For wavefunctions whose fourier spectrum (wavenumber or frequency) is positive, the local phase gradient can sometimes be negative; examples of this 'backflow' occur in quantum mechanics and optics. The backflow probability P (fraction of the region that is backflowing) is calculated for several cases. For waves that are superpositions of many uncorrelated components, P = (1 − r)/2, where r is a measure of the dispersion (mean/r.m.s.) of the component frequencies or wavenumbers. In two dimensions (backflow in spacetime, or wave propagation in the plane) the boundary of the backflowing region includes the phase singularities of the wave.
|Translated title of the contribution||Quantum backflow, negative kinetic energy, and optical retro-propagation|
|Pages (from-to)||1 - 15|
|Number of pages||15|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - Sep 2010|