On quasi-periodic lattice Schrödinger operators
Copyright policy )On quasi-periodic lattice Schrödinger operators
The aim of the paper is to review a number of developments over the recent years on the following topics: (1) spectrum and eigenfunctions of Schrödinger operators on \(\mathbb{Z}\) and \(\mathbb{Z}^D\) with a quasi-periodic potential, (2) linear Schrödinger equations with time periodic potential, (3) KAM theory for nonlinear PDE. The paper mainly surveys the works of the author and his collaborators. Compared with earlier research in the areas listed above, there are two new methods extensively used in the contributions considered: (1) subharmonic function techniques, (2) the theory of semi-algebraic sets.
Schrödinger operator, Melnikov problems, Asymptotic distributions of eigenvalues in context of PDEs, review, KAM theory, spectrum, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, semi-algebraic sets, Spectrum, resolvent, Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems, subharmonic function, Random linear operators, Selfadjoint operator theory in quantum theory, including spectral analysis, PDEs in connection with quantum mechanics
Schrödinger operator, Melnikov problems, Asymptotic distributions of eigenvalues in context of PDEs, review, KAM theory, spectrum, Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion, semi-algebraic sets, Spectrum, resolvent, Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems, subharmonic function, Random linear operators, Selfadjoint operator theory in quantum theory, including spectral analysis, PDEs in connection with quantum mechanics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!