Mathematical and Numerical Methods for Time-Dependent Quantum Mechanics - from Dynamics to Quantum Information (17w5010)


Emmanuel Lorin (Carleton University)

André Bandrauk (U Sherbrooke)

(University of Calgary)


The Casa Matemática Oaxaca (CMO) will host the "Mathematical and Numerical Methods for Time-Depedent Quantum Mechanics - from Dynamics to Quantum Information" workshop from August 13th to August 18th, 2017.

Modern laser technology is today the unique source of ultrafast (few cycle) intense laser pulses, with intensities exceeding the internal electric field in atoms and molecules The interaction of such pulses with atoms and molecules leads to a new regime of laser-matter interaction, a highly nonlinear nonperturbative regime where new nonlinear physical phenomena occur such as High Harmonic Generation, HHG, from which the shortest pulse has been created, the attosecond (asec=10^{-18} second) pulse, the natural time scale of the electron. Such pulses are new tools for imaging electron motion and their interaction with these new intense pulses.

Currently one of the major experimental discoveries in the nonlinear nonperturbative regime laser–matter interaction is the Laser Pulse Filamentation, which was observed by Mourou and Braun in 1995 as the propagation of pulses over large distances in gases with focused narrow intense cores described by soliton theories. This technology is now applied to medical surgery and atmospheric science and has catalyzed intensive investigation in physics, computer science and applied mathematics to understand new effects such as self-transformation of these pulses into white light, intensity clamping, multiple filamentation, to further potential applications in wave guide writing, atmospheric remote sensing, even lightning guiding. This regime engenders many new mathematical questions due to the highly nonlinear nonperturbative effects occurring as well as the need for new accurate and efficient numerical methods, due to different microscopic and macroscopic spatio-temporal scales.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide 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 in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.