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 |
lectures
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 | Application of mean field theory | Can apply the mean-field theory to simple models |
Class 5 | Landau theory | Explain the concept of Landau theory |
Class 6 | Dynamical critical phenomena | Explain differences of dynamical critical phenomena from static case |
Class 7 | Examples of exactly solvable models | Explain a few examples of exactly solvable models and their basic properties |
Class 8 | Scaling theory | Apply the scaling theory to simple examples |
Class 9 | Basics of renormalization group | Explain the concept of renormalization group |
Class 10 | Real space renormalization | Apply the real space renormalization to simple model |
Class 11 | Momentum space renormalization | Apply the momentum space renormalization to simple model |
Class 12 | Systems with continuous symmetry | Explain a few examples with continuous symmetries and differences from those with discrete symmetries |
Class 13 | Quantum phase transition | Explain differences between quantum and thermal phase transitions |
Class 14 | Basics of non-equilibrium phenomena | Explain differences between equilibrium and non-equilibrium systems |
Class 15 | Developments in non-equilibrium statistical mechanics | Explain recent developments in non-equilibrium statistical mechanics |
To be specified.
To be given during the course
Final exam, reports, etc.
It is better if students have successfully finished the above related courses.