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:
- Time-dependent single-particle Schrödinger equation
- Spectral methods
- PDE integration
- Non-interacting many-body systems
- Bogoliubov transformation
- 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.
See also the SPUR listing.
