Mathematical Theory of Resonances (08w5092)


Tanya Christiansen (University of Missouri)

Richard Froese (University of British Columbia)

(University of California at Berkeley)


The Banff International Research Station will host top researchers in its workshop on "Mathematical Theory of Resonances" next week, October 19 - October 24, 2008. One of the fundamental predictions of quantum theory is that the allowed energy levels of confined quantum systems can take on only a discrete set of values. These numbers are called eigenvalues and lie on the real number line. The theory of quantum systems where particles are not confined, but can can escape to infinity, is more subtle. Here a continuum of energy levels is possible and there may be no eigenvalues. Nevertheless there is a discrete set of numbers, called resonances, that describe quantum states that, although not confined forever, persist for a long time. Resonances are complex numbers, ahd contain information both about the energy and the lifetime of the resonant state.

Resonances show up in other physics problems (for example, in acoustic scattering) and in pure mathematics. Researchers have discovered many connections between the position of resonances and the underlying geometry and dynamics. However many questions still remain.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).