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.
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.
phase transition, critical phenomena, renormalization group, non-equilibrium, fluctuations
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||Practical and/or problem-solving skills|
|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|
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.
To be given during the course
It is better if students have successfully finished the above related courses.