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Host: Institute for Mathematics and its Applications
Homepage: http://www.ima.umn.edu/reactive/spring/rf8.html
Email: staff@ima.umn.edu
Organizers: C. David Levermore, Anton Arnold, Naoufel Ben Abdallah, Ken T.-R. McLaughlin
Description:
Dispersive corrections to classical and semiclassical transport equations arise from the rudimentary incorporation of quantum
effects into macroscopic flow descriptions. These models play an increasing role in the study of nanometer scale electronic
devices and of fluids at extremely low temperatures. Advantages of dispersively corrected transport equations over fully
quantum mechanical descriptions are that they are numerically more tractable and that they allow for a more classical coupling
of the quantum system to the environment.
This workshop will have two thrusts. First, it will examine the mathematical derivation of dispersive correction terms both in linear and weakly nonlinear settings using Wigner transforms and in strongly nonlinear setting using tools from integrable systems. Second, the computational issues raised by the interplay between nonlinear and dispersive effects in, for example, quantum dots and wires, nonlinear optics, and superfluids.
Date received: August 27, 1999
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