Relativistic effects in quantum walks: Klein's paradox and Zitterbewegung

Abstract

Quantum walks are not only algorithmic tools for quantum computation but also not trivial models which describe various physical processes. The paper compares one-dimensional version of the free particle Dirac equation with discrete time quantum walk (DTQW). We show that the discretized Dirac equation when compared with DTQW results in interesting relations. It is also shown that two relativistic effects associated with the Dirac equation, namely Zitterbewegung (quivering motion) and Klein's paradox, are present in DTQW, which can be implemented within non-relativistic quantum mechanics.

4 pages, 3 figures

References in corpus (4)

• Chiral tunneling and the Klein paradox in graphene
• Zitterbewegung of electronic wave packets in semiconductor nanostructures
• Free Dirac evolution as a quantum random walk
• Single atom quantum walk with 1D optical superlattices

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