Initiating from the creation and annihilation operators in a harmonic oscillator, field quantization is introduced. Based on this concept, the Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity, BEC of an ideal Bose gas, and superfluidity of liquid helium-4 are comprehensively explained.
The lecture contents for each period are summarized as follows; however, the contents may undergo slight changes while the course is in progress. Reading the textbook as a preparation and
rereading the notebook and the textbook as a review will take about 4 hours every week.
1) The creation and annihilation operators in a harmonic oscillator
Based on the commutation relation between the momentum and position operators, the creation and annihilation operators are introduced.
2) Field quantization
Using an electromagnetic field as an example, a field quantization method is introduced.
3) Many-particle states
The many-particle states of bosons and fermions are explained.
4) Many-particle Hamiltonian
After introducing the method of forming a many-particle Hamiltonian, the Hamiltonian of an electron–phonon coupling is explained as an example.
5) Superconductivity phenomena
Students will study superconductivity phenomena, including the zero resistance and the Meissner effect.
6) Effective Hamiltonian of a superconductor
Students will study the effective Hamiltonian of a superconductor with electron–phonon coupling.
7) Ground state of a superconductor
The ground-state properties of superconductors, including the superconducting energy gap, are explained.
8) Superconductor at a finite temperature
The superconducting properties at finite temperature, including the superconducting gap and specific heat, are explained.
9) Currents in a superconductor
The electric current properties in a superconductor, including the permanent current under a magnetic field and the Josephson effect, are explained.
As the first step in the study of superfluids, the BEC of ideal bosons is introduced.
11) Superfluid phenomena
Superfluid phenomena, including zero viscosity, are introduced.
12) Superfluid wave function
The macroscopic superfluid wave function is introduced.
13) Phonons and rotons
The elemental excitations of the superfluid state, such as phonons and rotons, are explained.
14) Critical velocity and vortex
The critical velocity, where the superfluid state breaks down, and quantized vortexes of the superfluid state are explained.