy to simulate the dynamics of such agents in a prescribed potential landscape, analytical progress even for the simplest set-ups has been difficult. Here I present an exact solution for the dynamics of active Brownian particle in a uniform gravitational field as described by the equations of motion of Ref. [3]. We show that the problem maps to the noisy overdamped pendulum or dynamics in a tilted washboard potential. Close to the underlying classical bifurction we unravel a resonance for the diffusion coefficient. We derive the corresponding Fokker-Planck equation and use techniques familiar from quantum mechanics to provide a complete solution. The scaling behavior at the resonance is rationalized in terms of a simple harmonic oscillator picture.

[1] C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).

[2] C. Kurzthaler, C. Devailly, J. Arlt, T. Franosch, W. C. K. Poon, V. A. Martinez, and A. T. Brown, Probing the spatiotemporal dynamics of catalytic janus particles with single-particle tracking and differential dynamic microscopy, Physical Review Letters 121, 078001 (2018).

[3] B. ten Hagen, F. Kümmel, R. Wittkowski, D. Takagi, H. Löwen, and C. Bechinger, Gravitaxis of asymmetric self-propelled colloidal particles, Nature Communications 5, 4829 (2014).

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**Kirill Polovnikov (LPTMS (visitor), Skoltech & Laboratoire Poncelet)**

### Constrained fractal polymer chain in curved geometry: how far is KPZ?

Can intrinsic curvature of the space yield a similar regime of fluctuations as a certain type of random potentials? In this talk by means of scaling analyses of the free energy and computer simulations I will discuss stretching of a fractal polymer chain around a disc in 2D (or a cylinder in 3D) of radius R. The typical excursions of the polymer away from the surface scale as \Delta \sim R^{\beta}, with the Kardar-Parisi-Zhang (KPZ) growth exponent \beta=1/3 and the curvature-induced correlation length is described by the KPZ exponent z=3/2. Remarkably, the uncovered KPZ scaling is independent of the fractal dimension of the polymer and, thus, is universal across the classical polymer models, e.g. SAW, randomly-branching polymers, crumpled unknotted rings. The one-point distribution of fluctuations, as found in simulations, can be well described by the squared Airy law, connecting our 2D polymer problem with the (1+1)D Ferrari-Spohn universality class of constrained random walks. A relation between directed polymers in quenched random potential (KPZ) and stretched polymers above the semicircle will be explained.

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**Alberto Imparato (Aarhus University, Denmark)**

### Critical behaviour of interacting thermodynamic machines

It is known that in an equilibrium system approaching a critical point, the response to a change in an external thermodynamic force can become significantly large. In other words, an equilibrium system at the verge of a second-order phase transition is highly susceptible to external thermodynamic forces.

Starting from this premise, in my talk I will discuss the properties of systems of interacting thermodynamic machines that operate at the verge of a phase transition. I will focus on the performance of different types of out-of-equilibrium machines converting heat or other forms of energy into useful work. Specifically, I will consider:

i) an out-of-equilibrium lattice model consisting of 2D discrete rotators, in contact with heath reservoirs at different temperatures,

ii) an out-of-equilibrium Frenkel--Kontorova model moving over a periodic substrate and in a position dependent temperature profile,

iii ) a transverse field Ising model undergoing a quantum phase transition, and operating as a battery-charger system.

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**Zohar Nussinov (Wahsington University in St Louis, Missouri)**

### Thermalization bounds and a universal collapse of the viscosities of supercooled liquids

We will derive bounds on the equilibration times in open and closed systems. For open systems, we will find that thermalization times cannot, typically, be shorter than Planck's constant divided by the temperature; a more general (and accurate) relation involving the heat capacities will be explained . For closed systems, the inequalities that we will obtain suggest that non-adiabatically driven systems may display long range correlations. We will explain how such long range correlations appear in certain soluble models and relate these correlations to the geometry of state manifolds. We will review how experimental measurements of equilibrated systems may be used to infer the average properties of eigenstates of many body Hamiltonians and detail the corresponding classical phase space picture. We will then piece these results together to predict the viscosity and relaxation times of supercooled liquids and glasses. These predictions will be compared to the viscosities and dielectric relaxation times of glass formers of all known types. The comparison shows that the viscosities/relaxation times of all known supercooled liquids collapse onto a universal curve with only one (nearly uniform) liquid dependent parameter over 16 decades. The collapsed universal curve is predicted by the theory. Time permitting, we will explain how related ideas may be used to infer the number of ground states of spin glass systems.

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**Maxym Dudka (Institute for Condensed Matter Physics, National Academy of Sciences, Lviv, Ukraine)**

### Phase transitions in three-dimensional random anisotropy Heisenberg model: two case studies

This talk concerns the study of ordering in random anisotropy magnets. Such magnets constitute a wide class of magnetic systems, with structural disorder described by a random anisotropy model that was introduced in the early 1970s by Harris, Plischke and Zuckermann. Despite extensive studies, the problem of the nature of a low-temperature phase of random anisotropy systems remains a very intriguing issue. While, for large values of local anisotropy strength, the majority of studies predict spin-glass, there is much discussion about ordering for small and moderate values of such strength. It appears that the answer to this question depends also on the local axis distribution. Field-theoretical renormalization group results predict an absence of the ferromagnetic order for uniform continuous distribution while preserving long-range order for discrete anisotropic distribution. We study phase transitions in the three-dimensional random anisotropy model with three-component order parameter by means of extensive Monte Carlo simulations for two different random anisotropy axis distributions and two different values of local anisotropy strength for each disorder distribution case. For the case of the anisotropic disorder, we have found evidence of universality by finding critical exponents and universal dimensionless ratios independent of the strength of the disorder. In the case of isotropic disorder distribution the situation is very involved: we have found two phase transitions in the magnetization channel which are merging for larger lattices remaining a spin glass phase transition.