Random Schrr Odinger Operators Arising from Lattice Gauge Elds I: Existence and Examples Mathematics Subject Classiication

Random Schrr Odinger Operators Arising from Lattice Gauge Elds Ii: Determinants Mathematics Subject Classiication

We introduce and study the variational problem to maximize the determinant of a random selfadjoint operators obtained from discrete abelian or nonabelian lattice gauge elds. We prove the existence of minima and give rough estimates of the functional for multi-particle operators.

Determinants of Random Schrr Odinger Operators Arrizing from Lattice Gauge Elds

For a class of bounded random selfadjoint operators (Lu)(n) =

Institute for Mathematical Physics Existence and Semi{classical Limit of the Least Energy Solution to a Nonlinear Schrr Odinger Equation with Electromagnetic Fields Existence and Semi-classical Limit of the Least Energy Solution to a Nonlinear Schrr Odinger Equation with Electromagnetic Elds

Towards quantum localisation in Gaussian random potentials

At suuciently low energies there is no absolutely continuous spectrum for a quantum-mechanical particle moving in multi-dimensional Euclidean space under the innuence of certain Gaussian random potentials. Since the pioneering work of Anderson 1] models of a single quantum-mechanical particle moving under the innuence of a random potential have attracted much attention from both physicists 2,3]...

Discrete random electromagnetic Laplacians

We consider discrete random magnetic Laplacians in the plane and discrete random electromagnetic Laplacians in higher dimensions. The existence of these objects relies on a theorem of Feldman-Moore which was generalized by Lind to the nonabelian case. For example, it allows to realize ergodic Schrr odinger operators with stationary independent magnetic elds on discrete two dimensional lattices ...