Quantum walks as massless Dirac Fermions in curved Space-Time

TL;DR

This paper demonstrates how certain quantum walks can simulate the behavior of massless Dirac fermions in curved space-time, including black hole horizons, through a new continuous limit procedure.

Contribution

It introduces a novel method to derive continuous limits of quantum walks that replicate relativistic fermion dynamics in curved space-time.

Findings

Quantum walks can model massless Dirac fermions in curved space-time.

A specific quantum walk simulating fermion propagation near a black hole horizon was constructed.

Numerical simulations confirm the theoretical predictions.

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.