7th Warsaw School of Statistical Physics

26 June – 2 July 2022, Sandomierz, Poland

Lecture abstracts

 

Stéphane Douady

Dynamical Models of Plant Growth

The course will show how much non-linear dynamical systems concepts such as instabilities and bifurcations are relevant for morphogenesis, in living or not systems, and for instance in plants. It will insist on the fact that the understanding of the final shape is more dependent on its history of growth, or morphogenesis, step by step, rather than by optimizing some function on the final shape. It will thus show that history is an essential but forgotten parameter that exert a strong constraint on the possible results. A good example will be phyllotaxis, the spiral arrangements of leaves in plants, where the fibonacci numbers appear conspicuously.

 

Joseph O. Indekeu

Lectures on Interfaces and Wetting

In the lectures on Interfaces and Wetting we discuss the phenomenology of phase transitions and critical phenomena that take place at surfaces or interfaces in condensed matter systems. We discuss some of the studies that have been performed since 2010 and for the most part in the domain of density-functional models of wetting in systems with short-range forces. Time permitting, the four systems that will be addressed are: 1. the two-dimensional Ising model with a surface, 2. a two-density continuum model for short-range forces, 3. adsorbed colloid-polymer mixtures with finite-range depletion attraction and 4. adsorbed binary gas mixtures of Bose-Einstein condensates at zero temperature. For the Ising model exact results are analysed, while for the other systems mean-field theory is employed. For systems 2 and 3, thermal fluctuation effects are studied by means of renormalization group calculations starting from an interface potential description. Using the interface potential, for systems 3 and 4 also the three-phase contact line and its associated line tension are studied in the vicinity of a wetting phase transition. Related earlier lectures on Interfaces and Wetting covering developments on topics 2 and 4, on the line tension at wetting and on other topics, can be found in Physica A 389, 4332 (2010).

 

Giuseppe Mussardo

Out of Equilibrium Physics of Classical Field Theories

In these lectures we study the equilibration properties of classical integrable field theories at a finite energy density, with a time evolution that starts from initial conditions far from equilibrium. These classical field theories may be regarded as quantum field theories in the regime of high occupation numbers. This observation permits to recover the classical quantities from the quantum ones by taking a proper h -> 0 limit. In particular, the time averages of the classical theories can be expressed in terms of a suitable version of the LeClair-Mussardo formula relative to the Generalized Gibbs Ensemble. For the purposes of handling time averages, our approach provides a solution of the problem of the infinite gap solutions of the Inverse Scattering Method.

 

Daniel Rothman

Earth's Carbon Cycle: Complex Kinetics, Nonlinear Dynamics, and Catastrophic Change

The carbon cycle is a loop between photosynthesis, which creates molecular oxygen and consumes CO2, and respiration, which uses oxygen to convert the products of photosynthesis back to CO2. The cycle's importance for climate is well known. Less recognized---and much less understood---is the central role the cycle plays in the organization and stability of life. These lectures emphasize the latter theme; their objective is to show how concepts and methods of statistical and nonlinear physics can be used to learn how the carbon cycle works. We first examine how microbial organisms attempt to close the loop. Obervations indicate that respiration rates are timescale invariant. The progressive slowing down leaves the cycle 0.1% incomplete; remarkably, this tiny feedback error is responsible for the oxygen we breathe. We explain these observations by constructing a model inspired by glassy dynamics, and use it to successfully predict scaling laws for the organization of microbial life deep beneath the seafloor. Next, we ask whether the cycle is stable. Observational data suggest that it is not, and that the most rapid changes in CO2 levels are associated with mass extinction. We show that a simple model of an excitable carbon cycle explains an apparent threshold---defined in terms of a critical rate of CO2 injection---for catastrophic change. These results yield a scaling law for the critical rate, which we use to estimate the threshold for a modern mass extinction.

 

Robert Seiringer

Foundations of Density Functional Theory

Given that the Schrödinger equation for atoms and molecules cannot be solved efficiently numerically, in practice one has to resort to approximate theories for doing calculations. Density Functional Theory is probably the most successful and widely used method in quantum chemistry. In this talk I will explain its mathematical structure, and outline some recent results on the validity of the local density approximation, the uniform electron gas and the sharp constant in the Lieb-Oxford inequality. (Joint work with Elliott Lieb and Mathieu Lewin.)