By Jean Bourgain
This ebook offers an outline of modern advancements within the sector of localization for quasi-periodic lattice Schrödinger operators and the idea of quasi-periodicity in Hamiltonian evolution equations. The actual motivation of those versions extends again to the works of Rudolph Peierls and Douglas R. Hofstadter, and the versions themselves were a spotlight of mathematical study for 2 many years. Jean Bourgain the following units forth the consequences and strategies which have been found within the previous couple of years. He places specified emphasis on so-called "non-perturbative" tools and the real function of subharmonic functionality concept and semi-algebraic set equipment. He describes numerous purposes to the idea of differential equations and dynamical platforms, particularly to the quantum kicked rotor and KAM idea for nonlinear Hamiltonian evolution equations.Intended basically for graduate scholars and researchers within the basic sector of dynamical structures and mathematical physics, the booklet offers a coherent account of a giant physique of labor that's almost immediately scattered within the literature. It does so in a refreshingly contained demeanour that seeks to show the current technological "state of the art."