M V Berry 1996 J. Phys. A: Math. Gen. 29 6617 doi:10.1088/0305-4470/29/20/016
Quantum fractals in boxes
M V Berry
Show affiliationsA 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 
.
- PACS
-
02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
-
28A80 Fractals (See also 37Fxx)
81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
-
Issue 20 (21 October 1996)
Received 22 April 1996
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Quantum fractals in boxes
M V Berry 1996 J. Phys. A: Math. Gen. 29 6617
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