Unit STATISTICAL MECHANICS

Course
Physics
Study-unit Code
55A00003
Location
PERUGIA
Curriculum
Fisica della materia
Teacher
Maria Cristina Diamantini
Teachers
  • Maria Cristina Diamantini
Hours
  • 42 ore - Maria Cristina Diamantini
CFU
6
Course Regulation
Coorte 2021
Offered
2022/23
Learning activities
Affine/integrativa
Area
Attività formative affini o integrative
Academic discipline
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)"Statistical physics", L.D. Landau and 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.
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