2024 Faculty Courses School of Science Undergraduate major in Physics
Statistical Mechanics II（Lecture)
- Academic unit or major
- Undergraduate major in Physics
- Instructor(s)
- Syuichi Murakami
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Mon / 5-6 Thu
- Class
- -
- Course Code
- PHY.S312
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Topics of this course include (1) grandcanonical ensemble, (2) basics of quantum statistical mechanics, in particular physics of fermions and bosons, (3) basics of statistical mechanics of interacting systems, and (4) phase transitions and critical phenomena.
Through this course, students will understand basic properties of physical phenomena based on grandcanonical ensemble, statistics of fermions or bosons, and understand various phase transitions which can be observed experimentally.
Course description and aims
Through this course, students will be able to (1) explain grandcanonical ensembles, (2) explain basic properties of fermions and bosons,(3) calculate physical properties of fermions and bosons, and (4) explain basics of phase transitions and critical phenomena.
Keywords
grandcanonical ensemble, chemical potential, fermion, boson, Bose condensation, phase transition, critical exponent, mean-field theory
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
The contents will be explained through lectures. The 3rd, 4th, 5th, 6th, 10th, and 11th lectures might be in the on-demand format, and the details will be explained in the class. The tools such as T2SCHOLA and google forms will be used to communicate with students.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Conditions of thermal equilibrium and chemical potential | Explanation on conditions of thermal equilibrium and introduction of chemical potential |
| Class 2 | Chemical potential and grand canonical ensemble | Explanation on chemical potential, related physical quantities, and grand canonical ensemble |
| Class 3 | Properties of grand canonical ensemble | Explanation on properties of grand canonical ensemble, and calculation of the grand partition function of an ideal gas |
| Class 4 | Quantum mechanics of many-body systems | Explanation quantum mechanics of many-body systems and particle statistics |
| Class 5 | Grand partition function of many-body systems and particle statistics | Explanation on grand partition function of many-body systems and particle statistics |
| Class 6 | Fermions and Fermi statistics | Explanation on Fermi statistics and Sommerfeld expansion |
| Class 7 | Properties of fermion systems | Explanation on properties of fermion systems, such as chemical potential, specific heat, and spin susceptibility |
| Class 8 | Bosons and Bose statistics | Explanation on bosons and Bose statistics |
| Class 9 | Bose condensation | Explanation on Bose condensation |
| Class 10 | Basics of phases and phase transitions | Explanation on basics of phases and phase transitions |
| Class 11 | Landau theory | Explanation on Landau theory |
| Class 12 | Mean-field theory and order-disorder transitions | Explanation on mean-field theory and order-disorder transitions |
| Class 13 | Mean-field theory for magnets | Explanation on mean-field theory for magnets |
| Class 14 | Example of exactly solvable models | Explanation on exact solutions of the one-dimensional Ising model |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
N/A
Reference books, course materials, etc.
Handouts will be distributed
Evaluation methods and criteria
exam and reports
Related courses
- PHY.S301 ： Statistical Mechanics
- PHY.Q207 ： Introduction to Quantum Mechanics
- PHY.E205 ： Electromagnetism
Prerequisites
Basic knowledge on statistical mechanics (microcanonical and canonical ensembles), electromagnetism, and quantum mechanics