Notes for Physics

Here, I've included personal notes for various physics and mathematics courses, textbooks, and papers I've worked through over the years. All of these notes are not intended as polished works and by no means intended as stand-alone works, but are just compilations of thoughts and some calculations that helped me while I was going through the material in question. Hopefully, it'll serve to help others as well in their struggles.

I've provided the notes here; the references are all provided in the respective subsections. I really hope these help!

Quantum Thermodynamics, Channels, and Information

• V. Albert thesis, Sec. 1.1.2: "Open Quantum Systems"

• V. Albert thesis, Sec. 1.2: "What is a Lindbladian?" (Part 1)

• V. Albert thesis, Sec. 1.6.1: "The Playground and its Features"

• V. Albert thesis, Sec. 1.4: "Which Lindbladians are the Focus of this Work" and Sec. 1.6: "A Technical Introduction"

• V. Albert thesis, Sec. 1.2, "What is a Lindbladian?" (Part 2)

• V. Albert thesis, Sec. 2.1: "Four-Corners Partition of Lindbladians, with Examples"

• V. Albert thesis, Sec. 2.1, Extra: Derivation of the Matrix Elements of the Four-Corners Partition of the Lindbladian (GKSLian)

• V. Albert thesis, Sec. 2.3: Analytical Formula for Conserved Quantities

• V. Albert thesis, Sec. 2.3, Extra: Derivation of the Matrix Elements of the Four-Corners Partition of the Adjoint Lindbladian (Adjoint GKSLian)

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(References here.)

Shortcuts to Adiabaticity and Quantum Speed Limits

(References here.)

Topological Insulators, Superconductors, and Computing

• Path Ordering for the Wilzcek-Zee Phase: Merely a brief note explaining why the path ordering is necessary in the Wilczek-Zee phase.

(References here.)

Fluxons, Skyrmions, and Solitons

(References here.)

Conformal Field Theory and Chern-Simons Theory

(References here.)

Perturbative Quantum Many-Body / Field Theory

(References here.)

Path Integrals

(References here.)

Renormalization

(References here.)

Floquet Theory

• Notes on Classical Floquet Theory

• Notes on Quantum Floquet Theory

(References here.)

Finite-Temperature Field Theory

(References here.)

Classical Electrodynamics

(References here.)