Classical transport, steady states and large deviations in non equilibrium 1d systems

The lectures will review some properties of non-equlibrium diffusive systems in their steady state (existence of long-range correlations, non-locality of the large deviation function of the density, large deviation function of the current and its symmetries). They will also present some recent progresses as well as open problems on density and current fluctuations in non steady state situations or for non diffusive systems.

Critical Casimir forces

Long-ranged correlations in a fluid near its critical point lead to clearly identifiable effective forces acting on confining walls. The corresponding universal scaling functions are discussed for various boundary conditions and geometries. The theoretical predictions are compared with high precision experimental data for He^4 and He^3/He^4 wetting films near the superfluid phase transition as well as with synchrotron scattering data from classical binary liquid mixtures. Direct measurements and applications for colloidal suspensions are discussed in detail.

Elastohydrodynamics

The borderlands between elasticity and hydrodynamics lead naturally to a number of problems in elastohydrodynamics. I will discuss some phenomena this rich area: the physics of fluid-infiltrated soft solids, thin film elastohydrodynamics in adhesion and lubrication, and the mathematical description of singularities associated with touchdown.

Models of Life

Biology presents an astounding diversity
of discrete states or species, that coexist over
time-scales much longer than
the characteristic times of the underlying degrees of freedom.
Furthermore, these phenomena range from the scale of
gene regulatry patterns to cells and to that of populations.
On the sub-cellular scale, molecular competition and
positive feedback acting on short time scales maintain cells in
specialized states, setting the foundation for
complexity of __multicellular__ organisms. On larger scales,
competition in turn selects for ecosystems where
different species coexist over long intervals of time.
The lectures will explore how competition can act as an "engine"
for this diversity, using
tools from statistical mechanics and complex systems.
I will in particular introduce models of basic biological mechanisms,
including gene regulation, epigenetics, and mechanism for evolving
biological diversity in food webs and ecosystems.
The topics are partly covered in the book "Models of Life" (2014).

Nonlinear fluctuating hydrodynamics

The lecture will be about problems disussed in recently published two review type articles:

1. "The Kardar-Parisi-Zhang equation - a statistical physics perspective" [arXiv:1601.00499],

2. "Fluctuating hydrodynamics approach to equilibrium time correlations for anharmonic chains" [arXiv:1505.05987]

Loop soup models, their connections to classical and quantum spin systems, and their universal behaviour in 3D

Lecture notes: [pdf (38 MB)]

Many classical and quantum spin systems can be described by models of random
loops. I will describe the representations of Symanzik and Brydges-Fröhlich-Spencer
(classical), and of Tóth and Aizenman-Nachtergaele (quantum).

These are examples of “loop soup” models that display a universal behaviour in
dimensions 3 and higher: At low temperatures, the system contains macroscopic
loops and the joint distribution of their lengths is given by a Poisson-Dirichlet distribution.
This can be understood (and calculated) by viewing the loop distribution as the
invariant measure of an effective spit-merge process.

I will explain the relevant notions. If time permits, I will derive some consequences
of this universal behaviour regarding the nature of symmetry breaking in quantum
spin systems.