Quantum walks as massless Dirac Fermions in curved Space-Time
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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2012
- DOI:
- 10.48550/arXiv.1212.5821
- arXiv:
- arXiv:1212.5821
- Bibcode:
- 2012arXiv1212.5821M
- Keywords:
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- Quantum Physics;
- Mathematical Physics
- E-Print:
- Accepted as a regular article in PRA