Proposal for an experiment to measure the Hausdorff dimension of quantum mechanical trajectories

Details Proposal for an experiment to measure the Hausdorff dimension of quantum mechanical trajectories Proposal for an experiment to measure the Hausdorff dimension of quantum mechanical trajectories

1997-02-04

arxiv.org/abs/quant-ph/9702013v1

Phys.Rev. A55 (1997) 951

Physics

Quantum Physics

35 pages, LaTeX + 27 figures, ps and gif

Scientific paper

10.1103/PhysRevA.55.951

We make a proposal for a Gedanken experiment, based on the Aharonov-Bohm effect, how to measure in principle the zig-zagness of the trajectory of propagation (abberation from its classical trajectory) of a massive particle in quantum mechanics. Experiment I is conceived to show that contributions from quantum paths abberating from the classical trajectory are directly observable. Experiment II is conceived to measure average length, scaling behavior and critical exponent (Hausdorff dimension) of quantum mechanical paths.

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