Circular motion analogue Unruh effect in a 2+1 thermal bath: robbing from the rich and giving to the poor

Abstract

The Unruh effect states that a uniformly linearly accelerated observer with proper acceleration $a$ experiences the Minkowski vacuum as a thermal state at temperature $T_U=a/(2\pi)$. An observer in uniform circular motion experiences a similar effective temperature, operationally defined in terms of excitation and de-excitation rates, and physically interpretable in terms of synchrotron radiation, but this effective temperature depends not just on the acceleration but also on the orbital speed and the excitation energy. In this paper we consider an observer in uniform circular motion when the Minkowski vacuum is replaced by an ambient thermal bath, and we address the interplay of ambient temperature, Doppler effect, acceleration, and excitation energy. Specifically, we consider a massless scalar field in $2 + 1$ spacetime dimensions, probed by an Unruh-DeWitt detector, in a Minkowski (rather than proper) time formulation: this setting describes proposed analogue spacetime systems in which the effect may become experimentally testable, and in which an ambient temperature will necessarily be present. We establish analytic results for the observer's effective temperature in several asymptotic regions of the parameter space and provide numerical results in the interpolating regions, finding that an acceleration effect can be identified even when the Doppler effect dominates the overall magnitude of the response. We also identify parameter regimes where the observer sees a temperature lower than the ambient temperature, experiencing a cooling Unruh effect.

Non-linear effective field theory simulators in two-fluid interfaces

“…Notable examples include measurements of analogue Hawking radiation [37] around various effective horizons [7,8,10,38], and analogue black hole phenomena in dispersive draining vortex flows [11,12]. Building on the firm foundations laid by these previous simulators, recent developments are motivating and driving the extension of the underlying quantum field theories [26,14,23,6], fostering a symbiosis between experiment and theory within analogue gravity. This definition indicates that D j is an asymmetric, dimensionless, square matrix.…”

“…In the limit ρ 1 ≫ ρ 2 , the Atwood number A tends to unity, and the resulting equation represents the effective field theory for surface modes in an inviscid fluid. This correspondence is of particular relevance for creating gravity simulators of quantum processes that can take place on flat spacetime, such as the Unruh effect [22], as proposed in [23,6] on the interface of superfluid helium.…”

Third sound detectors in accelerated motion

“…The more fundamental and as yet unexamined issue is the crucial dependence on the precise properties only provided by the quantum vacuum state, which unify the perception of all non-accelerating observers travelling at any constant velocity. For an initial state differing from the quantum vacuum, such as a thermal state, this agreement between inertial observers is tainted by a Doppler-shifted spectrum according to their velocities [2]. Related previous analyses on an ambient temperature in 3 + 1 dimensions are given in [3,4] In the present paper, we tackle these two issues at hand.…”

“…The integrand is the twice-differentiated thermal Wightman function which eliminates the infrared divergence that would occur in the undifferentiated thermal Wightman function [2]. Using (11), the PSD for the full phase field ψ can be decomposed as…”

“…where σ 2 sn comes from the shot noise in the signal [5], while F(ω; T), known as the response function in the literature, comes from the analogue field fluctuations. The dimensionful constant κ in ( 16) arises from matching the normalisation of our fields to that in [2] (see appendix C), and is given by…”