Abstracts
Henk van Beijeren University of Utrecht, The Netherlands
On the kinetic theory of fluids
Boltzmann Equation
Derivation, adding boundary terms, H-theorem with and without boundary terms. Chapman Enskog solution,
adding fluctuating terms.
Enskog and Revised Enskog Equation
Derivation, H-theorem, Onsager's reciprocal relations
Ring Kinetic Equations
Non-analytic density dependence of transport coefficients, long time tails and their consequences.
Christophe Josserand Université Pierre et Marie Curie, Paris, France
Theory of supersolids
The discovery of the superconductivity, the superfluidity and the experimental observation of Bose-Einstein condensates have punctuated the 20th century. Until recently, it was believed that a supersolid state (a quantum solid showing superfluid properties) could not exist because of the contradiction between the long range order for a superfluid phase and the short scale of the solid structure. In 2004, E. Kim and M. Chan measured experimentally a sudden decrease in the rotational inertia of solid Helium below 100 mk that was interpreted as a direct observation of supersolidity. Since then more than seven other experiments have reproduced this result but the understanding of this transition is still questioned: for instance why does the supersolid fraction depend so strongly on the solid structure? Can we describe the supersolid state or dynamics? In this school, I will try to exhibit the important properties shared by the experiments done since 2004. Then I will discuss the theoretical issues of describing a supersolid. Finally, I will present how a supersolid model can be obtained from a mean-field approach, leading to a quantum solid model. This model will be used to revisit some experimental results.
Joachim Krug Universität zu Köln, Germany
Statistical physics of biological evolution
The mathematical theory of evolution is concerned with the changes in the genetic composition of populations that occur under the influence of the evolutionary forces of selection, mutation and demographic noise. In its focus on noisy, collective behavior in large ensembles of (relatively) simple constituents it displays many conceptual similarities to statistical physics, which have given rise to a fruitful interaction between the two fields in recent years. In these lectures I will introduce the basic concepts of the theory and describe some recent work, with particular emphasis on results that are relevant to evolution experiments with microbial populations.
Contents:
I. Introduction: Evolutionary forces and evolutionary regimes
II. Genotype spaces and fitness landscapes
III. Deterministic mutation-selection models of quasispecies type
IV. Adaptive walks and extremal statistics
V. Clonal interference and the speed of evolution
Literature:
K. Jain and J. Krug, Adaptation in simple and complex fitness landscapes, in: Structural approaches to sequence evolution, ed. by U. Bastolla, M. Porto, H.E. Roman and M. Vendruscolo (Springer, 2007) [arXiv:q-bio/0508008]
S.-C. Park, D. Simon and J. Krug, The speed of evolution in large asexual populations, J. Stat. Phys. 138 (2010) 381 [arXiv:0910.0219]
Jorge Kurchan École Supérieure de Physique et de Chimie Industrielles, Paris, France
The quest for a transition and order in glasses
1) From supercooled liquids to glasses : general phenomenology Laws of growth of timescale. Types of glasses: fragile and strong. Divergence in timescale: why do we care so much?
2) Equilibrium versus non equilibrium. Fluctuation dissipation. Aging dynamics. Effective temperatures.
3) A zoo of models, with static and dynamic transition. Why do we say that glasses are an unsolved problem, in spite of all these successful models?
4) What is a solid? Translational symmetry breaking, thermodynamic limit and order. Do solids flow? The example of crystals of soft particles at finite temperatures.
5) The ideal glass state (why do we care so much?). Are glasses true solids? Correlation lengths: point-to-set and complexity lengths.
6)
A brief overview of the mean field description of glasses: the random
first order scenario/density functional theory/mode-coupling theory. [why
do we call this "mean-field"?]
a) successes, b) impasse
Michael Schick University of Washington, Seattle, USA
A selection from the physics of biological membranes
These lectures will be devoted to two problems involving biological membranes, particularly the plasma membrane which surrounds all cells. The first is that of membrane fusion, the process by which two bilayer vesicles are brought together and, with the aid of intermediate molecules, form a connection with one another by means of which material from one can be transferred to the other. Such processes occur constantly in intracellular trafficing, whenever material leaves the cell, as in exocytosis, or enters the cell, endocytosis, and the infection of cells by viruses. For all its importance, it is not well understood. The second phenomenon is that of the occurrence of heterogenieties in the plasma membrane, or “rafts”, which are thought to consist of aggregates of cholesterol and saturated lipids which float in a sea of unsaturated lipids. This new paradigm for the organization of the plasma membrane has had an enormous impact. The major players in these systems will be introduced, and various theoretical approaches to them will be reviewed.
Wilhelm Zwerger Technische Universität München, Germany
Many-body physics with ultracold atoms and the search for a perfect fluid
In recent years, ultracold atoms have emerged as model systems that allow to study basic problems in many-body physics. The lectures provide an introduction to what ultracold atoms are and how - in gases that are a million times more dilute than air - the regime of strong interparticle interactions can be reached. Two examples are discussed in more detail: bosonic Luttinger-liquids confined in a quantum wire configuration by an optical lattice and Fermi gases at infinite scattering length that arises via a Feshbach resonance.
Interest in the latter system arises from both the general problem of the crossover from a BCS- to a BEC-type superfluid but also from recent devolopments in quantum field theory. Indeed, based on a calculation of the shear viscosity η and the entropy density s of certain strongly coupled field theories via the AdS/CFT-correspondence, Kovtun, Son and Starinets conjectured that their ratio is bounded below by the universal number ℏ/4π kB, a bound that appears to hold for all existing fluids. The substances that come closest to being perfect in the sense of a minimum value of η/s are the quark gluon plasma and ultracold atoms at infinite scattering length, the so called unitary Fermi gas. The lectures will provide an introduction to the origin and interpretation of this bound from a simple physics perspective. Moreover, quantitative results for η/s are presented in the normal phase of the unitary Fermi gas, a scale invariant, non-relativistic field theory. They show that its viscosity to entropy density ratio is only a factor seven or so above the Kovtun, Son and Starinets bound.
Literature:
I. Bloch, J. Dalibard and W. Zwerger: Many-Body Physics with Ultracold Gases, Rev. Mod. Phys. 80, 885 (2008)
T. Enss, R. Haussmann and W. Zwerger: Viscosity and scale invariance in the unitary Fermi gas, Annals of Physics 326, 770 (2011)