Summer school 2018 / Anatoli Polkovnikov / Part 1. Introduction to non-adiabatic response theory

The first lecture contains an illustrative introduction to the formalism of non-adiabatic response theory from both classical and quantum perspectives. Through basic examples, it explains the main mathematical objects and theorems that emerges in this formalism. The lecture timeline is below. Pedagogical review: https://arxiv.org/abs/1602.01062 00:00 CLASSICAL SYSTEMS / Canonical transformations 03:02 Infinitesimal canonical transformations. Gauge potentials 07:27 Example: A particle in a moving box 10:08 Example: Two-dimensional rotation 13:34 Example: "Second quantization" in the classical context 20:32 Example: Anharmonic oscillator and the Gross-Pitaevskii equation 26:23 Canonical transformation to a moving frame. Adiabatic gauge potentials 33:23 Example: A particle in a piston. Dilations 46:20 QUANTUM SYSTEMS / Unitary transformations 54:03 Example: A two-level system in a magnetic field 1:03:23 Example: A two-level system in a time-dependent magnetic field. Adiabatic theorem 1:10:51 Unitary transformation to a moving frame 1:13:59 Example: A particle in a moving box. Galilean term