Statistical Physics III

Key Features

Statistical mechanics is an academic study relating the motion of molecules, atoms, and particles, which obey quantum mechanics, to the macroscopic properties of the assembly of these particles. In the present course, Statistical Physics III, we apply the principles of thermodynamics and statistical mechanics, which we learned in Statistical Mechanics I and II, to ideal quantum gasses and various interacting systems. We will find that unexpected properties emerge from very simple many-particle systems. In this series of lectures, I try to present the logical structures as simply as possible, and to introduce important examples from condensed matter physics and from astrophysics.

I have prepared detailed lecture notes for use in your study, and have added comments and footnotes on the parts that may be tricky for beginners. It is very important for you to participate actively in your learning, in order to gain a deep understanding of the subject and to enhance your ability. Taking the course Physics Tutorial IV, synchronized with the present lecture, is strongly recommended.

Course Contents

1. Basics of quantum statistical mechanics
   [fermions and bosons, distribution function of ideal quantum gasses, distribution function and entropy]
2. Ideal Fermi gas
   [ground state, ideal Fermi gas at finite temperature, systems related to ideal Fermi gas]
3. Ideal Bose gas
   [Bose-Einstein condensation, black-body radiation: photon gas in vacuums, phonons in solids]
4. Interacting systems and phase transitions
   [non-ideal classical gases, phase transitions in the Ising model]

Course Aims

1. To understand basic concepts in quantum many-body systems and their relationship to properties of real materials, and to perform simple calculations.
2. To understand cooperative phenomena and to master a simple approximation method.

Course Requirements

Good acquaintance with thermodynamics and statistical mechanics as taught in Statistical Physics I, II

Relevant Courses

Quantum Mechanics I, II, Statistical Physics I, II

Grading

Term-end examination. Short paper assignment.

---