Course: 2022/2023

Statistical Physics

(18316)

Requirements (Subjects that are assumed to be known)

Probability and Statistics,
Mechanics and Relativity,
Quantum Physics.

Skills and learning outcomes

Description of contents: programme

1. Foundations of Statistical Physics.
- Microscopic and macroscopic states.
- Thermodynamic limit.
- Phase space.
- Liouville's theorem.
2. Microcanonical ensemble - Equilibrium of an isolated system.
- Entropy and the second Principle of Thermodynamics.
- Application to the ideal gas and the two state system.
- First Principle of Thermodynamics.
3. Canonical and Grand canonical ensembles - Equilibrium of a system with an energy reservoir and an energy and particle reservoir.
- Partition Function.
- Density Matrix.
- Fluctuations.
- Maximizing Entropy.
- Free Energy.
- System of Harmonic Oscillators.
- Application to Paramagnetism.
4. Classical Gases.
- Ideal Gas.
- Equipartition Theorem.
- Virial Theorem.
- Gibbs Paradox.
- Maxwell Distribution. Maxwell-Boltzmann Statistics.
- Diatomic Gas.
5. Quantum Gases I.
- Density of States.
- Relativistic Systems.
- Photon Gas.
- Phonon Gas.
6. Quantum Gases II.
- Bosons and Fermions.
- Bose-Einstein statistics.
- Ideal Bose Gas.
- Bose-Einstein condensates.
- Fermi-Dirac statistics.
- Ideal Fermi Gas.
- Electron Gas.

Learning activities and methodology

AF1. THEORETICAL-PRACTICAL CLASSES. Weekly sessions of 100 minutes, divided in two 50 minutes parts with a break, where the theoretical concepts are explained. Students will have basic reference texts to facilitate the understanding of the classes. In the recitations the problems and activities proposed after the theoretical sessions are solved and discussed. There will be mid term tests for evaluating the competences and skills acquired by the students and for helping them improving their learning strategies. This entails 22 hours in face-to-face sessions for 3 ECTS courses.
AF2. TUTORING SESSIONS. Every week there will be a one hour face-to-face tutoring session available for students in the subject webpage.
AF3. STUDENT INDIVIDUAL WORK OR GROUP WORK. Student's individualized work is fundamental for understanding results, proofs and exercises and develop problem solving skills. Discussing concepts and solving problems in small groups of students is an excellent complementary activity for improving teamwork competences and for self-assessment.
AF9. FINAL EXAM. Global assessment of knowledge, skills and capacities acquired throughout the course. It entails 4 hours 100% on-site.
MD1. THEORY CLASS. Classroom presentations by the teacher on the blackboard or with IT and audiovisual support in which the subject's main concepts are developed and where material and bibliography to complement student learning is provided.
MD2. PRACTICAL CLASS. Resolution of practical cases and problem, posed by the teacher, and carried out individually or in a group.
MD3. TUTORING SESSIONS. Individual or in-group tutorial sessions for the resolution of doubts by the teacher.
MD6. LABORATORY PRACTICAL SESSIONS. Applied/experimental learning in workshops and laboratories under the tutor's supervision.

Assessment System

- % end-of-term-examination 60
- % of continuous assessment (assigments, laboratory, practicals...) 40

Basic Bibliography

- F. Mandl. Statistical Physics. Wiley. 1988
- L.D. Landau and E.M. Lifshitz. Statistical Physics Volume 5. Butterworth-Heinemann. 1980
- R.K. Pathria and P.D. Beale. Statistical Mechanics. ELSEVIER. 2011

- David Tong · Lectures on Statistical Physics : http://www.damtp.cam.ac.uk/user/tong/statphys.html

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The course syllabus may change due academic events or other reasons.