By Jean Bourgain
This publication offers an summary of contemporary advancements within the region 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 a long time. Jean Bourgain right here units forth the consequences and methods which were came across within the previous few years. He places unique emphasis on so-called "non-perturbative" equipment and the real position of subharmonic functionality idea and semi-algebraic set equipment. He describes quite a few functions to the idea of differential equations and dynamical platforms, specifically to the quantum kicked rotor and KAM concept for nonlinear Hamiltonian evolution equations.
Intended basically for graduate scholars and researchers within the common region of dynamical platforms and mathematical physics, the publication offers a coherent account of a big physique of labor that's shortly scattered within the literature. It does so in a refreshingly contained demeanour that seeks to exhibit the current technological "state of the art."
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Green's Function Estimates for Lattice Schr?dinger Operators and Applications. (AM-158) (Annals of Mathematics Studies) by Jean Bourgain
by George
4.3
