We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It
has previously been conjectured that these should be described by a Gaussian Random …

In this paper we study random features manifested in components of energy eigenfunctions
of quantum chaotic systems, given in the basis of unperturbed, integrable systems. Based on …

Nonlinear instability and refraction by ocean currents are both important mechanisms that go
beyond the Rayleigh approximation and may be responsible for the formation of freak …

One manifestation of classical ergodicity is a complete loss of memory of the initial
conditions due to the eventual uniform exploration of phase space. In quantum versions of …

We study the statistical distribution of components in the non-perturbative parts of energy
eigenfunctions (EFs), in which main bodies of the EFs lie. Our numerical simulations in five …

In most realistic models for quantum chaotic systems, the Hamiltonian matrices in
unperturbed bases have a sparse structure. We study correlations in eigenfunctions of such …

We discuss a modification to random matrix theory eigenstate statistics that systematically
takes into account the nonuniversal short-time behavior of chaotic systems. The method …

In the dissertation, I include two topics of my research in nonlinear dynamic systems. In the
first topic, we use numerical optimization techniques to investigate the behavior of the …