Institute for Mathematical Physics on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Field on Separation of Variables in the Schrr Odinger Equation for a Particle Interacting with External Eld

On Bound States Concentrating on Spheres for the Maxwell-Schrödinger Equation

We study the semiclassical limit for the following system of Maxwell-Schrr odinger equations: waves for the nonlinear Schrr odinger equation interacting with the electrostatic eld: the unknowns v and represent the wave function associated to the particle and the electric potential respectively. By using localized energy method, we construct a family of positive radially symmetric bound states (...

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

Time-dependent Rescalings and Lyapunov Functionals for the Vlasov-poisson and Euler-poisson Systems, and for Related Models of Kinetic Equations, Uid Dynamics and Quantum Physics

We investigate rescaling transformations for the Vlasov-Poisson and Euler-Poisson systems and derive in the plasma physics case Lyapunov functionals which can be used to analyze dispersion eeects. The method is also used for studying the long time behaviour of the solutions and can be applied to other models in kinetic theory (2-dimensional symmetric Vlasov-Poisson system with an external magne...

The Erwin Schrr Odinger International Institute for Mathematical Physics Rayleigh{type Isoperimetric Inequality with a Homogeneous Magnetic Field Rayleigh-type Isoperimetric Inequality with a Homogeneous Magnetic Eld

We prove that the two dimensional free magnetic Schrr odinger operator, with a xed constant magnetic eld and Dirichlet boundary conditions on a planar domain with a given area, attains its smallest possible eigenvalue if the domain is a disk. We also give some rough bounds on the lowest magnetic eigenvalue of the disk. Running title: Magnetic Rayleigh-type inequality.

The Erwin Schrr Odinger International Institute for Mathematical Physics on Finite 4d Quantum Field Theory in Non-commutative Geometry on Finite 4d Quantum Field Theory in Non-commutative Geometry 1

The truncated 4-dimensional sphere S 4 and the action of the self-interacting scalar eld on it are constructed. The path integral quantization is performed while simultaneously keeping the SO(5) symmetry and the nite number of degrees of freedom. The usual eld theory UV-divergences are manifestly absent.