Module page
Meccanica statistica
| academic year: | 2013/2014 |
| instructor: | Federico Ricci Tersenghi |
| degree course: | Mathematics (magistrale) |
| type of training activity: | affine e integrativa |
| credits: | 6 (48 class hours) |
| scientific sector: | FIS/02 Fisica teorica, modelli e metodi matematici |
| teaching language: | italiano |
| period: | I sem (01/10/2013 - 18/01/2014) |
Lecture meeting time and location
Presence: highly recommended
Module subject:
Introduction to probability theory and stochastic processes. The method of
statistical ensembles.
Entropy, internal energy, free energy. States and thermodynamic observables.
Variational principles. Relaxation toward thermodynamical equilibrium.
Phase transitions.
Spontaneous symmetry breakdown. Ferromagnetic models. Spin glasses. Neural
networks.
Interpolation methods. Recognition of the order parameters.
The phenomenon of the spontaneous replica symmetry breaking.
Applications in the economic and sociological frame.
Applications in the biological and medical frame.
The problem of the construction of statistical mechanics models for the
immunological system.
Suggested reading:
F. Guerra, Introduzione alla Meccanica Statistica, corso INdAM, con
appendici.
F. Guerra, Introduction to Mean Field Spin Glass Theory: Methods and
Results, corso tenuto a Les Houches 2005.
Autori vari: materiale monografico.
Tutto il materiale sara' fornito nel corso delle lezioni.
Testi di riferimento:
Marc Mezard, Giorgio Parisi, Miguel Virasoro, Spin Glass Theory and
Beyond, Singapore, World Scientific, 1987.
David Ruelle, Statistical Mechanics. Rigorous Results, New York, W.A.
Benjamin Inc., 1969.
D.J. Amit, Modeling brain functions: The world of attractor neural
network, Cambridge University Press, 1992.
Type of course: standard
Knowledge and understanding:
Successful students will be able to deal with topics concerning the
applications of statistical mechanics at equilibrium and off equilibrium,
and will become proficient and acquainted with subjects such as
variational principles, probabilistic evolution laws, phase transitions,
treatment of complex systems.
Skills and attributes:
Successful students will be able to confront with
the analysis of the structure of complex systems through statistical
mechanics techniques, with the purpose of applications in the case of
physical systems, social and economical systems, and problems in biology
and medicine.
Personal study: the percentage of personal study required by this course is the 65% of the total.