Winter 2024

Computational quantum dynamics

Taught by M. Schmitt

Modern experiments employing ultrafast pump-probe techniques or quantum simulation are opening up the exciting realm of far-from-equilibrium quantum dynamics. These developments have directed theoretical attention to questions about thermalization, non-equilibrium phases of matter, and transient dynamical phenomena. Since analytical approaches are typically limited, numerical methods are key to understand the theoretical models. This lecture will cover a variety of computational tools for the simulation of quantum dynamics, namely:

  1. Time-dependent single-particle Schrödinger equation
    • Spectral methods
    • PDE integration
  2. Non-interacting many-body systems
    • Free fermions
    • Bogoliubov transformation
  3. Interacting many-body systems
    • Exact diagonalization
    • Semiclassical approaches
    • Tensor network methods
    • Neural quantum states

Throughout the course, we will implement these methods in exercises and interactive sessions. The resulting codes will be used to investigate a variety of quantum dynamical phenomena, such as

  • Quantum chaos
  • Non-equilibrium dynamics
  • Thermalization
  • Dynamical phase transitions
  • Information spreading

Materials