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New Journal of Physics

Quantum carpets woven by Wigner functions

O. M. Friesch, Irene Marzoli, Wolfgang P. Schleich

Published Mar 6, 2000• 56 citations
Publisher

Abstract

The dynamics of many different quantum systems is characterized by a regular net of minima and maxima of probability stretching out in a spacetime representation. We offer an explanation to this phenomenon in terms of the Wigner function. This approach illustrates very clearly the crucial role played by interference.
DOI
10.1088/1367-2630/2/1/004

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Abstract We analyze the structures emerging in the spacetime representation of the probability density woven by a slightly relativistic particle caught in a one‐dimensional box. In particular, we evaluate the relativistic effects on the revival time and the specific changes produced in the intermode traces, which quantum carpets consist of. Moreover, we present a detailed mathematical analysis of such quantum carpets pursuing the approach of a kernel. Here we represent the probability distribution as a superposition of interfering Airy function‐type structures along straight world lines. We also show that this phenomenon can be enhanced by many orders of magnitude in semiconductors with narrow band‐gap (e.g. as in InSb) and small effective mass of the electron, whereby due to the strong nonparabolicity of the semiconductor conduction band, the electron energy vs momentum dispersion relation behaves in a pseudo‐relativistic way.