INGLESE

Synthetic Program:

1) Short Review of statistical ensembles
2) Phase Transitions and Critical Phenomena
3) Mean Field Theories
4) Renormalization Group
5) Kinetic Theory and Boltzmann Equation
6) Markovian processes

General reference books
- Statistical Mechanics- Author: K. Huang, WILEY
- Meccanica Statistica Elementare – Authors: M. Falcioni and A. Vulpiani,
Springer-Verlag Mailand
-Statistical Mechanics - Authors: R K Pathria, Paul D. Beale, AP

For the part on Critical Phenomena
- Introduction to Phase Transitions and Critical Phenomena -
Author: E. Stanley, Oxford Science
For the recalls of statistical ensembles
- Introduction to Modern Statistical Mechanics - Author: D. Chandler,
Oxford University Press

The course is aimed at providing basic notions and methods of statistical physics and at the same time at presenting its modern applications in physics and beyond.
The course is therefore finalized to a learning process at the end of which the student will be able to manage a broad range of theoretical methods of general use in many branches of science
Concerning communicative skills, the course is aimed at developing the student's ability in presenting in a clear and rigorous ways statistical methods

Statistical ensembles, basic probability theory, operator formalism

The course is structured in 52 hours of frontal lectures (6h for recalls of introductory concepts, 24h for Phase Transitions and Critical Phenomena, Mean Field Theories, Renormalization Group, 22 h for Kinetic Theory and Boltzmann Equation and Markovian processes)
16 hours for classroom exercises and 4 hours of assisted study.
Attendance is not compulsory but strongly recommended.

The examination is oral interview based on the discussion of the arguments illustrated during the course with a typical duration of 45 minutes. Together with the evaluation of the degree of knowledge reached by the student, the interview is aimed to evaluate the students' ability in managing statistical methods and in demonstrating theorems at their basis.

1) A short review of statistical ensembles (1 CFU)


2) Kinetic Theory and Markov Chains (2 CFU)
The Boltzmann Equation- H theorem and its objections – The Master Equation – The Fokker-Plank Equation – The Langevin Equation

3) Fluctuation-Dissipation theorems (1CFU) - Einstein Fluctuation theory – Linear Response Theory – Onsager Relations

4) Phase Transitions and Critical Phenomena (2 CFU)
The order parameter – The Correlation function – critical exponents – Scale invariance – The Ising and granular gas model – The Onsager Solution in one dimension. Random percolation.

5) Mean field theories (1CFU): Landau theory, Weiss theory and Ornstein-Zernicke theory.
6) Renormalization Group (1CFU) Block spins – The one-dimensional Ising model – The gaussian model - Migdal-Kadanoff method for the two-dimensional Ising model. Random Percolation on the triangular lattice.

English

Synthetic Program:

1) Short Review of statistical ensembles
2) Phase Transitions and Critical Phenomena
3) Mean Field Theories
4) Renormalization Group
5) Kinetic Theory and Boltzmann Equation
6) Markovian processes

General reference books
- Statistical Mechanics- Author: K. Huang, WILEY
- Meccanica Statistica Elementare – Authors: M. Falcioni and A. Vulpiani,
Springer-Verlag Mailand
-Statistical Mechanics - Authors: R K Pathria, Paul D. Beale, AP

For the part on Critical Phenomena
- Introduction to Phase Transitions and Critical Phenomena -
Author: E. Stanley, Oxford Science
For the recalls of statistical ensembles
- Introduction to Modern Statistical Mechanics - Author: D. Chandler,
Oxford University Press

The course is aimed at providing basic notions and methods of statistical physics and at the same time at presenting its modern applications in physics and beyond.
The course is therefore finalized to a learning process at the end of which the student will be able to manage a broad range of theoretical methods of general use in many branches of science
Concerning communicative skills, the course is aimed at developing the student's ability in presenting in a clear and rigorous ways statistical methods

Statistical ensembles, basic probability theory, operator formalism

The course is structured in 52 hours of frontal lectures (6h for recalls of introductory concepts, 24h for Phase Transitions and Critical Phenomena, Mean Field Theories, Renormalization Group, 22 h for Kinetic Theory and Boltzmann Equation and Markovian processes)
16 hours for classroom exercises and 4 hours of assisted study.
Attendance is not compulsory but strongly recommended.

The examination is oral interview based on the discussion of the arguments illustrated during the course with a typical duration of 45 minutes. Together with the evaluation of the degree of knowledge reached by the student, the interview is aimed to evaluate the students' ability in managing statistical methods and in demonstrating theorems at their basis.

1) A short review of statistical ensembles (1 CFU)


2) Kinetic Theory and Markov Chains (2 CFU)
The Boltzmann Equation- H theorem and its objections – The Master Equation – The Fokker-Plank Equation – The Langevin Equation

3) Fluctuation-Dissipation theorems (1CFU) - Einstein Fluctuation theory – Linear Response Theory – Onsager Relations

4) Phase Transitions and Critical Phenomena (2 CFU)
The order parameter – The Correlation function – critical exponents – Scale invariance – The Ising and granular gas model – The Onsager Solution in one dimension. Random percolation.

5) Mean field theories (1CFU): Landau theory, Weiss theory and Ornstein-Zernicke theory.
6) Renormalization Group (1CFU) Block spins – The one-dimensional Ising model – The gaussian model - Migdal-Kadanoff method for the two-dimensional Ising model. Random Percolation on the triangular lattice.