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.
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.
grandcanonical ensemble, chemical potential, fermion, boson, Bose condensation, phase transition, critical exponent, mean-field theory
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
The contents will be explained through lectures. A (few) report problems may be assigned.
In every exercise class students will be given some problems and solve them. Explanations on the
solutions will also be given.
|Course schedule||Required learning|
|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|
|Class 15||Non-equilibrium statistical mechanics||Explanation on linear response theory|
H. Tasaki, Statistical Mechanics II, Baihukan (Japanese)
R. Kubo, et al, Exercises on Thermodynamics and Statistical Mechanics, Shoukabo(Japanese)
examinations, reports, presentations in exercise classes, etc
Basic knowledge on statistical mechanics (microcanonical and canonical ensembles), electromagnetism, and quantum mechanics