Heilbronn Colloquium 2019: Zeev Rudnick30 Jul 2019, by Events in
Thursday 5 September 2019 at 16:00
Organised in collaboration with the School of Mathematics, University of Bristol, UK
Quantum Chaos, Eigenvalue Statistics and the Fibonacci Sequence
Zeev Rudnick, Professor of Mathematics, Tel Aviv University, Israel
One of the outstanding insights in the field of “Quantum Chaos” is a conjectural description of local statistics of the energy levels of simple quantum systems according to crude properties of the dynamics of classical limit, such as integrability, where one expects Poisson statistics, versus chaotic dynamics, where one expects Random Matrix Theory statistics. These insights were obtained by physicists in the last quarter of the 20-th century (much of it in Bristol!). However, mathematicians are far behind in understanding the scope and validity of this theory. The first part of the lecture will be dedicated to an introduction to these conjectures, which I believe deserve to be better known in the mathematics community.
In the second part, I will describe more recent work on statistics of the minimal gap between the first N eigenvalues for one such simple integrable system, a rectangular billiard having irrational squared aspect ratio. When the aspect ratio is the “golden ratio”, the problem involves some curious and entertaining properties of the Fibonacci sequence.
Short Bio: Zeev’s main interests are in number theory, mathematical physics and quantum chaos, and his world-leading research in these fields has attracted numerous awards and prizes. For example, in 2001 he received the Erdos Prize of the Israel Mathematical Union and he was elected a Fellow of the American Mathematical Society in 2012. He was an invited speaker at the International Congress of Mathematicians in 2014 and his current research is supported by an ERC Advanced Grant.
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