Unruh Temperature Research Articles

Full inverse Compton Scattering: Total transfer of energy and momentum from electrons to photons

In this article we discuss a peculiar regime of Compton Scattering that assures the maximum transfer of energy and momentum from free electrons propagating in vacuum to the scattered photons. We name this regime Full Inverse Compton Scattering (FICS) because it is characterized by the maximum and full energy loss of the electrons in collision with photons: up to 100% of the electron kinetic energy is indeed transferred to the photon. In the case of relativistic electrons, characterized by a large Lorentz factor (γ≫1), FICS regime corresponds to an incident photon energy equal to mec22, i.e. approximately 255.5 keV. We interpret such an astonishing result as FICS being the time reversal of direct Compton Scattering of very energetic photons (of energy much greater than mec2) onto atomic electrons. Although the cross section of Compton scattering is decreasing with the energy of the incident photon, making the process less probable with respect to other reactions (pair production, nuclear reactions, etc.) when high energetic photons are bombarding a target, the kinematics straightforwardly implies that the back-scattered photons would have an energy reaching asymptotically mec22. FICS is instead the unique suitable working point in Compton scattering for achieving the total transfer of (kinetic) energy exactly from the electron to the photon. Experiencing transitions from the initial momentum to zero in the laboratory system, in FICS the electron is also subject to very large negative acceleration; this fact can lead to possible experiments of sensing the Unruh temperature and related photon bath. On the other side of the energy dynamic range, low relativistic electrons can be completely stopped by moderate energy photons (tens of keV), leading to full exchange of temperature between electron clouds and photon baths. Cosmic gamma ray sources can be affected in their evolution by this peculiar FICS regime of Compton scattering.

Distribution of distance-based quantum resources outside a radiating Schwarzschild black hole

Abstract This study aims to investigate the distribution of distance-based quantum resources for fermionic fields in curved Schwarzschild spacetime (SST), as well as for bosonic fields in both flat Minkowski and curved SSTs. To achieve this, we will examine the quantum resources between an observer falling into a Schwarzschild black hole (SBH) and their stationary partner, who shares a Gisin state. Additionally, we will explore the quantum resources that arise when two uniformly accelerated detectors interact with bosonic fields in the Minkowski vacuum. Furthermore, we will investigate the interactions between these detectors and bosonic fields in the Hartle–Hawking and Boulware vacuums outside the SBH. At an infinite Hawking temperature, the quantum resources for the fermionic fields degrade; the rate of degradation is dependent on the distance between the observer and the event horizon, the fermionic frequency mode, and the Gisin state parameters. In the case of the bosonic fields, our results show that entanglement decreases monotonically, either towards zero or a constant value. Moreover, with increasing Unruh temperature, coherence and discord undergo sudden death followed by a sudden birth, and entanglement cannot be revived for a given initial state. Based on our findings, it appears that the Fermi–Dirac and Bose–Einstein statistics represent the primary differences in quantum resource distribution between the fermionic and bosonic cases. These findings may be essential for enhancing our understanding of the distribution of quantum resources in relativistic frameworks.

Locating quark-antiquark string breaking in QCD through chiral symmetry restoration and Hawking-Unruh effect

The relationship between QCD and the string model offers a valuable perspective for exploring the interaction potential between quarks. In this study, we investigate the restoration of chiral symmetry in connection with the Unruh effect experienced by accelerating observers. Utilizing the Schwinger model, we analyze the critical point at which the string or chromoelectric flux tube between quark-antiquarks breaks with increasing separation between quarks. In this study, the critical distance for quark-antiquark chromoelectric flux tube or string breaking is determined to be rc=1.294±0.040 fm. The acceleration and Unruh temperature corresponding to this critical point signify the transition of the system's chiral symmetry from a broken to a restored state. Our estimates for the critical acceleration (ac=1.14×1034 cm/s2) and Unruh temperature (Tc=0.038 GeV) align with previous studies. This analysis illuminates the interplay between chiral symmetry restoration, the Unruh effect, and the breaking of the string or chromoelectric flux tube within the context of quark interactions.

