Reliable quantum master equation of the Unruh-DeWitt detector

Abstract

In this paper, we present a method for estimating the validity range of the quantum Markovian master equation as applied to the Unruh-DeWitt (UDW) detector within a broader context, particularly without necessitating an exact solution for the detector's evolution. We propose a relaxed van Hove limit (i.e., late-time limit) and offer a perturbative estimate of the error order resulting from the standard derivation procedure of open quantum dynamics. Our primary findings include reliability criteria for the Markov approximation and conditions for the applicability of the rotating wave approximation. Nevertheless, the specific forms of these validity conditions rely on the details of the detector-field system, such as the spacetime background, the trajectory of the detector, and the type of quantum field being analyzed. Finally, we illustrate our results by reexamining the open dynamics of an accelerating UDW detector undergoing the Unruh effect, where the validity conditions narrow the parameter space to ensure the solution's reliability regarding the quantum Markovian master equation.

15 pages, 3 figures, to match the published version, to appear in PRD

References in corpus (32)

• How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile
• Transition rate of the Unruh-DeWitt detector in curved spacetime
• Considerations on the Unruh Effect: Causality and Regularization
• Internal Consistency of Fault-Tolerant Quantum Error Correction in Light of Rigorous Derivations of the Quantum Markovian Limit
• Staying positive: going beyond Lindblad with perturbative master equations
• Entanglement dynamics for uniformly accelerated two-level atoms
• Interferometric Unruh detectors for Bose-Einstein condensates
• Static detectors and circular-geodesic detectors on the Schwarzschild black hole
• Phenomenology of Non-Custodial Warped Models
• The Fulling-Unruh effect in general stationary accelerated frames
• Non-Markovian time evolution of an accelerated qubit
• Uncertainty relation in Schwarzschild spacetime
• Open quantum system approach to Gibbons-Hawking effect of de Sitter space-time
• Hot Accelerated Qubits: Decoherence, Thermalization, Secular Growth and Reliable Late-time Predictions
• Understanding Hawking radiation in the framework of open quantum systems
• Entanglement dynamics for uniformly accelerated two-level atoms coupled with electromagnetic vacuum fluctuations
• Dissipation in the Caldeira-Leggett model
• Unruh-like effects: Effective temperatures along stationary worldlines
• Qubits on the Horizon: Decoherence and Thermalization near Black Holes
• Hot Cosmic Qubits: Late-Time de Sitter Evolution and Critical Slowing Down
• Effective master equations for two accelerated qubits
• Unruh detectors and quantum chaos in JT gravity
• Inversion of statistics and thermalization in the Unruh effect
• Entanglement dynamics in a Kerr spacetime
• Fisher information as a probe of spacetime structure: Relativistic quantum metrology in (A)dS
• Quantum estimation in an expanding spacetime
• (1+1)D Calculation provides evidence that quantum entanglement survives a firewall
• Qubit Heating Near a Hotspot
• Bell inequalities violation within non-Bunch-Davies states
• Fisher Information of a Black Hole Spacetime
• Extraction of entanglement from quantum fields with entangled particle detectors
• Relative entropy formulation of thermalization process in a Schwarzschild spacetime