Final PhD Oral Examination (Thesis Title: “Scale Symmetry and the Non-Equilibrium Quantum Dynamics of Ultra-Cold Atomic Gases”)

Thesis Abstract:

The study of the quantum dynamics of ultra-cold atomic gases has become a forefront of atomic research. Experiments studying dynamics have become routine in laboratories, and a plethora of phenomena have been studied.

Theoretically, however, the situation is often intractable unless one resorts to numerical or semiclassical calculations. In this thesis we apply the symmetry associated with scale invariance to study the dynamics of atomic gases, and discuss the implications of this symmetry on the full quantum dynamics. In particular we study the time evolution of an expanding two-dimensional Bose gas with attractive contact interactions, and the three-dimensional Fermi gas at unitarity. To do this we employ a quantum variational approach and exact symmetry arguments. It is shown that the time evolution due to a scale invariant Hamiltonian produces an emergent conformal symmetry. This emergent conformal symmetry has implications on the time evolution of an expanding quantum gas. In addition, we examine the effects of broken scale symmetry on the expansion dynamics. To do this, we develop a non-perturbative formalism that classifies the possible dynamics that can occur. This formalism is then applied to two systems, an ensemble of two-body systems, and for the compressional and elliptic flow of a unitary Fermi gas, both in three spatial dimensions.