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

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**Marcel Filoche **(École Polytechnique)

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*The landscape of wave localization*

In disordered systems or in complex geometry, standing waves can undergo a strange phenomenon that has puzzled physicists and mathematicians for over 60 years, called “wave localization”. This localization, which consists of a concentration (or a focusing) of the energy of the waves in a very restricted sub-region of the whole domain, has been demonstrated experimentally in mechanics, acoustics and quantum physics. We will present a theory which brings out an underlying and universal structure, the localization landscape, solution to a Dirichlet problem associated with the wave equation [1]. In quantum systems, this landscape allows us to define an “effective localization potential” which predicts the localization regions, the energies of the localized modes, the density of states, as well as the long-range decay of the wave functions. This theory holds in any dimension, for continuous or discrete systems. We will present the major mathematical properties of this landscape. Finally, we will review applications of this theory in mechanics, semiconductor physics, as well as molecular and cold atom systems.

[1] M. Filoche & S. Mayboroda, Proc. Natl Acad. Sci. (2012) 109:14761-14766.

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**Guillaume Roux (**LPTMS**,** Université Paris Saclay)

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*Coexistence and phase separation of pairs and fermions in a one-dimensional model with pair-hopping*

We consider a simple model of spinless fermions in which the kinetic energy competes with a pair-hopping term. We show by means of numerical calculations that there exists a phase in which part of the fermions are paired while the others remain unpaired. These elementary components makes two mixed Luttinger liquids, one for pairs and one for fermions. A simple two-fluid model accounts remarkably well for the observed numerical data. Adding nearest-neighbour interaction leads to a rich phase diagram in which we observe a regime in which the two previous Luttinger liquids get phase separated. In the context of impurity physics, this model on a finite size chain allows for the creation of a single pair interacting with a fermionic bath or a single fermion interacting with a paired fermions bath.

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**Alessio Squarcini (Max-Planck-Institute for Intelligent Systems, Stuttgart)**

### Long-range medium-mediated interactions: two exactly solvable models

(Egalement par zoom

https://us06web.zoom.us/j/88613589674?pwd=djRyNVN0dUVJMXhMOG1rem9OVG5WUT09

Meeting ID: 886 1358 9674

Passcode: 253305)

In this talk I will discuss two situations in which long-range effects such as ordering and forces emerge in certain systems of classical statistical mechanics and how such models are handled through exact techniques.

The first part of my talk revolves around the following question: can order extend over distances larger than the bulk correlation length? I will show how a network of Ising boxes connected by channels is able to exhibit an extraordinarily long-range ferromagnetic order over distances which grow exponentially with the cross sections of the channels. The emergence of such a new length scale follows from an exact calculation based on the diagonalization of the transfer matrix for the square lattice Ising model. The analytical study is flanked by extensive Monte Carlo simulations [1].

The second phenomenon I will discuss is the critical (or thermodynamical) Casimir effect [2]. Chemically inhomogeneous colloidal particles immersed in a critical binary mixture are subjected to a fluctuation-induced-force known as the critical Casimir effect. By modeling a binary mixture at its demixing critical point by means of the critical Ising model in two dimensions, and exploiting its scaling limit description in terms of a Conformal Field Theory, I determine the exact density profiles and correlation functions around various particles whose boundaries are formed by patches with different chemical structure and preference of the binary mixture components. The formalism encompasses several interesting configurations, including Janus particles, colloidal quadrupoles and needles with inhomogeneous patches of symmetry breaking boundary conditions. Within the framework of the ‘’Small Particle Operator Expansion’’ I determine the exact asymptotic behavior of the interaction free energy between these colloids, and colloids confined by a wedge-shaped wall. The theoretical predictions are confirmed by numerical results available in the literature.

References

[1] D. B. Abraham, A. Maciolek, AS, and O. Vasilyev, Action at a distance in classical uniaxial ferromagnetic arrays, Phys. Rev. E 96, 042154 (2017).

[2] AS, A. Maciolek, E. Eisenriegler, and S. Dietrich, Critical Casimir interaction between colloidal Janus-type particles in two spatial dimensions, J. Stat. Mech. 043208 (2020).

**Jordan Horowitz (University of Michigan)**

__Nonequilibrium thermodynamic limits to fluctuations and response__

(Egalement par zoom

https://us06web.zoom.us/j/87028439751?pwd=MDVNUFp0clJvKy9qOVNEQldVL1grUT09

Meeting ID: 870 2843 9751

Passcode: 317775)

Thermodynamics is a remarkably successful theoretical framework, with wide ranging applications across the natural sciences. Unfortunately, thermodynamics is limited to equilibrium or near-equilibrium situations, whereas most of the natural world, especially life, operates very far from thermodynamic equilibrium. Research in nonequilibrium statistical thermodynamics is beginning to shed light on this domain. In this talk, I will present a collection of such predictions, namely a series of equalities and inequalities---akin to the Fluctuation-Dissipation theorem but valid arbitrarily far from equilibrium---that link a system’s response to the strength of nonequilibrium driving. These results open new avenues for experimentally characterizing nonequilibrium response and suggest design-principles for high-sensitivity, low-noise devices. I will also discuss how they rationalize known energetic requirements of some common biochemical motifs and provide new limits to others. Finally, I will demonstrate how they can be used to derive Green-Kubo relations for the transport coefficients of homogenous active fluids in terms of steady-state current fluctuations.

**Julian Legendre (CPHT, École Polytechnique)**

Two topological models on the kagome lattice: tuning the quantum anomalous Hall phase with ferromagnetism and a Z2 topological insulator with spin-orbit coupling

(Egalement par zoom

https://us06web.zoom.us/j/82521180172?pwd=eG1LMmhGRGg2ak0rM2ozdkFrQy83dz09

Meeting ID: 825 2118 0172

Passcode: 298577)

Topological phases, contrarily to many other phases of matter, cannot be understood in terms of local order parameters. Depending on the symmetries and the dimension of the system under consideration, an appropriate topological invariant describes the topological phase. For instance, the (first) Chern number characterizes the quantum anomalous Hall (QAH) phase associated to the Haldane model. With "two copies" of the Haldane model, we can restore time-reversal symmetry; the system is then characterized by a Z2 topological invariant. In this talk, we explore two topological phases, respectively associated to non zero Chern number and Z2 invariant, for two examples of kagome lattice physical systems.

First, we are interested by the kagome magnet Co3Sn2S2. It shows an impressive behavior of the QAH conductivity driven by the interplay between ferromagnetism in the z direction and antiferromagnetism in the xy plane. Motivated by these facts, we show how such a tuning of the QAH conductivity via the external tuning of the magnetic order can be described.

Then, we investigate the topological phases of a spin-orbit coupled tight-binding model with flux on the kagome lattice. This model is time-reversal invariant and shows Z2 topological insulating phases. We show the stability of the topological phase towards spin-flip processes and different types of on-site potentials. To describe the topological properties of the system we use a numerical approach based on the twisted boundary conditions and we develop an analytical approach related to smooth fields in the Brillouin Zone.