Thermal effect in a causal diamond: open quantum systems approach

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.

25 pages, 5 figures

References in corpus (10)

• Towards a derivation of holographic entanglement entropy
• Quantum algorithm for simulating the dynamics of an open quantum system
• Entanglement dynamics for uniformly accelerated two-level atoms
• The Unruh effect and entanglement generation for accelerated atoms near a reflecting boundary
• Experimental simulation of open quantum system dynamics via Trotterization
• Solution of the Lindblad Equation in the Kraus Representation
• Entanglement generation in atoms immersed in a thermal bath of external quantum scalar fields with a boundary
• Entanglement dynamics for uniformly accelerated two-level atoms coupled with electromagnetic vacuum fluctuations
• Semiclassical Methods in Curved Spacetime and Black Hole Thermodynamics
• Conformal mapping of Unruh temperature