Topics in Modern Statistical Physics

The students entering the course are expected to have completed an introductory lecture of statistical physics and thermodynamics as well as the standard undergraduate level courses (classical and quantum mechanics, electrodynamics). Some knowledge on fluid mechanics and stochastic processes is useful.

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In this course we discuss selected topics in many-body classical statistical mechanics, with applications to biophysics and soft condensed matter. The focus will be on equilibrium, as well as non-equilibrium phenomena.

1. General introduction to biophysics and soft condensed matter.

2. Statistical mechanics of simple one-component liquids: Mayer expansion, pair correlation function, structure factor, Ornstein-Zernike relation, closure relations, hard-sphere fluids.

3. Multi-component systems: osmotic pressure, phase transitions, Landau theory, effective interactions, application in depletion interactions, membranes.

4. Inhomogeneous fluids: thermodynamic description of surface tension, classical density functional theory, gas-liquid interface, wetting/drying, hydrophobic interactions, sedimentation.

5. Charged classical fluids: dilute ionic solutions in bulk and confinement, electrostatic screening, Debye-Hückel theory, Poisson-Boltzmann theory, Derjaguin-Landau-Verwey- Overbeek effective interactions, fluctuations beyond mean-field theory, ionic liquids.

6. Polymer physics: freely-jointed chain, Rouse model, scaling laws, proteins, supramolecular polymers, self-assembly.

7. Liquid crystals: phenomenology, Onsager and Maier-Saupe theory, Landau-de Gennes expansion, nematic elasticity, influence of external fields.

8. Non-equilibrium physics: Many-body Brownian motion, hydrodynamic interactions, fluctuation-dissipation theorem, Onsager reciprocity, transport coefficients, dynamical density functional theory.

1. J.-P. Hansen and I. R. MacDonald - Theory of simple liquids

2. P. G. de Gennes and J. Prost – The physics of liquid crystals

3. J. K. G. Dhont – An introduction to the dynamics of colloids

4. S. R. de Groot and P. Mazur – Non-equilibrium thermodynamics

5. J.-L. Barrat and J.-P. Hansen, Basic concepts for simple and complex liquids

The student is able to understand the physical mechanisms behind various processes underlying soft condensed matter and biophysics, including the theoretical calculations leading to these results. The student knows what are the main interactions relevant in this field, and how to compute effective interactions. The student will have a working knowledge on how to apply statistical mechanics to more complex problems of classical (complex) fluids, in and out of equilibrium.

Mid-term exam (30%), hand-in exercises (30%), final exam (40%).