Dispersive Quantization

Abstract

The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, nondifferentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics and nonlinear dispersion are proposed as open problems.

Additional information

Notes on contributors

Peter J. Olver

Peter J. Olver received his Sc.B. from Brown University in 1973 and his Ph.D. from Harvard University in 1976. He is the author of over 100 research papers in a wide range of subjects, as well as four books, on Applications of Lie Groups to Differential Equations, on Equivalence, Invariants, and Symmetry, on Classical Invariant Theory, and an undergraduate text coauthored with his wife Cheri Shakiban on Applied Linear Algebra. He is currently serving as Department Head of the School of Mathematics at the University of Minnesota. On those rare occasions when he is not doing mathematics, administrating, or trying to finish the PDE text [10], he relaxes by playing the piano, gardening, and boating on the Mississippi.