Unravelling quantum carpets: a travelling-wave approach

Generic channel and ridge structures are known to appear in the time-dependent position probability distribution of a one-dimensional quantum particle confined to a box. These structures are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of the probability density, wherein each contributing term corresponds simultaneously to (i) a real wave propagating at a quantized velocity and (ii) to the time-averaged structure of the position distribution along a quantized direction in spacetime. The approach leads to new predictions of channel locations, widths and depths, and is able to provide more structural details than earlier approaches based on partial interference and Wigner functions. Results are also applicable to light diffracted by a periodic grating, and to the quantum rigid rotator.