Universal aspects of quantum dynamics: quantum catastrophes and long-range interactions

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One of the greatest goals of physics is to identify universal patterns of behaviour in natural phenomena. Some of the best known examples are phase transitions which are changes in an equilibrium state. Near the transition, systems with different microscopic compositions behave in a universal way, with quantities diverging according to common set of critical exponents. This proposal concerns universality in non-equilibrium dynamics, and specifically in quantum dynamics. In particular, we will investigate non-equilibrium dynamics in cold atomic gases which are versatile systems that can mimic a large number of condensed matter, nuclear and astrophysical models in a controllable and experimentally accessible way. ******Thus far, attempts to find universality in quantum dynamics have centred on dynamics near phase transitions that inherit their universality from the phase transition itself (e.g. Kibble-Zurek mechanism). This proposal takes a radically different approach, what I call universality associated with singularities, and is inspired by the phenomenon of natural focusing where universal patterns in waves (rainbows, gravitational lensing, tidal bores, freak waves) can occur without a phase transition. In fact, although not immediately apparent, there are deep connections with phase transitions through the presence of singularities. This research aims to understand these connections. It is a remarkable result of Catastrophe Theory that generic singularities (those that occur without special symmetries) can only take on certain geometric shapes. This is what gives singularities their universality. We will use catastrophes in quantum waves as a means to categorize their dynamics as, like phase transitions, each class of catastrophe obeys a set of scaling laws with scaling exponents.******We will apply catastrophe theory to look for common patterns in the dynamics of atoms trapped in optical lattices, spin systems, and atoms interacting via long range forces which mimic gravity. To achieve this latter goal we will design experimentally feasible schemes where atoms in optical cavities interact via light-mediated interactions that extend over the entire length of the cavity. Realizing such long range interatomic interactions would open the door to laboratory astrophysics studies of the collective behaviour of gravitationally interacting particles, something which is currently lacking.******The research we will undertake is fundamental and applicable across a broad range of disciplines related to wave dynamics. A number of the quantum models that will be studied, such as spin chains and coupled Josephson junctions, are already under active investigation for their potential to be the basis of a future quantum computer. Canada is a world leader in this field. Understanding universal patterns of their behaviour will aid this effort.