A quantum walk simulation of extra dimensions with warped geometry

We investigate the properties of a quantum walk which can simulate the behavior of a spin 1/2 particle in a model with an ordinary spatial dimension, and one extra dimension with warped geometry between two branes. Such a setup constitutes a 1+ 1 dimensional version of the Randall-Sundrum model, which plays an important role in high energy physics. In the continuum spacetime limit, the quantum walk reproduces the Dirac equation corresponding to the model, which allows to anticipate some of the properties that can be reproduced by the quantum walk. In particular, we observe that the probability distribution becomes, at large time steps, concentrated near the low energy brane, and can be approximated as the lowest eigenstate of the continuum Hamiltonian that is compatible with the symmetries of the model. In this way, we obtain a localization effect whose strength is controlled by a warp coefficient. In other words, here localization arises from the geometry of the model, at variance with the usual effect that is originated from random irregularities, as in Anderson localization. In summary, we establish an interesting correspondence between a high energy physics model and localization in quantum walks.

Automated summary

In this study, we investigate the properties of a quantum walk that can simulate the behavior of a spin 1/2 particle in an additional dimension with warped geometry between two branes. The results show that, in the continuum spacetime limit, the quantum walk can reproduce the Dirac equation corresponding to the model, allowing us to anticipate some of the properties that can be reproduced. Specifically, we observe a concentration of the probability distribution near the low energy brane at large time steps, approximating the lowest eigenstate of the continuum Hamiltonian compatible with the symmetries of the model. This localization effect is controlled by a warp coefficient, indicating that it arises from the geometry of the model rather than random irregularities.