Dressed States Approach to Quantum Systems

Using the non-perturbative method of {\it dressed} states previously introduced in JPhysA, we study effects of the environment on a quantum mechanical system, in the case the environment is modeled by an ensemble of non interacting harmonic oscillators. This method allows to separate the whole system into the {\it dressed} mechanical system and the {\it dressed} environment, in terms of which an exact, non-perturbative approach is possible. When applied to the Brownian motion, we give explicit non-perturbative formulas for the classical path of the particle in the weak and strong coupling regimes. When applied to study atomic behaviours in cavities, the method accounts very precisely for experimentally observed inhibition of atomic decay in small cavities PhysLA, physics0111042

CONFORMAL MAPPING FOR SURFACE MODELLING

A conformal mapping method for obtaining electric potentials in a region close to a structured surface is developed. By neglecting one of the surface dimensions and assuming periodicity along the other, the resulting two-dimensional problem can be analytically treated. As examples of the method some arrays of monopoles and dipoles are calculated from which a surface model is proposed and exactly solved

Electric Potential and Field Near Pointed Shaped Surfaces

The trajectories of charged particles, emitted from within or from the close vicinity of pointed shaped surfaces, requires the knowledge of the electric field resulting from the potential bias between surface and detector, or screen. Frequently it is necessary the use of numerical methods for solving Laplace's equation as a result of difficulties in obtaining an analytical expression. Recently we have shown that, when any two coordinate surfaces of an orthogonal system are kept at two different but constant potentials, it is possible to obtain an analytical solution for the potential in a relatively simple manner. Using this general property of orthogonal coordinate systems, we present the solution for the electric potential and field in the vicinity of pointed sudaces for several cases of practical interest in field emission, field ionisation, atomprobe field ion spectroscopy and related phenomena