FISICA STATISTICA

Introducing the students to dynamical and chaotic systems with a few degrees of freedom, both dissipative and conservative, and to the study of thermodynamical systems with many degrees of freedom, through a microscopical and statistical approach, both classical and quantum.

1st Part. Introduction to dynamical systems: from chaos theory to the new science of complexity. Dissipative dynamical systems (fluxes and maps) in one and two dimensions. Fixed point and limit cycle attractors. Bifurcations. Fluxes in three dimensions. Routes toward chaos. Lyapunov exponents. Fractal dimension. Hamiltonian systems in one and two dimensions. Kam theorem.

2nd Part. The laws of thermodynamics. Thermodynamic potentials. Phase transitions. Kinetic theory of gases. The Boltzmann distribution function and transport equation. Liouville's theorem. The Boltzmann H theorem. Theory of the ensembles of Gibbs. Classical statistical mechanics in microcanonical, canonical and grancanonical ensembles. Partition function. Chemical potential. Quantum statistical mechanics. Density matrix and ensembles. Applications. Concluding remarks on cosmology, thermodynamics and the arrow of time.

1) Robert C. Hilborn, “Chaos and nonlinear dynamics”, Oxford University Press, 2nd Ed. 2000

2) Steven Strogatz, “Nonlinear dynamics and chaos”, Westview Press 2001

3) K. Huang, “Meccanica Statistica”, Zanichelli 1997