J. M. Yearsley, J. J. Halliwell, R. Hartshorn, A. Whitby
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.
View original:
http://arxiv.org/abs/1202.1783
No comments:
Post a Comment