A Tunable Unruh Effect: Accelerated Detectors in Kappa-Rindler Vacua

Arash Azizi

REVIEW 3 major objections 4 minor 1 cited by

A Tunable Unruh Effect: Accelerated Detectors in Kappa-Rindler Vacua

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read An accelerated Unruh-DeWitt detector in a $\kappa$-Rindler vacuum sees a perfectly thermal bath at temperature $T_\kappa=\kappa T_U$, so the perceived vacuum temperature can be dialed hotter or colder than the standard Unruh value.

desk verdict A self-contained detector derivation of a temperature formula already present in the author's prior paper; the KMS proof is valid but weak, and the stress-test objection misses that the Rindler trajectory has zero commutator in 1+1. read the letter →

arxiv 2507.00174 v3 pith:QFF5LTHT submitted 2025-06-30 hep-th

Arash Azizi This is my paper · ORCID

classification hep-th

keywords UnruheffectUnruh-DeWittdetectorkappa-RindlervacuumKMSconditionWightmanfunctionBogoliubovtransformationthermalacceleratedobserver

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper studies a uniformly accelerated Unruh-DeWitt detector coupled to a massless scalar field in a one-parameter family of $\kappa$-Rindler vacua, which interpolate between the Rindler vacuum and the Minkowski vacuum. Its central claim is that the detector's response is exactly thermal at the temperature $T_\kappa = \kappa T_U$, where $T_U = a/2\pi$ is the usual Unruh temperature and $\kappa$ is the vacuum parameter. If correct, the perceived temperature of the vacuum becomes continuously tunable: $\kappa>1$ gives an environment hotter than the standard Unruh bath and $\kappa<1$ gives a colder one. The paper verifies thermality from two independent directions, the Planck factor in the excitation rate and the KMS condition on the Wightman function, so the result is a perfect Planck spectrum rather than an approximation.

What carries the argument

The central object is the family of $\kappa$-vacua, defined by Rindler boost-mode expansions with frequencies rescaled by $\kappa$ and annihilation conditions $\hat{B}_{\Omega,\kappa}|0_\kappa\rangle=0$; the mode normalization carries $\sinh(\pi|\Omega|/\kappa)$. The load-bearing identity is the mapping $W_{\kappa,\mathrm{RTW}}(u,u')=W_{1,\mathrm{RTW}}((-u)^\kappa,(-u')^\kappa)$, which on an accelerated trajectory is equivalent to replacing the acceleration $a$ by $a\kappa$ in the standard Minkowski-vacuum Wightman function (4.9)-(4.12). This substitution turns $\sinh(a\Delta\tau/2)$ into $\sinh(a\kappa\Delta\tau/2)$, shifting the KMS period from $2\pi/a$ to $2\pi/(a\kappa)$ and thereby fixing the perceived temperature as $T_\kappa=\kappa T_U$.

What would settle it

Numerically evaluate the mode-sum completeness relation for the $\kappa$-Rindler modes over the full range of $\Omega$ on a fixed null slice; if the sum does not converge to a delta function for some $\kappa>0$, that vacuum is not well-defined and the KMS derivation of $T_\kappa=\kappa T_U$ fails.

Watch

Extended reading notes

Core claim

For a detector with energy gap $\omega$ moving with proper acceleration $a$ through a $\kappa$-Rindler vacuum, the transition rate contains the exact Planck factor $1/(e^{\omega/T_\kappa}-1)$ with $T_\kappa=\kappa a/2\pi$, and the vacuum Wightman function along the worldline, $W_\kappa(\Delta\tau)=-\frac{1}{4\pi}\ln[\frac{\mu^2 4}{a^2\kappa^2}\sinh^2(\frac{a\kappa}{2}(\Delta\tau-i\epsilon))]$, satisfies the KMS condition at inverse temperature $\beta_\kappa=2\pi/(a\kappa)$. The $\kappa$-vacua therefore form a continuous family of thermal vacua: $\kappa=1$ reproduces the Minkowski vacuum and the standard Unruh temperature, $\kappa\to0$ approaches the Rindler vacuum with detector temperature tending to zero, and every intermediate $\kappa$ gives a distinct boost-stationary state perceived as a perfect thermal bath.

Load-bearing premise

The load-bearing premise is that the $\kappa$-Rindler modes form a complete orthonormal basis in each chiral sector, so the state defined by annihilating them is a legitimate vacuum whose two-point function is (4.14); the paper does not prove this completeness, nor the Hadamard admissibility of the states.

