Breadcrumb
Asymptotic properties of spectra and eigenfunctions of quantum chaotic systems
Supervisor: Francesco Mezzadri
Theme: Quantum Chaos
The central problem is to understand how the chaotic nature of the underlying motion of classical systems affects the corresponding quantum mechanics. The main theoretical questions concern the behaviour of the eigenfunctions and eigenvalues in the semiclassical limit, that is as Planck's constant tends to zero. In particular, it is believed that in the semiclassical limit the energy levels of generic chaotic systems are correlated like the eigenvalues of large random Hermitian matrices. This is known as the Random Matrix Theory conjecture. The models used to study these problems will be quantum systems whose time evolution is discrete; these are known as quantum maps.