Effective photon mass in the presence of a gravity gradient emulated by an electromagnetic medium

Geometry- and gravity-induced effective photon mass is known to arise in many cases, such as various optical waveguides, Kaluza–Klein theories, and many other optical and general relativity situations. Here we study the appearance of effective photon mass in the Newtonian limit due to the presence of a gravity gradient emulated by an electromagnetic medium. The effective photon mass squared appears to be proportional to the local gravity gradient, and it becomes negative in an optical anti-waveguide around the unstable equilibrium location. A similar effect is observed in the emulated Kottler–Møller spacetime where the absolute value of the gravity-induced effective photon mass appears to coincide with the Unruh temperature. We demonstrate that similar to the Unruh effect, a bath of thermal radiation should be observed in an optical anti-waveguide near the unstable equilibrium, whose temperature is defined by the emulated local gravity gradient, and which remains unchanged in the c→∞ limit.

Maximal acceleration in Rainbow gravity

In this paper, we derive maximal acceleration of a massive particle in Rainbow gravity. Using eight-dimensional phase-space metric compatible with Rainbow gravity, we obtain the maximal acceleration, valid up to first order in the Rainbow gravity parameter η. Using the positivity condition on maximal acceleration, we find that the upper bound on the Rainbow gravity parameter is of the order of for positron and for a black hole. After obtaining the expression for maximal acceleration for different choices of Rainbow functions, we derive corresponding modifications to Unruh temperature. Comparing with the observational value of the Unruh temperature, we find the upper bound on η as for positron radiation. We then derive geodesic equations for different choices of Rainbow functions and also obtain the Newtonian limit of these geodesic equations. We find that the changes in the value of maximum acceleration, maximum temperature and Newtonian force equation are dependent on the choices of Rainbow functions.

Unruh effect using Doppler shift method in DSR framework

We study the Unruh effect in doubly special relativity (DSR) framework by generalising the Doppler-shift method to DSR. For both the scalar and Dirac particles, we observe a deviation in the power spectrum of Unruh radiation from the standard Bose–Einstein and Fermi–Dirac distributions, respectively, due to the presence of the frame independent length scale of DSR. We further show that this deviation results in the modification of Unruh temperature which then depends non-linearly on the proper acceleration in DSR.

$$\kappa $$-deformed power spectrum and modified Unruh temperature

$$\kappa $$-deformed power spectrum and modified Unruh temperature

Parameter estimation in n-dimensional massless scalar field

Quantum Fisher information (QFI) associated with local metrology has been used to parameter estimation in open quantum systems. In this work, we calculated the QFI for a moving Unruh–DeWitt detector coupled with massless scalar fields in n-dimensional spacetime, and analyzed the behavior of QFI with various parameters, such as the dimension of spacetime, evolution time, and Unruh temperature. We discovered that the QFI of state parameter decreases monotonically from 1 to 0 over time. Additionally, we noted that the QFI for small evolution times is several orders of magnitude higher than the QFI for long evolution times. We also found that the value of QFI decreases at first and then stabilizes as the Unruh temperature increases. It was observed that the QFI depends on initial state parameter θ, and Fθ is the maximum for θ = 0 or θ = π, Fϕ is the maximum for θ = π/2. We also obtain that the maximum value of QFI for state parameters varies for different spacetime dimensions with the same evolution time.

Relativistic path integrals

Classical and Quantum mechanics are the two milestones of physics and mathematics. The path integral describes the generalised form of action from classical to quantum mechanics. This paper has reviewed some fundamental concepts and results in classical dynamics and quantum mechanics. The research method of the whole project is mainly theoretical derivations of applied mathematics and mathematical physics. This paper provides different perspectives to investigate the applications of path integrals. This paper also builds a connection between path integrals and the Unruh temperature.

GEMS Embeddings of Hayward Regular Black Holes in Massless and Massive Gravities

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call ‘massless’. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher-dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity.

Using nanokelvin quantum thermometry to detect timelike Unruh effect in a Bose–Einstein condensate

It is found that the Unruh effect can not only arise out of the entanglement between two sets of modes spanning the left and right Rindler wedges, but also between modes spanning the future and past light cones. Furthermore, an inertial Unruh–DeWitt detector along a spacetime trajectory in one of these cones may exhibit the same thermal response to the vacuum as that of an accelerated detector confined in the Rindler wedge. This feature thus could be an alternative candidate to verify the “Unruh effect”, termed as the timelike Unruh effect correspondingly. In this paper we propose to detect the timelike Unruh effect by using an impurity immersed in a Bose–Einstein condensate (BEC). The impurity acts as the detector which interacts with the density fluctuations in the condensate, working as an effective quantum field. Following the paradigm of the emerging field of quantum thermometry, we combine quantum parameter estimation theory with the theory of open quantum systems to realize a nondemolition Unruh temperature measurement in the nanokelvin (nK\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{nK}$$\\end{document}) regime. Our results demonstrate that the timelike Unruh effect can be probed using a stationary two-level impurity with time-dependent energy gap immersed in a BEC within current technologies.

