2019 Statistical Mechanics II

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Academic unit or major
Undergraduate major in Physics
Instructor(s)
Sasamoto Tomohiro  Adachi Satoshi  Watabiki Yoshiyuki 
Course component(s)
Lecture / Exercise
Day/Period(Room No.)
Mon5-6(H114)  Thr5-8(5.6限:H114, 7.8限:H112,H116)  
Group
-
Course number
PHY.S312
Credits
3
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/4/4
Lecture notes updated
-
Language used
Japanese
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Course description and aims

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.

Student learning outcomes

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 that will be developed

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

Class flow

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

  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

Textbook(s)

N/A

Reference books, course materials, etc.

H. Tasaki, Statistical Mechanics II, Baihukan (Japanese)
R. Kubo, et al, Exercises on Thermodynamics and Statistical Mechanics, Shoukabo(Japanese)

Assessment criteria and methods

examinations, reports, presentations in exercise classes, etc

Related courses

  • PHY.S301 : Statistical Mechanics
  • PHY.Q207 : Introduction to Quantum Mechanics
  • PHY.E205 : Electromagnetism

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

Basic knowledge on statistical mechanics (microcanonical and canonical ensembles), electromagnetism, and quantum mechanics

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