Relativistic effects and rigorous limits for discrete- and continuous-time quantum walks

The mathematical relationship between the discrete-time and continuous-time quantum walks and the one-dimensional Dirac equation is explored by studying a class of solutions for each, expressed in terms of the generalized, regular, and modified Bessel functions, respectively. Rigorous limits connect...

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Bibliographic Details
Published in:Journal of mathematical physics 2007-08, Vol.48 (8), p.082102-082102-27
Main Author: Strauch, Frederick W.
Format: Article
Language:English
Subjects:
BESSEL FUNCTIONS
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DIRAC EQUATION
Effects
Exact sciences and technology
GRAPH THEORY
Mathematical methods in physics
MATHEMATICAL SOLUTIONS
Mathematics
ONE-DIMENSIONAL CALCULATIONS
Physics
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
Quantum theory
RELATIVISTIC RANGE
Sciences and techniques of general use
WAVE PACKETS
ZITTERBEWEGUNG
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Summary:The mathematical relationship between the discrete-time and continuous-time quantum walks and the one-dimensional Dirac equation is explored by studying a class of solutions for each, expressed in terms of the generalized, regular, and modified Bessel functions, respectively. Rigorous limits connecting these solutions are established. In addition, new analytical and numerical results are presented for quantum walks and the Dirac equation, including entanglement, relativistic localization and wave packet spreading, and normal and anomalous Zitterbewegung.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.2759837