Editorial extensions

If this is right

The standard Unruh effect is the $\kappa=1$ member of a continuous family, so an accelerated detector can register any temperature $T_\kappa=\kappa a/2\pi$ by changing the vacuum rather than the acceleration.
The Bogoliubov transformation (3.1) gives the relative particle content between any two $\kappa$-vacua, providing a controlled measure of mode mixing and squeezing across the family.
The kappa photon created when the detector clicks is non-local, with its amplitude across the horizon suppressed by $e^{-2\pi\omega/\kappa a}$, so hotter vacua correspond to more symmetric modes and colder vacua to modes confined to the detector's wedge.
Because the KMS condition holds exactly, the detector's response is exactly Planckian, not merely approximately thermal, for every $\kappa>0$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural check left implicit in the paper is whether the $\kappa$-vacua satisfy the Hadamard condition; if they do not, the formal KMS thermality may not make them physically admissible states, even though the derivation is internally consistent.
The simple substitution rule $a\to a\kappa$ suggests that analogue-gravity or accelerated-detector experiments that realize an effective Unruh temperature could, in principle, realize the $\kappa$-scaled temperatures by preparing the field in the corresponding $\kappa$-mode state.
The relative particle spectrum (3.5) depends on $1/\kappa-1/\kappa'$, so comparing two $\kappa$-vacua may reveal a two-temperature structure rather than a single shifted temperature; this is an extension the paper does not explore.
The paper treats only the boost-stationary $\kappa$-Rindler family; checking the translation-invariant $\kappa$-plane-wave vacua would show whether the scaling $T_\kappa=\kappa T_U$ survives in that family or is specific to Rindler modes.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Dear colleague,

Quick take: the central formula T_κ = κT_U is already in the author's earlier paper [23]; what's new here is a self-contained UDW detector derivation, a Bogoliubov analysis, a Wightman-function treatment, and figures. The derivation in Sec. 2 is standard and yields the Planck factor cleanly. The KMS check in Sec. 4 is valid but weaker than it looks; I'd advise not leaning on it as the main evidence of thermality.

The stress-test note's complaint doesn't hold up. In 1+1 massless scalar, two points on a uniformly accelerated worldline are spacelike separated, so the field commutator vanishes and the Wightman function should be real and even. Eq. (4.14) is correct in that respect; a sgn(Δτ) term would actually be wrong. The KMS condition then reduces to periodicity in imaginary time, which the sinh² form satisfies. So the proof is fine, just not deep.

What the paper does well: it is explicit, self-contained, and honest about using [23] for the mode basis and mapping. The Bogoliubov transformation and the Rindler limit check out. The figures are illustrative rather than load-bearing, but they make the κ-dial story easy to grasp.

Soft spots, in proportion: - Novelty is modest. The temperature scaling is established in [23]; this paper adds the detector response and KMS verification, which are routine. - The κ→0 limit is waved at with 'IR care' and no precise statement. A competent referee should ask for a rigorous statement. - The state's global definition is assumed: no proof of mode completeness or Hadamard condition for the κ-vacua. These are standard gaps for such constructions and may be fillable, but they're the right questions to ask. - The KMS proof, while valid, is a weak form of thermality because W is even; the response calculation does the real work.

Who it's for: people working on Unruh-DeWitt detectors, relativistic quantum information, or analogue gravity who might use a tunable temperature as a tool. It doesn't resolve a major problem, but it's a clean, useful extension.

Recommendation: send to peer review. It's not a desk reject; a referee can handle the questions above. I would not highlight the stress-test concern in the referee report.

Referee Report

3 major / 4 minor

Summary. The paper studies a one-parameter family of 'κ-Rindler vacua' for a massless scalar field in 1+1 dimensions, defined by the annihilation operators of the mode expansion (2.1)-(2.2). The main claim is that an accelerated Unruh-DeWitt detector coupled to such a vacuum responds as if immersed in a thermal bath at temperature Tκ = κa/(2π). The author supports this by a first-order perturbation calculation of the excitation amplitude (Section 2.3), a Bogoliubov analysis (Section 3), a Wightman-function computation with a KMS verification (Section 4), and mode-structure visualizations (Section 5). The κ=1 case is identified with the Minkowski vacuum and the κ→0 limit with the Rindler vacuum, so the family is presented as continuously interpolating between these limits.

