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arXiv:2610.26753

A General Master Equation for Two Accelerated Detectors: Stationary States and Entanglement

Riccardo Acquaviva, Paolo Facchi

quant-phSubmitted Oct 19, 2026• Announced Oct 20, 2026• 0 citations
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Abstract

We derive a general Gorini-Kossakowski-Lindblad-Sudarshan master equation for two co-located, uniformly accelerated two-level detectors weakly coupled to scalar fields in the Minkowski vacuum, retaining coherent and dissipative contributions for arbitrary orientations, field masses, and spacetime dimensions. For equal orientations, we determine stationary states and their entanglement for two couplings to massless fields in four dimensions: symmetric coupling yields acceleration-dependent concurrence, whereas rotating-wave coupling gives acceleration-independent concurrence.

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18 pages, 2 figures

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The master equation describing the completely positive time evolution of a uniformly accelerated two-level system in weak interaction with a scalar field in the Minkowski vacuum is derived and explicitly solved. The moving system is found to be subjected to dissipation that drives its density matrix to a purely thermal equilibrium state, exhibiting a nonvanishing probability of spontaneous excitation, this phenomenon being usually referred to as the Unruh effect. Remarkably, when the uniformly accelerating system is composed by two, independent two-level atoms, the corresponding asymptotic, equilibrium state turns out to be entangled.
The creation and destruction of entanglement between a pair of interacting two-level detectors accelerating about diametrically opposite points of a circular path is investigated. It is found that any nonzero acceleration has the effect of suppressing the vacuum entanglement and enhancing the acceleration radiation, thereby reducing the entangling capacity of the detectors. Given that for large accelerations the acceleration radiation is the dominant effect, we investigate the evolution of a two-detector system initially prepared in a Bell state using a perturbative master equation and treating the vacuum fluctuations as an unobserved environment. A general function for the concurrence is obtained for stationary and symmetric world lines in flat space. The entanglement sudden-death time is computed.
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