Quantum Chaos Gets Cracked - Quantum Unique Ergodicity (QUE) Conjecture Proven

In a seminar co-organized by Stanford University and the American Institute of Mathematics, Kannam Soundararajan, Professor of Mathematics, announced that he and Roman Holowinsky have proven a significant version of the quantum unique ergodicity (QUE) conjecture. The motivation behind the problem is to understand how waves are influenced by the geometry of their enclosure. Imagine sound waves in a concert hall. In a well-designed concert hall you can hear every note from every seat. The sound waves spread out uniformly and evenly. At the opposite extreme are "whispering galleries" where sound concentrates in a small area. The mathematical world is populated by all kinds of shapes, some of which are easy to picture, like spheres and donuts, and others which are constructed from abstract mathematics. All of these shapes have waves associated with them. Soundararajan and Holowinsky showed that for certain shapes that come from number theory, the waves always spread out evenly. For these shapes there are no "whispering galleries." Read More...

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