Significance. If the central claim holds, the paper offers a clean tunable generalization of the Unruh effect: one parameter continuously changes the perceived temperature between the Rindler and Minkowski limits and beyond, with potential applications in relativistic quantum information and analog models. The explicit mapping Wκ = W1∘(-u)^κ and the closed-form Bogoliubov coefficients are elegant, and the Section 2.3 excitation-amplitude computation is a genuine derivation of the Planck factor. However, the formal KMS proof in Section 4 is not valid as written, and the global/Hadamard status of the κ-vacua is not established. Both issues are local and fixable, but they are load-bearing for the paper's advertised 'rigorous' thermality claim.

major comments (3)

[§4.1–4.2, Eqs. (4.14), (4.16)–(4.20)] The total Wightman function in Eq. (4.14) is missing the finite imaginary part. For a massless scalar in 1+1 along the timelike Rindler trajectory the correct boundary value is W(Δτ) = -(1/(4π)) ln[ -(4/(a^2κ^2)) sinh^2((aκ/2)(Δτ-iϵ)) ], which for real Δτ≠0 gives W(Δτ) = real part - (i/4)sgn(Δτ). The expression in (4.14) uses +sinh^2, making W real and even in Δτ. Consequently the 'KMS verification' reduces to Wκ(τ-iϵ)=Wκ(τ+iϵ), a trivial statement for any real even analytic function; it does not enforce the asymmetric Planck spectrum. Additionally, the KMS relation is misstated in Eq. (4.15): the correct relation is W^>(τ-iβκ)=W^<(-τ), equivalently W^>(τ-iβκ)=W^>(τ), not W^>(τ-iβκ)=W^<(τ). With the corrected branch phase and the corrected KMS statement, the periodicity sinh(z-iπ)=-sinh z does provide a genuine KMS check; with (4.14) it does not. This error is load-bearing for the paper's KMS-based thermality claim, although it is fixable and does not invalidate the Section 2 response calculation.
[§2.2 and §4.1, Eqs. (2.1)–(2.2), (4.5)] The paper claims to be self-contained, but the completeness and orthonormality of the κ-mode basis, and hence the global definition of |0κ⟩ and the derivation of Eq. (4.5), are not proved here; the text defers to Ref. [23]. Since the Wightman function (4.14) and the detector response both assume that the modes in (2.1)–(2.2) form a complete basis with the stated normalization, the derivation is conditional on external results. Please state precisely which theorem or proposition from [23] supplies the mode basis and normalization, or include a proof sketch. It would also be useful to state whether the κ-vacua are Hadamard for all κ>0, since this is the usual admissibility criterion for vacua used in detector-response calculations.
[§2.2, §3.1, and §5.1, κ→0 limit] The claims that κ→0 gives the Rindler vacuum with vanishing temperature are not substantiated. The normalization N_{Ω,κ} = 8π|Ω|sinh(π|Ω|/κ) diverges in this limit, and the Wightman expression (4.14) contains aκ in the denominator, so the limit is singular. The text says only that the limit 'requires the usual IR care' and that logarithms and branch choices must be treated first. Because the interpolation between Rindler and Minkowski vacua is part of the paper's advertised framework, specify a concrete regularization (e.g., an IR cutoff before sending κ→0) and show that the regularized detector transition rate indeed tends to zero.

minor comments (4)

[§2.3, Eqs. (2.8)–(2.9)] The squared amplitude computed above Eq. (2.9) contains an overall factor of ω, but the rate in Eq. (2.9) is written as R ∝ 1/(e^{ω/Tκ}-1). For a derivative-coupled detector the rate normally carries an additional factor of |ω|; please specify whether R is the rate per unit bandwidth and give the precise prefactor, or state that only the detailed-balance ratio is being reported.
[§4.2, Eq. (4.15)] The notation for W^< is used inconsistently: if W^<(τ)=⟨Φ(0)Φ(τ)⟩, then stationarity gives W^<(τ)=Wκ(-τ+iϵ), not Wκ(τ+iϵ). The text should define the ordered functions in terms of Wκ with explicit arguments to avoid this ambiguity.
[§5, Figures 2–4] The captions and text describe Figures 2–4 as showing the mode structure, but the figures are not reproduced in the manuscript text made available to the referee. Ensure all figures are present and that the panels, axes, and color conventions are legible in the final version.
[§5.2] The statement that the ratio of the mode amplitude in u>0 to that in u<0 is proportional to e^{-2πω/κa} is used to explain the visual trend but no derivation or equation number is given; a brief derivation from the mode function in Eq. (2.1) would make the discussion self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: T_kappa = kappa T_U is computed from the explicitly defined kappa-vacuum state, not fitted or imported from a self-citation.

