Study-unit STATISTICAL MECHANICS
| Course name | Physics |
|---|---|
| Study-unit Code | 55A00003 |
| Location | PERUGIA |
| Curriculum | Fisica della materia |
| Lecturer | Maria Cristina Diamantini |
| Lecturers |
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| Hours |
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| CFU | 6 |
| Course Regulation | Coorte 2023 |
| Supplied | 2024/25 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | FIS/02 |
| Type of study-unit | Opzionale (Optional) |
| Type of learning activities | Attività formativa monodisciplinare |
| Language of instruction | Italian |
| Contents | Thermodynamics. Theory of phase transitions. Gas kinetic theory. Classical statistical mechanics. Black-body radiation and problems with classical statistical mechanics. Quantum statistical mechanics. Bose gas and Fermi gas. |
| Reference texts | 1)"Statitistical Mechanics" , K. Huang 2)"Fisica Statistica", L.D. Landau e E.M. Lifsits 3)"Statistical mechanics", R. K. Pathria 4)"Statistical mechanics", R. Kubo 5)Notes on critical phenomena, R. Percacci |
| Educational objectives | Acquisition of basic knowledges of classical and quantum statistics. Students should be able to compute the partition function for classical and quantum systems and derive the thermodynamic properties of these systems. |
| Prerequisites | Knowledges of thermodynamics and quantum mechanics |
| Teaching methods | theory courses |
| Other information | None |
| Learning verification modality | Exercises sessions to verify comprehension. The exam consists in a written and oral part. If the written score reaches a minimum of 18/30 the candidate can access to the oral part.The final score will be the average of the two scores. |
| Extended program | 1)Thermodynamics: laws of thermodynamics, entropy, thermodynamic potentials. Theory of first order phase transitions. 2)Gas kinetic theory. Micro-and macro states. Liouville theorem. BBGKY hierarchy. H-theorem. 3)Classical statistical mechanics. Microcanonical ensemble:probability density, entropy. Equipartition theorem. Gibbs paradox. Canonical and grand canonical ensembles. Equivalence between mean value and most probable value. Derivation of thermodynamics. 4)Quantum statistical mechanics. Density matrix. Fermions and bosons. Microcanonical, canonical and grand canonical ensembles. Grand canonical Fermi gas. Grand canonical Bose gas. Bose-Einstein condensation. 5)Ising model in the mean field approximation. Exact solution in one dimension. Continuos phase transitions, basics, order parameter. Critical Phenomena: critical exponents, strong correlations, universality, scaling laws. Scaling, the Kadanoff construction. Introduction to the renormalization group. |