Proposal for an Experiment to Measure the Hausdorff Dimension of Quantum Mechanical Trajectories
نویسنده
چکیده
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. PACS index: 03.65.Bz
منابع مشابه
Generalized Aharonov-Bohm Effect, Homotopy Classes and Hausdorff Dimension
We suggest as gedanken experiment a generalization of the Aharonov-Bohm experiment, based on an array of solenoids. This experiment allows in principle to measure the decomposition into homotopy classes of the quantum mechanical propagator. This yields information on the geometry of the average path of propagation and allows to determine its Hausdorff dimension. PACS index: 03.65.Bz
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