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arXiv · 1212.5821

Quantum walks as massless Dirac Fermions in curved Space-Time

Di Molfetta Giuseppe·Fabrice Debbasch·Marc E Brachet
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Abstract

A particular family of time- and space-dependent discrete-time quantum walks (QWs) is considered in one dimensional physical space. The continuous limit of these walks is defined through a new procedure and computed in full detail. In this limit, the walks coincide with the propagation of a massless Dirac fermion in an arbitrary gravitational field. A QW mimicking the radial propagation of a fermion outside and inside the event horizon of a Schwarzschild black hole is explicitly constructed and simulated numerically. Finally, the limiting procedure and the main result itself are carefully discussed.

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Di Molfetta Giuseppe, Fabrice Debbasch, Marc E Brachet. 2013-09-18. Quantum walks as massless Dirac Fermions in curved Space-Time. https://arxiv.org/abs/1212.5821

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