Learning Outcomes:
On completion of this module students should:
1. Have understood the meaning of the partition function and how to use it for calculation of thermodynamic properties of condensed matter systems;
2. Have understood the concept of statistical ensemble;
3. Be familiar with the concept of a phase transition and critical behaviour, and be able to describe the signatures of a phase transition;
4. Have understood the concept of fluctuations and describe their effect on thermodynamic quantities;
5. Be able to describe the geometry and elasticity of a polymer chain;
6. Be able to recognise the signatures of entropic forces and calculate their magnitude in molecular systems;
7. Be able to do basic calculations using the lattice models in condensed matter;
8. Be familiar with the ways of describing non-equilibrium processes in condensed matter and biophysics.
Indicative Module Content:
1. Phase transitions: Landau theory, critical fluctuations, scaling, renormalisation group method
2. Lattice models: transfer matrix method, exact solution of the Ising model, mean field theory
3. Polymers: statistics of an ideal chain, Gaussian chain, self-avoiding chain, worm-like chain
4. Entropic forces at the nanoscale: depletion interactions, entropic springs, polymer chain elasticity
5. Charged systems: Poisson-Boltzmann equation in planar, cylindrical and spherical geometry, charge binding, charge correlations, Wigner crystals, strong coupling theory
6. Diffusion and Brownian motion: Langevin equation, Gaussian random walk, Levy flights.
7. Non-equilibrium processes: Kramers problem, active particles