Connecting the circular and drifted Rindler Unruh effects

Abstract

In Minkowski spacetime quantum field theory, each stationary motion is associated with an effective, energy-dependent notion of temperature, which generalises the familiar Unruh temperature of uniform linear acceleration. Motivated by current experimental interest in circular motion, we analyse the effective temperature for drifted Rindler motion, generated by a boost and a spacelike translation (drift), and the way in which drifted Rindler motion can be smoothly (and in fact real analytically) deformed to circular motion through a third type of motion known as parator. For an Unruh-DeWitt detector coupled linearly to a massless scalar field in 2+1 and 3+1 spacetime dimensions, we establish analytic results in the limits of large gap, small gap and large drift speed. For fixed proper acceleration, the drifted Rindler temperature remains bounded in the large gap limit, in contrast to the circular motion temperature, which can be arbitrarily large in this limit. Finally, in 2+1 dimensions, we trace the vanishing of the circular motion temperature in the small gap limit to the weak decay of the Wightman function, and we show that, among all types of stationary motion in all dimensions, this phenomenon is unique to 2+1 dimensions and therein to circular and parator motion.

32 pages, 1 table. v2: Presentational clarifications, including new title. Real analyticity of the deformation mentioned

References in corpus (31)

• Analogue Gravity
• The Unruh effect and its applications
• Measurement of stimulated Hawking emission in an analogue system
• How often does the Unruh-DeWitt detector click? Regularisation by a spatial profile
• Wavepacket detection with the Unruh-DeWitt model
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• The Rotating Quantum Vacuum
• Acceleration Radiation for Orbiting Electrons
• Casimir forces on atoms in optical cavities
• Backreaction and Unruh effect: New insights from exact solutions of uniformly accelerated detectors
• Interferometric Unruh detectors for Bose-Einstein condensates
• General Relativistic Quantum Optics: Finite-size particle detector models in curved spacetimes
• Detection of acceleration radiation in a Bose-Einstein condensate
• Waiting for Unruh
• Broken covariance of particle detector models in relativistic quantum information
• Static detectors and circular-geodesic detectors on the Schwarzschild black hole
• The Fulling-Unruh effect in general stationary accelerated frames
• Unruh and analogue Unruh temperatures for circular motion in 3+1 and 2+1 dimensions
• Detecting Acceleration-Enhanced Vacuum Fluctuations with Atoms Inside a Cavity
• How often does the Unruh-DeWitt detector click beyond four dimensions?
• Classical analogue of the Unruh effect
• Circular motion analogue Unruh effect in a $2+1$ thermal bath: Robbing from the rich and giving to the poor
• Unruh-like effects: Effective temperatures along stationary worldlines
• Background Thermal Contributions in Testing the Unruh Effect
• Asymptotic states for stationary Unruh-DeWitt detectors
• Ambient temperature versus ambient acceleration in the circular motion Unruh effect
• Third sound detectors in accelerated motion
• How robust is the indistinguishability between quantum fluctuation seen from non-inertial frame and real thermal bath
• Stationary trajectories in Minkowski spacetimes
• Background thermal depolarization of electrons in storage rings
• Quantum Energy Inequalities along stationary worldlines

Cited by in corpus (4)

• Waiting around for Unruh
• Back-action from inertial and non-inertial Unruh-DeWitt detectors revisited in covariant perturbation theory
• Thermodynamic uncertainty relations for relativistic quantum thermal machines
• Probing non-equilibrium steady states of the Klein-Gordon field with Unruh-DeWitt detectors