Physics

FRANCESCO SCIORTINO

GENERAL OBJECTIVES:
The first main objective of the course is to introduce the students to the fundamental concepts of Statistical Mechanics (SM). Generally speaking the students must understand how to derive the thermodynamic description of a macroscopic system from its microscopic laws. This knowledge is of obvious relevance for their background in Physics and for the more specialised courses of the next years.
SPECIFIC OBJECTIVES:
A - Knowledge and understanding
OF 1) basic concepts in equilibrium SM and in probability theory
OF 2) computation rules in classical SM (microcanonical, canonical and grand canonical ensembles); equivalence between the different rules and their application to non-interacting systems;
OF 3) Basic concepts and example of interacting systems (Van Der Waals equation).
OF 4) Fundamental concepts and computation rules in Quantum SM; application to the quantum perfect gas, Bose-Einstein and Fermi-Dirac distributions;
OF 5) Thermodynamic properties of quantum bosonic and fermionic systems; high and low temperature limits; Sommerfeld expansion for a Fermionic gas; specific heat in a solid; Debye theory.
OF 6) Brief summary of quantisation of the electromagnetic radiation, black body radiation.
B - Application skills
OF 7) The second objective is to prepare the students to actively solve problems in physics where SM concepts are required. This will happen at first with problems structured with a conceptual scheme similar to the one discussed and applied during the course. However, as their preparation progresses, students are also expected to use SM concepts for solving new problems in different applications.
C - Autonomy of judgment
OF 8) The third and more ambitious objective is to teach the students to think in probabilistic and statistic terms, using concepts and methods from SM as a powerful problem solving tool, both in physics and in different fields (e.g. socio-economic systems, biological systems, medical applications)
D - Communication skills
OF 9) Besides having a clear understanding of the new acquired concepts in SM, the studend should correspondingly acquire the ability to communicate and transmit these concepts in a clear and direct way.
E - Ability to learn
OF 10) The students should become able to read and understand scientific books and articles where SM concepts are involved and should be able to deepen autonomously their knowledge in this field.

Thermodynamics

Richiami di termodinamica e meccanica classica Teorema di Liouville, ipotesi ergodica e ensemble microcanonico, postulato fondamentale della meccanica statistica Elementi di calcolo della probabilita' (assiomi, proprieta', esempi di distribuzioni notevoli) Ensemble microcanonico: additivita' entropia, teorema equipartizione, gas ideale classico. Riflessioni su concetto di entropia (paradosso di Gibbs, entropia come ignoranza, irreversibilita') Ensemble canonico: funzione di partizione, energia libera di Helmholtz, densita' di probabilita' dell'energia. Oscillatore armonico classico - relazione barometrica - gas di particelle relativistiche Relazioni di fluttuazione-dissipazione e equivalenza tra insieme canonico e microcanonico Gas perfetto. Equipartizione dell'energia. Statistica di Maxwell Boltzmann; condizioni di validita` della meccanica statistica classica. Distribuzione di Maxwell; Insieme gran canonico. Il gran potenziale. Funzioni termodinamiche nell' insieme gran canonico. Equivalenza insieme canonico e gran canonico Gas quantistici. Distribuzioni di Fermi-Dirac e di Bose-Einstein. Limite classico: alte temperature e/o basse densità. Gas di Fermi allo zero assoluto: energia di Fermi, energia media, pressione. Calore specifico di un gas di Fermi alle basse temperature. Condensazione di un gas di Bose-Einstein. Vibrazioni nei solidi, modello di Debye Spettro del corpo nero. Formula di Planck.

Statistical Mechanics di Kerson Huang, Wiley
Statistical Physics by Roberto Piazza Springer
S-K Ma, Statistical Mechanics, World Scientific, Singapore (1985)

in the classroom

Ability to solve statistical mechanics problems

Ability to orally explain the topics listed in the program