An introduction to the quantum backflow effect

6th International Workshop DICE2012 Spacetime – Matter – Quantum Mechanics: From the Planck Scale to Emergent Phenomena

物理学;力学

Yearsley, J.M.^1 ; Halliwell, J.J.^2

Centre for Quantum Information and Foundations, DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom^1

Theoretical Physics Group, Blackett Laboratory, Imperial College, London SW7 2BZ, United Kingdom^2

关键词: Backflow effect;    Classical limits;    Dimensionless number;    Gaussian Wave Packets;    Measurement model;    Negative currents;    Numerical results;    Quantum mechanical effects;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012055/pdf
DOI  :  10.1088/1742-6596/442/1/012055

学科分类：力学，机械学

来源: IOP

【 摘 要 】

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 cbm 0.04, discovered by Bracken and Melloy. This number has the unusual property of being independent of (and also of all other parameters of the model), despite corresponding to a quantum-mechanical 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.