Mapping curved spacetimes into Dirac spinors

Carlos Sabín

doi:10.1038/srep40346

Abstract

We show how to transform a Dirac equation in a curved static spacetime into a Dirac equation in flat spacetime. In particular, we show that any solution of the free massless Dirac equation in a 1 + 1 dimensional flat spacetime can be transformed via a local phase transformation into a solution of the corresponding Dirac equation in a curved static background, where the spacetime metric is encoded into the phase. In this way, the existing quantum simulators of the Dirac equation can naturally incorporate curved static spacetimes. As a first example we use our technique to obtain solutions of the Dirac equation in a particular family of interesting spacetimes in 1 + 1 dimensions.

Highlights

The growing interest in quantum simulators is not restricted to their potential role as non-universal post-classical computers
If the wavepacket is initially centered around an initial position at the right side of the wormhole throat (x0 > 0), we see that the probability density gets distorted with an intensity inversely proportional to the initial distance to the throat, as can be seen by comparing Fig. d) and f) with c) and e). In this way we are finding for the first time analytical solutions of the dynamics of Dirac particles in a spacetime containing a traversable wormhole
Our technique can be applied in a straightforward fashion to obtain solutions of the Dirac equation in a wormhole background out of numerical solutions of the free Dirac equation in flat spacetime and out of the experimental data obtained from the various multiplatform quantum simulators of the Dirac equation -without the need of engineering extra terms in the Hamiltonian

Summary

Introduction

The growing interest in quantum simulators is not restricted to their potential role as non-universal post-classical computers. We show that any solution of a free massless Dirac equation in 1 + 1 dimensions can be transformed into a solution of the same equation in curved spacetime, for a broad generic class of spacetime metrics.

Results

Conclusion