Entropy disorder and quantum correlations in two Unruh-deWitt detectors uniformly accelerating and interacting with a massless scalar field

This investigation focuses on studying the dynamics of entropy disorder and quantum correlations between two detectors interacting with a scalar field in a four-dimensional Minkowski space-time using the Unruh-deWitt model. The aim is to gain insights into the evolution of quantum resources in uniformly accelerated detectors that interact with a massless scalar field. To achieve this, useful metrics such as local quantum Fisher information (LQFI), quantum consonance, and linear entropy are employed to analyze the quantum correlations and entropy disorder. The results indicate that the quantum correlations are heavily reliant on the choice of the initial state of the detectors. Interestingly, the quantum correlations exhibit a surprising resurgence as the Unruh temperature increases for specific initial state parameters. However, for other values, the Unruh temperature takes over and leads to a monotonic decrease in the quantum correlations. In addition, the degree of disorder is observed to increase as the Unruh temperature increases. Furthermore, the investigation delves into how the energy spacing of the detector affects quantum correlations across various initial state parameters. Further elucidating the behavior of quantum resources in curved space-time, we demonstrate that some initial state parameters can cause sudden changes in correlation measures as a function of energy spacing. These results highlight the relevance of choosing adequate initial state parameters, as they have a significant impact on the variation of quantum resources in two Unruh-deWitt detectors.

Understanding thermal nature of de Sitter spacetime via inter-detector interaction

We investigate the interaction potential of two static detectors (atoms) at the same radial but different azimuthal coordinates in the de Sitter invariant vacuum. We show that for two detectors very far away from the cosmological horizon, the interaction potential is different from that of two static ones in a thermal bath in Minkowski spacetime at a temperature equal to the Gibbons-Hawking temperature, suggesting that de Sitter spacetime in regard to its thermal nature basically differs from a thermal bath in Minkowski spacetime. For two detectors very close to the cosmological horizon, the interaction potential behaves as ∼[TUρ4ln⁡(4TUρ)]−1 with TU and ρ the Unruh temperature associated with the proper acceleration and the proper separation of the detectors, which deviates dramatically from ∼(TUρ4)−1, the behavior of the interaction potential of two synchronously uniformly accelerated detectors in Minkowski spacetime, indicating that thermal nature of de Sitter spacetime also differs essentially from the Unruh thermal bath.

The universality of black hole thermodynamics

The thermodynamic properties of black holes — temperature, entropy and radiation rates — are usually associated with the presence of a horizon. We argue that any extremely compact object (ECO) must have the same thermodynamic properties. Quantum fields just outside the surface of an ECO have a large negative Casimir energy similar to the Boulware vacuum of black holes. If the thermal radiation emanating from the ECO does not fill the near-surface region at the local Unruh temperature, then we find that no solution of gravity equations is possible. In string theory, black holes microstates are horizonless quantum objects called fuzzballs that are expected to have a surface [Formula: see text] outside [Formula: see text]; thus the information puzzle is resolved while preserving the semiclassical thermodynamics of black holes.

Kappa vacua: enhancing the Unruh temperature

We provide further elaboration on kappa mode, which is a mode constructed by the linear combination of Rindler modes in the right and the left Rindler wedges, exhibiting norms with opposite signs. We establish a relation among different kappa vacua, resembling the thermofield double state. However, the energy of a kappa photon no longer exhibits a linear dependence on its frequency, unless the limit of κ → 0 (the Rindler vacuum) is taken into account. In other words, a kappa vacuum can be expressed in terms of the Rindler vacuum as the conventional thermofield double state, with the usual energy for a photon. However, it features a modified Unruh temperature given by {T}_{kappa }=frac{mathit{hslash a}}{2pi c{k}_B}kappa . Consequently, when a uniformly accelerated observer with an acceleration a is immersed in a κ-vacuum, they perceive a thermal bath. However, the temperature experienced by the observer is a modified Unruh temperature denoted as Tκ. Remarkably, the Unruh temperature can be enhanced by an arbitrary factor of κ.

