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Making Waves

Quantum Unique Ergodicity (QUE) Conjecture Proven

Via aimath.org

In a seminar co-organized by Stanford University and the American Institute of Mathematics, Soundararajan announced that he and Roman Holowinsky have proven a significant version of the quantum unique ergodicity (QUE) conjecture. “This is one of the best theorems of the year,” said Peter Sarnak, a mathematician from Princeton who along with Zeev Rudnick from the University of Tel Aviv formulated the conjecture fifteen years ago in an effort to understand the connections between classical and quantum physics.

The problems of quantum chaos can be understood in terms of billiards. On a standard rectangular billiard table the motion of the balls is predictable and easy to describe. Things get more interesting if the table has curved edges, known as a “stadium.” Then it turns out most paths are chaotic and over time fill out the billiard table, a result proven by the mathematical physicist Leonid Bunimovich.

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Via sciencedaily.com

“It is still a mystery, really,” says UBC computer science professor Prof. Dinesh Pai. “No one has ever completely mapped out the processes at the level of specific neurons, muscles and tendons.”

Pai is part of a UBC team leading an international initiative to do just that. “Essentially, we are reverse engineering the brain to produce the first working computational model of the complex interplay between our minds and our bodies.”

The project could produce great leaps forward in many areas, including medicine, industry and robotics. Although the project is just ramping up, the team’s mapping and modeling expedition is already producing some of the world’s most realistic computer simulations of the human body.

“Current robots have as much in common with human movements as helicopters do with seagulls,” Pai adds. “The challenges are similar, but they use completely different solutions.”

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