Nanoscience (2004)

Organizers: Peter Markowich (Vienna), Karl Unterrainer (Vienna)

The Nanoscience Program will focus on the following topics:

(1)Mathematical Modelling ín Nano Physics
PDE models for semiconductor and plasma structures in the micrometer scale have been around -and used successfully-for about 50 years: The occurance of nano devices in the last decade has changed the requirements on the employed mathematical models significantly: while micrometer scale devices can very well be modelled by classical (electro) mechanics equations based on the Maxwell equations and on Newtonian mechanics, nano semiconductor devices generally have to be described by using quantum mechanical techniques, based on the Schroedinger, Heisenberg or, equivalently, Wigner picture. A main goal for this programm will be to advance quantum mechanical modelling of nano structures using partial differential equations. Typical topics to be investigated are: quantum wave guides, Schoedinger-Poisson systems, stochastic Schroedinger equations, Gross-Pitaevskii equations for Bose-Einstein condensates (also they are generally larger than 'nano'...), inverse problems for Helmholtz equations.


(2)Nano Photonics:
We are studying semiconductor nano-structures with a special focus on self-assembled semiconductor quantum dots. These dots are formed by self-organisation during epitaxial growth. We are interested in the basics physical properties of these quantum dots as well as in the development of new devices. The quasi zero-dimensional density of states makes semiconductor quantum dots very attractive for quantum optical studies. Using a con-focal near-infrared microscope we investigate the micro-photoluminescence (µPL) and the photocurrent (PC) of semiconductor quantum dot structures. Dynamical properties of quantum dots are investigated by combining the latter techniques with time resolved pump&probe experiments. The experimental set-ups allow the complete optical and electrical investigation of single, isolated quantum dots. The goals are the performance of time-resolved optical experiments with a special focus on interlevel transitions which is enabled by mid-infrared and THz time-domain spectroscopy. Furthermore, the electronic manipulation of a single dot together with near-infrared optical monitoring should allow direct control of its electronic quantum states. This would lead to a direct exploitation of quantum dots as elements for quantum information processing.

(3)Analysis and Numerics of Kinetic Models in Nanoscience
Very often nano-structures are mathematically modelled by kinetic equations, based on phase-space descriptions of transport phenomena. To enhance our physical understanding of those nano-structures it is of paramount importance to advance the mathematical and numerical analysis of kinetic PDEs, both in the classical and in the quantum mechanical contexts. While topic (1) is modelling oriented, here we shall mainly deal with analytical and numerical issues of kinetic models. Particularly important analytical topics are scaling limits (semiclassical asymptotics, WKB techniques, mean free path limits..), and thermodynamic (large number of particles) limits in quantum and classical BBGKY hierarchies leading to (quantum) Boltzmann equations as in the Hartree and Hartree-Fock cases.

Talks in the framework of this thematic program... (by date) , (by name)

Pauli Fellows