The cost of building a wall for a fermion

TL;DR

This paper investigates the energy and detector response associated with creating or demolishing a wall for a massless Dirac field in 1+1 dimensions, revealing finite responses for smooth changes and divergences in rapid limits, with implications for quantum information.

Contribution

It provides a detailed analysis of the energy cost and detector response during wall creation or demolition for a Dirac field, highlighting differences in sensitivities and divergences.

Findings

Finite energy density and detector response for smooth wall evolution

Divergent energy density in rapid wall creation or demolition

Logarithmic divergence of detector response in rapid limits

Abstract

We analyse the energy cost of building or demolishing a wall for a massless Dirac field in (1+1)-dimensional Minkowski spacetime and the response of an Unruh-DeWitt particle detector to the generated radiation. For any smoothly-evolving wall, both the field's energy density and the detector's response are finite. In the limit of rapid wall creation or demolition, the energy density displays a delta function squared divergence. By contrast, the response of an Unruh-DeWitt detector, evaluated within first-order perturbation theory, diverges only logarithmically in the duration of the wall evolution. The results add to the evidence that a localised matter system may not be as sensitive to the rapid wall creation as the local expectation values of field observables. This disparity has potential interest for quantum information preservation scenarios.