Quantum fractals in boxes
- 21 October 1996
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 29 (20) , 6617-6629
- https://doi.org/10.1088/0305-4470/29/20/016
Abstract
A quantum wave with probability density , confined by Dirichlet boundary conditions in a D-dimensional box of arbitrary shape and finite surface area, evolves from the uniform state . For almost all positions , the graph of the evolution of P is a fractal curve with dimension . For almost all times t, the graph of the spatial probability density P is a fractal hypersurface with dimension . When D = 1, there are, in addition to these generic time and space fractals, infinitely many special `quantum revival' times when P is piecewise constant, and infinitely many special spacetime slices for which the dimension of P is 5/4. If the surface of the box is a fractal with dimension , simple arguments suggest that the dimension of the time fractal is , and that of the space fractal is .Keywords
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