Quantum detection of boundary conditions

TL;DR

This paper investigates how different boundary conditions at a connecting hypersurface influence the response of an Unruh-deWitt detector in a conical spacetime, revealing that boundary choices affect the detector's ability to sense spacetime conicity.

Contribution

It introduces the analysis of boundary condition effects on the quantum response function in conical spacetimes, extending previous work that assumed continuous scalar fields.

Findings

Boundary conditions significantly alter the detector's response.

The detector's response reflects combined effects of conicity and boundary conditions.

Different boundary conditions lead to physically inequivalent quantum dynamics.

Abstract

The quantum detection of spacetime conicity was investigated in reference [Phys. Lett. B 820, 136482 (2021)] through the analysis of the response function of an Unruh-deWitt detector coupled to a massless scalar field. In particular, it was shown that the detector can discern the presence of the deficit angle of a region of spacetime even when it is placed on a flat region with no conical deficit and (due to the rapid switching on and off) is classically isolated from the conical region. The scalar field was supposed to be continuous at the three dimensional timelike hypersurface connecting both regions and it was argued that the non-trivial effects on the response function were only due to the deficit angle of the outer conical region. In this paper, we study the response function of the Unruh-deWitt detector on the same classical framework, but exploring the effects of the choice of boundary conditions for the scalar field at the connecting hypersurface. These boundary conditions are extracted from the two-interval Sturm-Liouville theory and each one gives rise to a physically inequivalent sensible dynamics for the quantum field. We show that they play an important role on the response function of the detector, which effectively ``feels'' the combined effect of conicity + boundary condition.