Investigations of Quantum Backflow

Details Investigations of Quantum Backflow Investigations of Quantum Backflow

2012-02-08

arxiv.org/abs/1202.1783v2

Physics

Quantum Physics

31 pages, 13 figures. References added

Scientific paper

We investigate the backflow effect in elementary quantum mechanics -- the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We discuss various measurement models in which backflow may be seen in certain measurable probabilities. We compute the current and flux for states consisting of superpositions of gaussian wave packets. These are experimentally realizable but the amount of backflow is small. Inspired by the numerical results of Penz et al, we find two non-trivial wave functions whose current at any time may be computed analytically and which have periods of significant backflow, in one case with a backwards flux equal to about 70 percent of the maximum possible backflow, a dimensionless number $c_{bm} \approx 0.04 $, discovered by Bracken and Melloy. This number has the unusual property of being independent of $\hbar$ (and also of all other parameters of the model), despite corresponding to an obviously quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow.

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