Keywords :
Berry’s Random Waves, Bessel Functions, Central Limit Theorem, Fourth Moment Theorem, Gaussian Random Waves, High-Frequency Limit, Isotropy, Kac-Rice Formula, Monochromatic Random Waves, Nodal Length, Nodal Lines, Nodal Number, Nodal Points, Nodal Volumes, Phase Singularities, Quantum Chaos, Random Laplace Eigenfunctions, Random Plane Waves, Random Spherical Harmonics, Reduction Principle, Semiclassical Analysis, Stationarity, Universality, White Noise, Wiener Chaos
Abstract :
[en] This thesis examines the geometric behavior of smooth Gaussian random waves in the high-frequency limit. We focus, in particular, on a variation of the celebrated Berry’s Random Wave model, which plays a central role in various conjectures and results within the theory of Quantum Chaos. Our contribution to this field is a study of a variant we refer to as the Two-Energy Berry’s Random Wave model. We confirm that the corresponding nodal number exhibits some classical behaviors, such as asymptotic Gaussianity, while we also identify several new phenomena, including some non-universal features of variance asymptotic and novel variations of the so-called full correlation phenomena.
Institution :
Unilu - University of Luxembourg [Faculty of Science, Technology and Medicine (FSTM)], Esch-sur-Alzette, Luxembourg
