Analog Unruh effect of inhomogeneous one-dimensional Dirac fermions

TL;DR

This paper investigates the analog of the Unruh effect in one-dimensional Dirac fermions with spatially varying velocities, demonstrating how different velocity profiles influence particle creation and localization.

Contribution

It introduces a model for inhomogeneous Dirac fermions simulating an accelerating observer, analyzing how velocity profiles affect the analog Unruh effect and particle localization.

Findings

Ideal Unruh effect occurs for v(x) ∝ |x|

Modified Unruh effect persists for realistic velocity profiles

Particle creation is localized near |x| ≪ λ

Abstract

We study one-dimensional Dirac fermions in the presence of a spatially-varying Dirac velocity $v(x)$, that can form an approximate lab-based Rindler Hamiltonian describing an observer accelerating in Minkowski spacetime. A sudden switch from a spatially homogeneous velocity ($v(x)$ constant) to a spatially-verying velocity ($v(x)$ inhomogeneous) leads to the phenomenon of particle creation, i.e., an analog Unruh effect. We study the dependence of the analog Unruh effect on the precise form of the velocity profile, finding that while the ideal Unruh effect occurs for $v(x) \propto |x|$, a modified Unruh effect still occurs for more realistic velocity profiles that are linear for $|x|$ smaller than a length scale $\lambda$ and constant for $|x|\gg \lambda$ (such as $v(x)\propto \tanh \big(|x|/\lambda \big)$). We show that the associated particle creation is localized to $|x|\ll \lambda$.