Advanced statistics

Recommended Prerequisites

Thermodynamics and Statistical Physics.

Teaching Methods

Lectures where the theory is complemented with practical applications that are physically relevant. There should be an emphasis in the application of these methods to practical problems in the tutorial classes.

Learning Outcomes

- To acknowledge that the correlations among different components of a system may lead to new laws of Physics.
- To differentiate between systems in equilibrium and systems out of equilibrium.
- To become acquainted with the equations that describe the dynamics of systems out of equilibrium (master equation, Langevin equation and Fokker-Planck equation).
- To be able to evaluate critical exponents and partition functions for systems in equilibrium and propagators for systems out of equilibrium. To evaluate the effect of non-linearity through perturbation theory and the renormalisation group.

Work Placement(s)

No

Syllabus

- Equilibrium Statistical Physics:
- Review of Statistical Physics
- Fermi-Dirac and Bose-Einstein distributions and their applications, (electrons in a metal,  Bose-Einstein condensation)
- Phase transitions
- First and second order transitions
- Critical exponents, universality
- Renormalisation group

- Non-equilibrium Statistical Physics:
- Markov processes, master equation
- Stochastic processes, Langevin and Fokker-Planck equations and applictions  (Brownian motion)
- Fluctuation-dissipation theorem
- Dynamic scaling and renormalisation group.

Assessment Methods

Assessment
Resolution Problems: 100.0%

Bibliography

Stanley, H.E. (1987). Introduction to phase transitions and critical phenomena. Oxford University Press.
Landau, L.D., Lifshitz E. M. & Pitaevskii, L.P. (1980). Statistical physics I/II. Butterworth-Heinemann.
Ma S.-K. (1985), Statistical mechanics. World Scientific Publishing Company.
E. J. S. Lage (1995), Física estatística. Fundação Calouste Gulbenkian.
Plischke, M. & Bergersen, B. (2006), Equilibrium statistical physics. Imperial College Press.
Balescu, R. (1975). Equilibrium and non-equilibrium statistical mechanics. John Wiley & Sons.

Yeomans, J.M. (1992). Statistical mechanics of phase transitions. Clarendon, Oxford.

Goldenfeld, N. (1992). Lectures on phase transitions and the renormalization group. Addison-Wesley.

Gonçalves, E. & Lopes, N.M. (2000). Probabilidades - Princípios Teóricos. Escolar Editora.

Taylor, H. M. & Karlin, S. (1998). An introduction to stochastic modeling. Academic Press.