Relativistic quantum backflow

Quantum backflow is a remarkable and yet relatively unknown phenomenon that occurs in quantum mechanics. Itis the initially puzzling effect that for a free particle describedby a wavefunction, localised in x<0 and containing onlypositive momenta, the probability of remaining in x<0 canactually increase with time. Probability canflow backwards,i.e. in the opposite direction to the momentum in certaincases.

In this paper we discuss relativistic quantum backflow. The general theory of relativistic backflow is presented and it is shown that the backflow can be written as a function of a parameter epsilon, which is defined in terms of fundamental constants and the backflow period. Backflow eigenfunctions are determined numerically for a range of values of epsilon, and an explicit expression for the relativistic backflow eigenvalue in terms of the non-relativistic backflowconstant is presented. Backflow eigenvectors are then fitted with some standard functions, which lead to substantially higher backflow than has been found previously with fitting procedures, for some values of epsilon. In analysing the non-relativistic limit of the theory we show that this problem is one of those rare cases where the relativistic theory is intrinsically more simple than the non-relativistic theory.

J. Ashfaque, J. Lynch and P. Strange, “Relativistic Quantum Backflow”, Physica Scripta, 94, 125107, 1-7.
doi 10.1088/1402-4896/ab265c 
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