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2022　Statistical Mechanics III

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Academic unit or major
Graduate major in Physics
Instructor(s)
Sasamoto Tomohiro 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Mon3-4(S223)  Thr3-4(S223)  
Group
-
Course number
PHY.S440
Credits
2
Academic year
2022
Offered quarter
3Q
Syllabus updated
2022/4/20
Lecture notes updated
-
Language used
English
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Course description and aims

Phase transitions and critical phenomena are one of the most important topics in statistical mechanics. In this course, we review the theory of phase transition, various aspects of mean field theory and explain the scaling theory and renormalization group. In addition, we explain the role of symmetries, exactly solvable models and quantum phase transitions. We also discuss statistical physics for non-equilibrium systems. We cover not only the standard topics such as linear response theory and reciprocal relation but also more recent developments as Jarzynski equality and fluctuation theorem.

Student learning outcomes

The goal of this course is to deepen the understanding of statistical mechanics, in particular on the phase transitions and critical phenomena and on non-equilibrium systems.

Keywords

phase transition, critical phenomena, renormalization group, non-equilibrium, fluctuations

Competencies that will be developed

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

Class flow

lectures

Course schedule/Required learning

  Course schedule Required learning
Class 1 Review of the theory of phase transition Explain the notion of phase transitions
Class 2 Basics of phase transition Explain the quantities which characterize phase transitions
Class 3 Basics of mean field theory Explain the concept of mean field theory
Class 4 Landau theory Explain the concept of Landau theory
Class 5 Scaling theory Apply the scaling theory to simple examples
Class 6 Basics of renormalization group Explain the concept of renormalization group
Class 7 Momentum space renormalization Apply the momentum space renormalization to simple model
Class 8 Systems with continuous symmetry Explain a few examples with continuous symmetries and differences from those with discrete symmetries
Class 9 Topics related to critical phenomena Explain a few examples of topics related to critical phenomena
Class 10 Basics of non-equilibrium phenomena Explain differences between equilibrium and non-equilibrium systems
Class 11 Stochastic processes Explain how to model non-equilibrium systems by stochastic processes
Class 12 Brownian motion Explain basic properties of the Brownian motion
Class 13 Linear response theory Explain basic properties of linear response theory
Class 14 Topics related to non-equilibrium phenomena Explain basic properties of topics related to non-equilibrium phenomena

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)

Not specified.

Reference books, course materials, etc.

To be given during the course

Assessment criteria and methods

Reports, etc.

Related courses

  • ZUB.S205 ： Thermodynamics and Statistical Mechanics I
  • ZUB.S310 ： Thermodynamics and Statistical Mechanics II

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

It is better if students have successfully finished the above related courses.

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