full rationale

The paper defines the kappa-vacuum by the explicit mode expansions (2.1)-(2.2) and the annihilation conditions B_Omega,kappa |0_kappa> = 0. The detector excitation rate is then computed in first-order perturbation theory: the delta function (2.7) fixes Omega = -omega/a, and the modulus-squared amplitude contains the Planck factor 1/(exp(2 pi omega/(kappa a)) - 1), from which T_kappa = kappa a/(2 pi) is read off (Eqs. (2.8)-(2.10)). This is a derivation from the state definition, not a fitted input renamed as a prediction. Likewise, the Wightman-function route derives Eq. (4.14) from the mode expansion; the mapping identity (4.7) and the substitution a -> a kappa follow from the definition of the kappa-modes, so the KMS check at beta_kappa = 2 pi/(a kappa) tests the constructed state rather than assuming the answer. The citation to the author's earlier work [23] is explicitly non-load-bearing: the text states that the present paper relies only on Eqs. (2.1)-(2.2), (4.7), (4.14), and the Bogoliubov analysis in Sec. 3, all of which are reproduced in the manuscript. The unproved completeness of the mode basis and the absence of a Hadamard check are genuine support gaps, and the Sec. 4.2 KMS verification is open to the objection that Eq. (4.14) is real on the real axis so that (4.20) is a trivial analyticity statement; however, these are correctness or rigor concerns, not circularity. No circular step can be exhibited.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The only continuous parameter is κ, which labels the vacuum state rather than being fitted to data. The IR scale μ is a regulator, not a physical free parameter. The main extracted input from prior literature is the mode basis itself, inherited from the author's earlier papers, and the standard UDW formalism. No new particles or forces are introduced.

assumptions (4)

domain assumption The chiral mode functions in (2.1)-(2.2) form a complete orthonormal basis of solutions to the massless Klein-Gordon equation in 1+1 dimensions for every κ, so the annihilation conditions define a unique Fock vacuum.
The paper states in Sec. 2.2 that specifying the annihilation conditions fixes the state, but does not prove completeness or orthonormality of the mode set. The Wightman function derivation and detector rate depend on this mode decomposition being exact.
domain assumption The detector response at first order in perturbation theory with the derivative coupling (2.3) captures the perceived temperature of the vacuum.
Standard UDW detector theory, cited to [28,29], is invoked without derivation. The identification of the Planck factor with temperature assumes the response rate is the correct operational thermometer.
domain assumption The KMS condition at inverse temperature β_κ = 2π/(aκ) is a sufficient criterion for the detector to perceive a thermal bath at T_κ = κa/(2π).
The paper verifies KMS along the trajectory and reads off the temperature. This is standard QFT thermal-state characterisation, but the paper does not discuss the subtlety that in 1+1 the commutator vanishes on the Rindler trajectory, which is why W^> = W^<.
ad hoc to paper The κ→0 limit gives a well-defined Rindler vacuum with vanishing temperature, with IR divergences handled by the usual regularization.
Sec. 2.2 and Sec. 5.1 state this limit 'requires IR care' but no explicit construction of the limiting state is given. The claim that T_κ→0 and excitations vanish is plausible but not rigorously demonstrated.

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Cite this review

Pith. "Pith review of A Tunable Unruh Effect: Accelerated Detectors in Kappa-Rindler Vacua." pith.science (2026). https://pith.science/paper/QFF5LTHT

@misc{pith2026250700174,
  author       = {Pith},
  title        = {Pith review of: A Tunable Unruh Effect: Accelerated Detectors in Kappa-Rindler Vacua},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QFF5LTHT}},
  note         = {Machine review of arXiv:2507.00174}
}

abstract

We study the response of an accelerated Unruh-DeWitt detector to a one-parameter family of ``kappa Rindler'' vacua, which generalize the standard Unruh effect. These states, parameterized by $\kappa$, continuously interpolate between the Rindler ($\kappa \to 0$) and Minkowski ($\kappa=1$) vacua. We find the detector registers a perfect thermal bath at a tunable temperature $T_\kappa = \kappa T_U$. This result establishes a framework for environments perceived as both ``hotter'' ($\kappa>1$) and ``colder'' ($\kappa<1$) than the standard Unruh temperature. We establish this thermality by demonstrating the KMS condition for the Wightman function and by analyzing the associated particle creation process. Furthermore, we visualize the spacetime structure of the created field quanta, revealing an intuitive link between the $\kappa$-controlled symmetry of the modes and the perceived temperature. Our work provides a comprehensive framework for a modulated Unruh effect, bridging formal QFT with clear visual intuition.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Modulated Accelerating Mirrors as a Physical Realization of the Kappa-Gamma Vacuum
hep-th 2025-09 conditional novelty 6.0 of 10

A modulated Carlitz-Willey mirror realizes the κγ vacuum on future null infinity: the trajectory sets the temperature, the boundary pump phase sets the squeeze angle.

