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).
- 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
|✔ Specialist skills||Intercultural skills||Communication skills||Critical thinking skills||✔ Practical and/or problem-solving skills|
Given in a usual lecture style in English.
|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)
Lecture notes will be distributed via OCW-i.
Evaluated based on midterm report (40-50%) and final examination (50-60%).
It is highly desired that students have mastered undergraduate quantum mechanics and statistical mechanics.