It is well known that the rotational motion does not induce Unruh effect, because the Minkowski vacuum coincides with the vacuum state defined by the pure rotating observers. However, are there Rindler particles carrying orbital angular momentum (OAM), and do they produce observable effect? To answer these questions, we need an accelerated observer having a vortex structure in the transverse dimensions and carrying well-defined OAM. Here we consider the angular momentum characteristics of Unruh effect in the theory of scalar field and electromagnetic field for the first time. We find that the rotation and vortex structure of a uniformly accelerated observer lead to the definite angular momentum correlation between Rindler particles and their counterparts in Minkowski vacuum. When interacting with the Unruh thermal bath, the accelerated vortex observer carrying the OAM of l can absorb and emit Rindler particles with the same OAM, and the particle energy is determined by the angular velocity of the rotation. The absorption rate is not equal to the emission rate in general. Both the absorption and emission processes in the thermal bath are correlated with the emission process of particles with OAM of +l or -1 in Minkowski vacuum. This effect may promote a potential scheme to detect the Unruh effect. The OAM provides a potential approach to filter out the background noise so that the signal particles could be extracted sufficiently.
Traditionally the physics of the Unruh effect, i.e. the q.f.t. in the wedges $W_R$ or $W_L$ in Minkowski space is related to the physics in the Rindler Fock space, which is a proplematical strategy. In a careful analysis we show that the correct dual q.f.t. lives rather in the thermal Rindler Hilbert space and turns out to be unitarily equivalent to the corresponding Minkowski space theory in contrast to the Rindler Fock space theory. We show in particular that in thermal Rindler Hilbert space a new sort of objects occurs, viz., quasi-particle/hole creation/annihilation operators of thermal Ri…
A great deal of evidence has been mounting over the years showing a deep connection between acceleration, radiation, and the Unruh effect. Indeed, the fact that the Unruh effect can be codified in the Larmor radiation emitted by the charge was used to propose an experiment to experimentally confirm the existence of the Unruh thermal bath. However, such connection has two puzzling issues: (1) how the quantum Unruh effect can be codified in the classical Larmor radiation and (2) the fundamental role played by zero-Rindler-energy modes of the Unruh thermal bath in such a context. Here we generali…
The interplay between acceleration and radiation harbors remarkable and surprising consequences. One of the most striking is that the Larmor radiation emitted by a charge can be seen as a consequence of the Unruh thermal bath. Indeed, this connection between the Unruh effect and classical bremsstrahlung was used recently to propose an experiment to confirm (as directly as possible) the existence of the Unruh thermal bath. This situation may sound puzzling in two ways: first, because the Unruh effect is a strictly quantum effect while Larmor radiation is a classical one, and second, because of …
We investigate the Unruh effect for a massless scalar field in the two dimensional Minkowski space in the presence of a uniformly accelerated perfect mirror, with the trajectory of the mirror chosen in such a way that the mirror completely masks the Rindler horizon from the space-time region of interest. We find that the characteristic thermodynamical properties of the effect remain unchanged, i.e. the response of a uniformly co-accelerated Unruh detector and the distribution of the Rindler particles retain their thermal form. However, since in this setup there are no unobserved degrees of fre…
We study the temperatures for the circular and drifted Rindler motions by employing the Unruh-DeWitt detector method. In the circular motion, the temperature is increasing along the radius of the circular motion until it reaches the maximum, and then it is decreasing and eventually vanishing at the limit to the radius where the proper acceleration is infinite. In fact, the temperature is proportional to the proper acceleration quadratically near the origin of the circular motion as compared to the usual Unruh effect depending on the linear proper acceleration. On the other hand, in the drifted…
We derive the solutions of gravitational waves in the future (F) expanding and the past (P) shrinking Kanser spacetimes as well as in the left (L) and right (R) Rindler wedges in the Regge-Wheeler gauge. The solutions for all metric components are obtained in an analytic form in each region. We identify the master variables, which are equivalent to massless scalar fields, to describe the gravitational degrees of freedom for the odd parity and even parity modes under the transformation in the two-dimensional plane symmetric space. Then, the master variables are quantized, and we develop the qua…
