An introduction to the quantum backflow effect
Abstract
We present an introduction to the backflow effect in 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 show that the effect is present even for simple states consisting of superpositions of gaussian wave packets, although the size of the effect is small. Inspired by the numerical results of Penz et al, we present a wave function whose current at any time may be computed analytically and which has periods of significant backflow, with a backwards flux equal to about 70 percent of the maximum possible backflow, a dimensionless number c_{bm} ≈ 0.04, discovered by Bracken and Melloy. This number has the unusual property of being independent of hslash (and also of all other parameters of the model), despite corresponding to a quantummechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We conclude by discussing a specific measurement model in which backflow may be identified in certain measurable probabilities.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 June 2013
 DOI:
 10.1088/17426596/442/1/012055
 arXiv:
 arXiv:1301.4893
 Bibcode:
 2013JPhCS.442a2055Y
 Keywords:

 Quantum Physics
 EPrint:
 10 pages, 9 figures. To appear in proceedings of the 2012 DICE Conference (edited by T.Elze)