Green's Function Estimates For Lattice Schrodinger Operators And Applications

This book presents an overview of recent developments in the area oflocalization for quasiperiodic lattice Schrodinger operators and the theory ofquasiperiodici... » 

This book presents an overview of recent developments in the area oflocalization for quasiperiodic lattice Schrodinger operators and the theory ofquasiperiodicity in Hamiltonian evolution equations. The physical motivationof these models extends back to the works of Rudolph Peierls and Douglas R.Hofstadter and the models themselves have been a focus of mathematicalresearch for two decades. Jean Bourgain here sets forth the results andtechniques that have been discovered in the last few years. He puts specialemphasis on socalled nonperturbative methods and the important role ofsubharmonic function theory and semialgebraic set methods. He describesvarious applications to the theory of differential equations and dynamicalsystems in particular to the quantum kicked rotor and KAM theory for nonlinearHamiltonian evolution equations.Intended primarily for graduate students and researchers in the general area ofdynamical systems and mathematical physics the book provides a coherentaccount of a large body of work that is presently scattered in the literature.It does so in a refreshingly contained manner that seeks to convey the presenttechnological state of the art. «