Title：Quantum chaology and the singing of the primes

Speaker: Michael Berry

Time: 14:00,April 7（Monday）

Location: Room 215, No. 8 Hainayuan Building

Abstract:

    Although envisioned by Einstein in 1917, it was only in the 1970s that the implications for quantum mechanics of chaos in the classical limiting dynamics was recognised as a problem. The solution emerged from several directions. There is no sharp quantum-classical boundary, but rather a rich borderland. The talk will concentrate on energy levels. Semiclassical asymptotics, in the form of Gutzwiller’s trace formula, gives the quantum spectrum as a sum over classical periodic orbits. The recognition that correlations between close-lying levels depend on long periodic orbits, which enjoy a universal phase space democracy, leads to random-matrix level statistics, while short orbits give nonuniversal correlations between more distant levels, and failure of random-matrix theory. A bonus was the discovery that the Riemann zeros share the same statistics, with unexpected connections between quantum chaology and prime numbers. If time permits, wavefunctions, time-dependence and  and many-body quantum chaos will be touched on.

Biography:

Sir Michael was elected a Fellow of the Royal Society in 1982 and knighted in 1996. In recognition of his scientific achievements, Sir Michael has received numerous prestigious awards. He was awarded the Wolf Prize in Physics and the Dirac Medal, both honoring his seminal contributions to theoretical physics. He is also a recipient of the Royal Medal of the Royal Society and the Lilienfeld Prize from the American Physical Society, further cementing his legacy in the global scientific community. His contributions extend beyond research, with his work influencing a variety of fields and continuing to inspire physicists worldwide.