Thermal effect in a causal diamond: open quantum systems approach

TL;DR

This paper models a finite-lifetime observer in a causal diamond as an open quantum system, revealing a thermal state with temperature inversely related to the observer's lifetime, consistent with known results and useful for entanglement protocols.

Contribution

It introduces an open quantum systems framework to characterize the thermal state of a finite-lifetime observer in a causal diamond, providing a new derivation and practical applications.

Findings

The steady-state density matrix is thermal with a temperature inversely proportional to lifetime.

The approach aligns with established thermal results from other methods.

It facilitates entanglement harvesting in the causal diamond.

Abstract

A static observer with a finite lifetime has causal access to only a limited region of spacetime known as the causal diamond. The presence of an apparent horizon in the causal diamond, due to the observer's finite lifetime, is the origin of an Unruh-like thermal effect. Thus, even though the observer is static and the background is flat, the finite-lifetime observer experiences a thermal bath in the Minkowski vacuum. In this article, we provide an open quantum systems approach that yields a complete thermal characterization via the observer's steady-state density matrix, which is shown to be thermal with a temperature inversely proportional to its lifetime. This associated diamond temperature agrees with the established result derived from other methods. Moreover, our approach is particularly useful for designing entanglement harvesting protocols in the causal diamond. In addition, we introduce an insightful procedure that defines diamond coordinates using conformal transformations, and which leads to a more direct derivation of the thermal properties.