Andrea De Luca (Oxford)

Solution of a minimal model for many-body quantum chaos

I will present a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space and the time evolution is specified as a random circuit, which is random in space but periodic in time (Floquet). Each site is coupled via a random matrix to its neighbour on one side during the first half of the evolution period, and to its neighbour on the other side during the second half of the period. I will introduce a diagrammatic formalism useful to average the many-body dynamics over realisations of the random matrices. This approach leads to exact expressions in the large-q limit and sheds light on the universality of random matrices in many-body quantum systems and the ubiquitous entanglement growth in out-of-equilibrium dynamics. I will also discuss universal behaviour which goes beyond random matrix theory and the role played by space dimensionality which emerges through a mapping into the classical Potts model, exact at large q.

Thierry Dauxois (ENS Lyon & CNRS)

Energy cascade in internal wave attractors

Internal gravity waves play a primary role in geophysical fluids : they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. In addition to their very interesting and very unusual theoretical properties, these waves are linked to one of the important questions in the dynamics of the oceans: the cascade of mechanical energy in the abyss and its contribution to mixing.

Combining the physics of waves, dynamical systems theory and oceanography, I will discuss a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multi-scale internal wave motion. I will also provide explicit evidence of a wave turbulence framework for internal waves. Finally, I will show how beyond this regime, we have a clear transition to a cascade of small-scale overturning events which induce mixing.

Mathias Casiulis (LPTMC)

Collective motion in an ideal spin fluid

Collective motion, the macroscopic alignment of velocities in a system of particles, is a key feature of active matter systems. From simple Vicsek-like models to real-life experiments, many different systems seem to feature collective motion, often accompanied by exotic correlations and phase separation properties. These phenomena are however generally observed in non-equilibrium dynamics only, and many models are built up in an ad hoc manner to reproduce experimental data.

In the last few years, some works tried to link the exotic features of active systems to well-known equilibrium dynamics, by studying the low Peclet number limit of active systems for instance [1], thereby finding links between the usual 2d melting transition and the acclaimed MIPS (Motility-Induced Phase Separation), for instance.

The aim of my work is to study, in a toy-model that was designed to be as simple as possible [2], whether collective motion can exist in a conservative framework, when introducing a spin-velocity coupling in a spin fluid. In this talk, I will discuss the model itself, its numerical phenomenology and its links to various other systems and results of statistical mechanics.

[1] L. Cugliandolo, P. Digregorio, G. Gonella, and A. Suma, Phase Coexistence in Two-Dimensional Passive and Active Dumbbell Systems, PRL 119, 268002 (2017)

[2] S. Bore, M. Schindler, K. Lam, E. Bertin, and O. Dauchot, Coupling Spin to velocity: collective motion of Hamiltonian polar particles, J. Stat. Mech. 033305 (2016)

Alexis Poncet (LPTMC)

Tagged particles in single-file systems

Single-file systems, in which particles confined to a channel cannot overtake each other, exhibit a well-known subdiffusive scaling.
This anomalous behavior is a direct consequence of strong spatial correlations induced by the geometrical constraints. Even if this fact has been recognized qualitatively for a long time, up to now there has been no full quantitative determination of these correlations.
In this talk, we present several theoretical approaches that enable us to derive expressions for multiple-tag observables in the Symmetric Exclusion Process (SEP). We will cover the cases of both high-density and arbitrary-density systems, and of both unbiased and biased tagged particles.

Mathieu Salanne (Phénix Jussieu)

Modeling supercapacitors at the molecular scale

The electric double layer is generally viewed as simply the boundary that interpolates between an electrolyte solution and a metal surface. Contrary to that view, recent studies have shown that the interface between ionic liquids and metallic electrodes can exhibit structures and fluctuations that are not simple reflections of surrounding bulk materials [1]. The charge of the electrode is screened by the interfacial fluid and induces subtle changes in its structure, which cannot be captured by the conventional Gouy-Chapman theory.

In recent years, this topic has been more intensively addressed in order to develop more efficient supercapacitors [2]. The latter are electrochemical devices that store the charge at the electrode/electrolyte interface through reversible ion adsorption. In order to understand the molecular mechanisms at play, we have performed molecular dynamics simulations on a variety of systems made of ionic liquids and electrodes of different geometries ranging from planar to nanoporous. A key aspect of our simulations is to use a realistic model for the electrodes, by allowing the local charges on the atoms to vary dynamically in response to the electrical potential caused by the ions and molecules in the electrolyte [3].

These simulations have allowed us to gain strong insight on the structure and dynamics of ionic liquids at electrified interfaces. From the comparison between graphite and nanoporous carbide-derived carbon (CDC) electrodes, we have elucidated the microscopic mechanism at the origin of the increase of the capacitance enhancement in nanoporous carbons [4]. We have also studied the impact of the carbon texture, by comparing CDC with perforated graphene materials [5].

References:

1.       Fedorov, M.V., Kornyshev, A.A., Chem. Rev., 114 (2014), 2978-3036

2.       Salanne, M., Rotenberg, B., Naoi, K., Kaneko, K., Taberna, P.L., Grey, C.P., Dunn, B., Simon, P., Nature Energy, 1 (2016), 16070

3.       Merlet, C., Pean, C., Rotenberg, B., Madden, P.A., Simon, P., Salanne, M., J. Phys. Chem. Lett., 4 (2013), 264-268         

4.       Merlet, C., Rotenberg, B., Madden, P.A., Taberna, P.L., Simon, P., Gogotsi, Y., Salanne, M., Nature Materials, 11 (2012), 306-310

5.       Mendez-Morales, T., Burbano, M., Haefele, M., Rotenberg, B., Salanne M., J. Chem. Phys., 148 (2018), 193812