### 2023　Statistical Mechanics (Ceramics course)

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Academic unit or major
Undergraduate major in Materials Science and Engineering
Instructor(s)
Kamiya Toshio  Izawa Seiichiro
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue7-8(S7-201)  Fri7-8(S7-201)
Group
-
Course number
MAT.C203
Credits
2
2023
Offered quarter
3Q
Syllabus updated
2023/9/8
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

This course starts from reviwing thermodynamics and aims to learn statistical mechanics from the microscopic point of view. Starting from Maxwell-Boltzmann distribution, which is applied to statistics of gasous atoms and molecules, studients will learn fundamental and applications of general classical and quantum statistical phyisics.

### Student learning outcomes

At the end of this course, students will be able to:
(1) Know how to treat many body systems statistically.
(2) Understand the relationship between the microscopic statistical mechanics and the macroscopic thermodynamics.
(3) Understand which quantum statistics can be applied to what problems.
(4) Understand how to calculate physical properties using statistical distribution functions

### Keywords

Ergodic hypothesis, Maxwell-Boltzmann distribution, Boltzmann distribution, Fermi-Dirac distribution, Bose-Einstein distribution, thermodynamic functions, free energy, distribution function, physical properties

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

Students would be given exercise problems when required. At the beginning of each class, solusions to exercise problems are reviewed. Questions are accepted anytime during each class.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Review of thermodynamics Review thermodynamics to be needed to understand statistical physics
Class 2 Kinetic theory of gases, Maxwell distribution Understand the thermal equilibrium statistics of gaseous atoms and molecules
Class 3 Maxwell distribution, fundamental of classical statistical physics I Understand the thermal equilibrium statistics of gaseous atoms and molecules under potential
Class 4 fundamental of classical statistical physics II Explain the concept of ergodic hypothesis, derivate distribution function in the phase space
Class 5 Canonical theory, principle of equal a priori probabilities for quantum statistical physics Understand the canonical theory and the principle of equal a priori probabilities for quantum statistical physics
Class 6 Grand canonical distribution, fundamental of quantum statistical physics Understand the grand canonical distribution and fundamental of quantum statistical physics
Class 7 Fundamental of quantum statistical physics, applications of classical statistical physics Understand the fundamental of quantum statistical physics and applications of classical statistical physics
Class 8 Review of distribution functions Review the 1st to 7th classes
Class 9 Theory of ideal Bose gas and specific heat of solids Derive the theory of specific heat of solids based on phonon distribution
Class 10 Theory of thermal radiation Derive the theory of thermal distribution based on Bose-Einstein statistics of photons
Class 11 Theory of ideal Fermi gas and electrons in metal Derive the electronic properties of metals based on Fermi-Dirac distribution and free electron model
Class 12 Theory of electrons in semiconductor Derive the electronic properties of semiconductors considering band structure with forbidden gap
Class 13 Phase transition Understand phase transitions from the viewpoints of statistical physics
Class 14 Review Review of statistical physics

### Out-of-Class Study Time (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)

Textbook will be specified at the class. Related text and materials will be distributed.

### Reference books, course materials, etc.

R.P. Feynman, Statistical Mechanics, Addison-Wesley

### Assessment criteria and methods

Students will be evaluated by exerciese problems given in the classes and by a term-end examination

### Related courses

• MAT.A204 ： Thermodynamics of Materials
• MAT.P204 ： Physical Chemistry (Thermodynamics)
• MAT.P301 ： Solid State Physics (Lattice)
• MAT.P303 ： Solid State Physics (Electrons)
• MAT.P205 ： Physical Chemistry (Phase Diagram)

### Prerequisites (i.e., required knowledge, skills, courses, etc.)

Students must have successfully completed Thermodynamics of Materials (MAT.A204) or have equivalent knowledge.
Statistical Mechanics(M)(MAT.M202) and Physical Chemistry (Statistical Mechanics)(MAT.P305) cannot be taken if one taks Statistical Mechanics(C).

### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

Toshio Kamiya　kamiya.t.aa[at]m.titech.ac.jp
Sei-ichiro Izawa　izawa.s.ac[at]m.titech.ac.jp

### Office hours

(Kamiya, Izawa) Contact by e-mail in advance to schedule an appointment.