COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics
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Mathematics Colloquium: Quantum Chaos: Origins and Contemporary Research Avenues


Neill 5W, 4:10pm

Steven L. Tomsovic

Quantum Chaos is a rather loosely defined modern field of research that encompasses a wide variety of physical systems. It began with the study of quantum systems with clearly identifiable classical counterparts displaying chaotic motion, where the research sought novel quantum phenomena which could be associated with the chaos, but has expanded even to systems without classical analogs. The main methods of analysis for understanding quantum chaotic systems are semiclassical theory, random matrix theory, and nonlinear sigma models, which is an effective quantum field theory for disordered systems. In this talk, after discussing a bit of the history and context for quantum chaos, I will discuss two contemporary research projects in which I am involved, to give a flavor of where the field is today. The first is an application in quantum information theory describing how much entanglement exists in bi-partite systems whose component subsystems are chaotic with tunable interaction strength. There is a universality in the transition from unentangled eigenstates to essentially fully entangled eigenstates as the strength increases. The second example is oriented toward ultra-cold atoms in optical lattices. It is shown that a semiclassical theory, which goes beyond the heavily used truncated Wigner approximation, accurately captures many-body interferences in the mean-field solutions of Bose-Hubbard systems. Refreshments served at 3:30 p.m. Hacker Lounge (Neill 216)