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2017　Statistical Mechanics III

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Academic unit or major
Graduate major in Physics
Instructor(s)
Sasamoto Tomohiro 
Class Format
Lecture     
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H115)  Fri3-4(H115)  
Group
-
Course number
PHY.S440
Credits
2
Academic year
2017
Offered quarter
3Q
Syllabus updated
2017/3/17
Lecture notes updated
-
Language used
Japanese
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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 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

Textbook(s)

To be specified.

Reference books, course materials, etc.

To be given during the course

Assessment criteria and methods

Final exam, 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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