2017 Quantum Mechanics of Many-Body Systems

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Academic unit or major
Graduate major in Physics
Nishida Yusuke 
Class Format
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(H116)  Fri3-4(H116)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

Many-body quantum mechanics provides a way to describe systems consisting of many particles based on quantum mechanics.
The objective of this course is to learn the partition function represented by field functional integral (1st-4th classes), methods to treat inter-particle interactions (5th-8th classes), spontaneous symmetry breaking and its consequences (9th-12th classes), linear response theory and correlation functions (13th-15th classes).

Student learning outcomes

- Being able to explain the partition function represented by field functional integral, methods to treat inter-particle interactions, spontaneous symmetry breaking and its consequences, linear response theory and correlation functions.
- Being able to apply them to concrete problems and explain physical phenomena theoretically.


Field Functional Integral, Perturbation Theory, Spontaneous Symmetry Breaking, Linear Response Theory

Competencies that will be developed

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

Class flow

Given in a usual lecture style in English.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Path Integral in Quantum Mechanics Understand contents and results in each class and should be able to derive and explain them by oneself.
Class 2 Second Quantization
Class 3 Coherent States
Class 4 Partition Functions of Free Bose and Fermi Gases
Class 5 Generating Functional and Feynman Diagrams
Class 6 Hartree and Fock Energies
Class 7 Random Phase Approximation and Screening
Class 8 Self-Energy and Quasiparticles
Class 9 Superfluidity: Bose-Einstein Condensation
Class 10 Superfluidity: Supercurrent and Landau Criterion
Class 11 Superconductivity: BCS Theory and Gap Equation
Class 12 Superconductivity: Meissner Effect and Zero Resistivity
Class 13 Measurement and Linear Response
Class 14 Correlation Funcitons
Class 15 Ohm's Law and Conductivity


A. Altland and B. Simons "Condensed Matter Field Theory" (Cambridge University Press)
H. Bruus and K. Flensberg "Many-Body Quantum Theory In Condensed Matter Physics" (Oxford University Press)
L. S. Brown "Quantum Field Theory" (Cambridge University Press)

Reference books, course materials, etc.

Lecture notes will be distributed via OCW-i.

Assessment criteria and methods

Evaluated based on midterm report (40-50%) and final examination (50-60%).

Related courses

  • ZUB.Q313 : Quantum Mechanics III
  • ZUB.S310 : Thermodynamics and Statistical Mechanics II

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

It is highly desired that students have mastered undergraduate quantum mechanics and statistical mechanics.

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