Lectures

Lecture 1: Second quantization formalism for harmonic oscillator

• Example: Coherent states
• Example: Phonons in solids

Lecture 2: Second quantization formalism for bosons

• Example: Magnons in magnetic materials.
• Example: Bogoliubov theory of superfluids.

References

• Chapters 3, 4.5 and 6 of Nazarov and Danon textbook.

Lecture 3: Second quantization formalism for fermions

• Example: Hubbard clusters.
• Example: Hartree-Fock theory of electrons in metals.
• Example: BCS theory of superconductivity.

References

• Chapters 3 and 5 of Nazarov and Danon textbook.

Lecture 4: Time-dependent perturbation theory

• Example: Dyson vs. Magnus expansion for driven harmonic oscillator.

Additional references

S. Blanes, F. Casas, J. A. Oteo, and J. Ros, A pedagogical approach to the Magnus expansion, Eur. J. Phys. 31, 907 (2010). [PDF]

Lecture 5: Floquet theory of periodically driven quantum systems

• Example: Periodically driven harmonic oscillator.
• Example: Floquet topological insulators.

Lecture 7: Quantization of electromagnetic field

• Example: Casimir effect.
• Example: Squeezed and Fock states of nonclassical light.
• Example: Light-matter interaction.

Lecture 10: Dissipative quantum mechanics

• Example: Damped harmonic oscillator.
• Example: Qubit coupled to dissipative environment.