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.
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.
Ergodic hypothesis, Maxwell-Boltzmann distribution、Boltzmann distribution, Fermi-Dirac distribution, Bose-Einstein distribution, thermodynamic functions, free energy, distribution function
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
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|
|Class 1||First law of thermodynamics||Understand the first law of thermodynamics|
|Class 2||Second law of tehrmodynamics, thermodynamic functions||Understand the second law of thermodynamics and important thermodynamic functions|
|Class 3||Kinetic theory of gases||Understand the thermal equillibrium statistics of gasous atoms and molecules|
|Class 4||Fundamental of classical statistical mechanics I||Derivate distribution function for gasous atoms and molecules at thermal equillibrium|
|Class 5||Fundamental of classical statistical mechanics II||Explain the concept of ergodic hypothesis, derivate distribution function in the phase space|
|Class 6||Canonical distribution and grand canonical distribution||Derive distribution functions for gases with interaction|
|Class 7||Midterm review of the first half of this course||Review the 1st to 6th classes|
|Class 8||Fundamental of quantum statistical mechanics I||Derive Fermi-Dirac distribution for anti-symmetric particles|
|Class 9||Fundamental of quantum statistical mechanics II||Derive Bose-Einstein distribution for symmetric particles|
|Class 10||Theory of ideal Bose gas and specific heat of solids||Derive the theory of specific heat of solids based on phonon distribution|
|Class 11||Theory of thermal radiation||Derive the theory of thermal distribution based on Bose-Einstein statistics of photons|
|Class 12||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 13||Theory of electrons in semiconductor||Derive the electronic properties of semiconductors considering band structure with forbidden gap|
|Class 14||Magnetic susceptibility||Apply Fermi-Dirac distribution to spin systems and derive their magnetic properties|
|Class 15||Bose-Einstein condensation||Learn what happens if electrons make Cooper paiers that follows Bose-Einstein distribution|
Textbook will be specified at the class. Related text and materials will be distributed.
R.P. Feynman, Statistical Mechanics, Addison-Wesley
Students will be evaluated by exerciese problems given in the classes and by a term-end examination
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).
Toshio Kamiya kamiya.t.aa[at]m.titech.ac.jp
Satoru Matsuishi matsuishi.s.aa[at]m.titech.ac.jp
(Kamiya, Matsuishi) Contact by e-mail in advance to schedule an appointment.