If an Unruh-DeWitt detector operates for an infinite proper time along the trajectory of a uniformly accelerated observer in Fock space then induced transition rate of the detector is proportional to Planck distribution. For a realistic detector which operates only for a finite period, the instantaneous transition rate contains both transient and non-transient terms. In particular, the non-transient term contains a residue evaluated at the pole of the two-point function. We show here by considering a massless scalar field that unlike in Fock quantization, the short-distance two-point function …
The energy of a particle moving on a spacetime, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here we find the explicit expressions for the coordinate transformations from rainbow Minkowski spacetime to accelerated frame. The corresponding metric is also obtained which we call as rainbow-Rindler metric. So far we are aware of, no body has done it in a concrete manner. Here this is found from the first principle and hence all the parameters are properly identified. The advant…
Existence of Unruh effect is often understood from the property of two-point function along Rindler trajectory where it satisfies KMS condition. In particular, it exhibits the so-called KMS periodicity along imaginary time direction. Corresponding period is then identified with reciprocal of Unruh temperature times Boltzmann constant. We show here that the two-point function including leading order perturbative corrections due to polymer quantization, the quantization method used in loop quantum gravity, violates KMS condition in low-energy regime. This violation is caused by correction terms …
Quantization of the Proca field in the Rindler wedge and the interaction of uniformly accelerated currents with massive vector bosons from the Unruh thermal bath
Mixing transformations for a uniformly accelerated observer (Rindler observer) are analyzed within the quantum field theory framework as a basis for investigating gravitational effects on flavor oscillations. In particular, the case of two charged boson fields with different masses is discussed. In spite of such a minimal setting, the standard Unruh radiation is found to loose its characteristic thermal interpretation due to the interplay between the Bogolubov transformation hiding in field mixing and the one arising from the Rindler spacetime structure. The modified spectrum detected by the R…
We investigate a two-level Unruh-DeWitt detector coupled to a massless scalar field or its proper time derivative in $(1+1)$-dimensional Minkowski spacetime, in a quantum state whose correlation structure across the Rindler horizon mimics the stationary aspects of a firewall that Almheiri et al have argued to ensue in an evaporating black hole spacetime. Within first-order perturbation theory, we show that the detector's response on falling through the horizon is sudden but finite. The difference from the Minkowski vacuum response is proportional to $ω^{-2}\ln(|ω|)$ for the non-derivative dete…
Ultracold fermionic atoms in an optical lattice, with a sudden position-dependent change (a quench) in the effective dispersion relation, have been proposed by Rodríguez-Laguna et al. as an analogue spacetime test of the Unruh effect. We provide new support for this analogue by analysing a massless scalar field on a $(1+1)$-dimensional continuum spacetime with a similar quench: an early time Minkowski region is joined at a constant time surface, representing the quench, to a late time static region in which left and right asymptotically Rindler domains are connected by a smooth negative curvat…
An equivalence is demonstrated, by an explicit first order quantum calculation, between the Minkowski photon emission rate in the inertial frame for an accelerating charge moving on a Rindler trajectory with additional transverse drift motion and the combined Rindler photon emission and absorption rate of the same charge in the Rindler frame in the presence of the Davies Unruh thermal bath. The equivalence also extends, for the Bremsstrahlung emitted by the same charge as calculated using the machinery of classical electrodynamics. The equivalence is shown to also hold for the case of accelera…