Unruh effect and Takagi's statistics inversion in strained graphene

We present a theoretical study of how a spatially varying quasiparticle velocity in honeycomb lattices, achievable using strained graphene or in engineered cold-atom optical lattices that have a spatial dependence to the local tunneling amplitude, can yield the Rindler Hamiltonian embodying an observer accelerating in Minkowski space-time. Within this setup, a sudden switch on of the spatially varying tunneling (or strain) yields a spontaneous production of electron-hole pairs, an analog version of the Unruh effect characterized by the Unruh temperature. We discuss how this thermal behavior, along with Takagi's statistics inversion, can manifest themselves in photoemission and scanning tunneling microscopy experiments. We also calculate the average electronic conductivity and find that it grows linearly with frequency $\ensuremath{\omega}$. Finally, we find that the total system energy at zero environment temperature looks like Planck's blackbody result for photons due to the aforementioned statistics inversion, whereas for an initial thermally excited state of fermions, the total internal energy undergoes stimulated particle reduction.

Remarks on the Bell-Clauser-Horne-Shimony-Holt inequality

We discuss the relationship between the Bogoliubov transformations, squeezed states, entanglement, and maximum violation of the Bell-Clauser-Horne-Shimony-Holt (Bell-CHSH) inequality. In particular, we point out that the construction of the four bounded operators entering the Bell-CHSH inequality can be worked out in a simple and general way, covering a large variety of models, ranging from quantum mechanism to relativistic quantum field theories. Various examples are employed to illustrate the above mentioned framework. We start by considering a pair of entangled spin-one particles and a squeezed oscillator in quantum mechanics, moving then to the relativistic complex quantum scalar field and to the analysis of the vacuum state in Minkowski space-time in terms of the left and right Rindler modes. In the latter case, the Bell-CHSH inequality turns out to be parametrized by the Unruh temperature.

Entanglement harvesting of accelerated detectors versus static ones in a thermal bath

We make a detailed comparison between entanglement harvesting for uniformly accelerated detectors in vacuum and static ones in a thermal bath at the Unruh temperature and find that, for a small energy gap relative to the Heisenberg energy of the detectors, static detectors in the thermal bath can harvest more entanglement and possess a comparatively larger harvesting-achievable range than the uniformly accelerated ones; however, as the energy gap grows sufficiently large, the uniformly accelerated detectors are instead likely to harvest more entanglement and possess a relatively larger harvesting-achievable range than inertial ones in the thermal bath. In comparison with static detectors in vacuum, there exist phenomena of acceleration-assisted entanglement harvesting but never that of thermal-noise-assisted one. A notably interesting feature is that, although both the amount of entanglement harvested and the harvesting-achievable interdetector separation for static detectors in a thermal bath are always a decreasing function of temperature, they are not always so for uniformly accelerated detectors as acceleration (Unruh temperature) varies, suggesting the existence of the anti-Unruh effect in the entanglement harvesting phenomena of the accelerated detectors.

Using Unruh temperature and generalized chemical potential as alternative pathway to determine the Hubble parameter

Hubble constant is found relating velocities and distances of galaxies. Actually Cepheid stars and cosmic background radiation present two distinct values for the Hubble constant. Theoretically such a Hubble parameter naturally emerges from the scale factor variations considered in cosmological models. On the other hand Unruh effect relates temperature to accelerated observers. Such a relation plots a search for physical constraints aiming to justify the referred effect. Here we establish a relation between the Unruh temperature and that one from ensemble fugacity, which can be obtained from an generalized chemical potential. Then, we find a dependence on the quantities involved in the generalized chemical potential for the cosmological constant. Finally, we determine a new relation for the Hubble parameter.

Thermalization by a synthetic horizon

Synthetic horizons in models for quantum matter provide an alternative route to explore fundamental questions of modern gravitational theory. Here, we apply these concepts to the problem of emergence of thermal quantum states in the presence of a horizon, by studying ground-state thermalization due to instantaneous horizon creation in a gravitational setting and its condensed matter analogue. By a sudden quench to position-dependent hopping amplitudes in a one-dimensional lattice model, we establish the emergence of a thermal state accompanying the formation of a synthetic horizon. The resulting temperature for long chains is shown to be identical to the corresponding Unruh temperature, provided that the post-quench Hamiltonian matches the entanglement Hamiltonian of the pre-quench system. Based on detailed analysis of the outgoing radiation we formulate the conditions required for the synthetic horizon to behave as a purely thermal source, paving a way to explore this interplay of quantum-mechanical and gravitational aspects experimentally.