Novel Phase-Space Methods to Simulate Strongly-Interacting Many-Body Quantum Dynamics
This event is part of the PhD Final Oral Exams.
Dissertation Committee: Anatoli Polkovnikov, Alex Sushkov, Liam Fitzpatrick, Claudio Chamon, Christopher Laumann
Understanding the collective behaviour of many-body quantum systems is an important subject in many areas of physics. With advances in ultra-cold gas experiments, the dynamics of strongly-interacting systems can now be studied in the lab. However, there is a paucity of theoretical techniques available to simulate such systems. One technique is phase-space methods, often known as the Trucated Wigner Approximation; however, its applicability in its naive form is limited. In this work, we expound on techniques to expand the regimes in which it can be effective. This involves creating a novel phase-space that is tailored to the problem at hand, and associated classical equations of motion. We show techniques for lattice systems with local finite Hilbert spaces, for fermionic systems, and for many-body localized systems. In all cases, we benchmark the accuracy of the approximation against exact results.