We analyse the response of a spatially extended direction-dependent local quantum system, a detector, moving on the Rindler trajectory of uniform linear acceleration in Minkowski spacetime, and coupled linearly to a quantum scalar field. We consider two spatial profiles: (i) a profile defined in the Fermi-Walker frame of an arbitrarily-accelerating trajectory, generalising the isotropic Lorentz-function profile introduced by Schlicht to include directional dependence; and (ii) a profile defined only for a Rindler trajectory, utilising the associated frame, and confined to a Rindler wedge, but …
The incorporation of classical general relativity into quantum field theory yields a surprising result -- thermodynamic particle production. One such phenomenon, known as the Unruh effect, causes empty space to effervesce a thermal bath of particles when viewed by an observer undergoing uniformly accelerated motion. These systems will have a Rindler horizon which produces this Unruh radiation at the Fulling-Davies-Unruh temperature. For accelerated charges, the emission and absorption of this radiation will imprint the FDU temperature on photons emitted in the laboratory. Each of these photons…
We study the radiative process of two entangled two-level atoms uniformly accelerated in a thermal bath, coupled to a massless scalar field. First, using the positive frequency Wightman function from the Minkowski modes with a Rindler transformation we provide the transition probabilities for the transitions from maximally entangled symmetric and anti-symmetric Bell states to the collective excited state in $(1+1)$ and $(1+3)$ dimensions. We observe a possible case of \emph{anti-Unruh-like} event in these transition probabilities, though the $(1+1)$ and $(1+3)$ dimensional results are not comp…
We investigate the relation between the time-ordered vacuum correlation functions for interacting real scalar fields in Minkowski spacetime and in the Rindler wedge. The correlation functions are constructed perturbatively within the in-in formalism, often employed in calculations in more general spacetimes. We prove to all orders in perturbation theory that the time-ordered vacuum correlation functions can be calculated in the in-in formalism with internal vertices restricted to any Rindler wedge containing the external points. This implies that the Minkowski in-in (or in-out) perturbative ex…
We studied the change of the nonlocal correlation of the entanglement in Rindler spacetime by showing that the Unruh effect can be interpreted as a noisy quantum channel having a complete positive and trace preserving map with an operator sum representation. It is shown that the entanglement fidelity is obtained in analytic form from the operator sum representation, which agrees well numerically with the entanglement monotone and the entanglement measure obtained previously. Non-zero entropy exchange between the system Q and the region II of the Rindler wedge indicates the nonlocal correlation…
University of York（约克大学）；Universidade Estadual Paulista（圣保罗州立大学）；Universidade de São Paulo（圣保罗大学）；Austrian Academy of Sciences（奥地利科学院）；Rutherford Appleton Laboratory（鲁瑟福阿普尔顿实验室）；University of Strathclyde（思克莱德大学）；Universidade Federal do Pará（帕拉联邦大学）；University of Oxford（牛津大学）
We investigate the fate of initial entanglement between two accelerated detectors with respect to an observer attached to one of the detectors. Both $(1+1)$ and $(1+3)$ spacetime dimensions are being considered here, with the detectors interacting with real massless scalar fields through monopole terms. The investigation is being performed for both non-thermal as well as thermal fields. In general, irrespective of the detectors moving in the same Rindler wedge or opposite wedges, increase of the field temperature reduces the initial entanglement. In all situations, degradation of entanglement …
We introduce a method to compute particle detector transition probability in spacetime regions of general curved spacetimes provided that the curvature is not above a maximum threshold. In particular we use this method to compare the response of two detectors, one in a spherically symmetric gravitational field and the other one in Rindler spacetime to compare the Unruh and Hawking effects: We study the vacuum response of a detector freely falling through a stationary cavity in a Schwarzschild background as compared with the response of an equivalently accelerated detector traveling through an …
The possibility of chiral symmetry restoration by acceleration is considered. The Thermalization Theorem formalism and the large $N$ limit (with $N$ being the number of pions) are employed to solve the lowest-order approximation to QCD at low energies in Rindler spacetime. It is shown that chiral symmetry is restored for accelerations higher than the critical value $a_c=4πf_π$, with $f_π$ being the pion decay constant. The results are completely analogous to those obtained in the inertial, finite-temperature case, evincing the ontic character of the Unruh effect.
