A quantum walk simulation of extra dimensions with warped geometry

TL;DR

This paper demonstrates how a quantum walk can simulate a spin 1/2 particle in a warped extra dimension, reproducing localization effects akin to those in high energy physics models like Randall-Sundrum.

Contribution

It introduces a quantum walk model that simulates a warped extra dimension and reproduces localization effects related to high energy physics theories.

Findings

Quantum walk reproduces Dirac equation in warped geometry.

Probability distribution localizes near the low energy brane.

Localization strength is controlled by the warp coefficient.

Abstract

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.