Reference graph

Works this paper leans on

34 extracted references · 20 canonical work pages · cited by 1 Pith paper

[23]

Azizi,Kappa vacua: enhancing the Unruh temperature,JHEP07(2023) 064, [arXiv:2301.13672]

A. Azizi,Kappa vacua: enhancing the Unruh temperature,JHEP07(2023) 064, [arXiv:2301.13672]

arXiv 2023
[1]

W. G. Unruh,Notes on black-hole evaporation,Phys. Rev. D14(Aug, 1976) 870–892

1976
[2]

S. A. Fulling,Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time, Phys. Rev. D7(May, 1973) 2850–2862

1973
[3]

P. C. W. Davies,Scalar production in Schwarzschild and Rindler metrics,Journal of Physics A: Mathematical and General8(apr, 1975) 609

work page 1975
[4]

S. W. Hawking,Black hole explosions?,Nature248(1974), no. 5443 30–31. – 17 –

work page 1974
[5]

S. W. Hawking,Particle Creation by Black Holes,Commun. Math. Phys.43(1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]

1975
[6]

N. D. Birrell and P. C. W. Davies,Quantum Fields in Curved Space. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, UK, 1982

1982
[7]

R. M. Wald,Quantum Field Theory in Curved Space-Time and Black Hole Thermodynamics. Chicago Lectures in Physics. University of Chicago Press, Chicago, IL, 1994

1994

Show all 34 references

[8]

B. S. DeWitt,General Relativity: An Einstein Centenary Survey. Univ. Pr., Cambridge, UK, 1979

1979
[9]

Peres and D

A. Peres and D. R. Terno,Quantum information and relativity theory,Rev. Mod. Phys.76 (Jan, 2004) 93–123

2004
[10]

R. B. Mann and T. C. Ralph,Relativistic quantum information,Classical and Quantum Gravity 29(nov, 2012) 220301

2012
[11]

P. M. Alsing and I. Fuentes,Observer-dependent entanglement,Classical and Quantum Gravity 29(oct, 2012) 224001

2012
[12]

A. G. S. Landulfo and G. E. A. Matsas,Sudden death of entanglement and teleportation fidelity loss via the Unruh effect,Phys. Rev. A80(Sep, 2009) 032315

2009
[13]

Martín-Martínez and J

E. Martín-Martínez and J. León,Population bound effects on bosonic correlations in noninertial frames,Phys. Rev. A81(May, 2010) 052305

2010
[14]

Martín-Martínez and I

E. Martín-Martínez and I. Fuentes,Redistribution of particle and antiparticle entanglement in noninertial frames,Phys. Rev. A83(May, 2011) 052306

2011
[15]

D. E. Bruschi, A. Dragan, I. Fuentes, and J. Louko,Particle and antiparticle bosonic entanglement in noninertial frames,Phys. Rev. D86(Jul, 2012) 025026

2012
[16]

Su and T

D. Su and T. C. Ralph,Quantum communication in the presence of a horizon,Phys. Rev. D90 (Oct, 2014) 084022

2014
[17]

T. G. Downes, T. C. Ralph, and N. Walk,Quantum communication with an accelerated partner, Phys. Rev. A87(Jan, 2013) 012327

2013
[18]

Foo and T

J. Foo and T. C. Ralph,Continuous-variable quantum teleportation with vacuum-entangled Rindler modes,Phys. Rev. D101(Apr, 2020) 085006

2020
[19]

Tjoa,Quantum teleportation with relativistic communication from first principles,Phys

E. Tjoa,Quantum teleportation with relativistic communication from first principles,Phys. Rev. A106(Sep, 2022) 032432

2022
[20]

R. H. Jonsson, E. Martín-Martínez, and A. Kempf,Information Transmission Without Energy Exchange,Phys. Rev. Lett.114(Mar, 2015) 110505

2015
[21]

Polo-Gómez, L

J. Polo-Gómez, L. J. Garay, and E. Martín-Martínez,A detector-based measurement theory for quantum field theory,Phys. Rev. D105(Mar, 2022) 065003

2022
[22]

Azizi,Kappa vacua: Infinite number of new vacua in two-dimensional quantum field theory, arXiv:2212.03781

A. Azizi,Kappa vacua: Infinite number of new vacua in two-dimensional quantum field theory, arXiv:2212.03781

arXiv
[24]

Azizi,Kappa plane wave modes and continuous squeezing in quantum field theory,Phys

A. Azizi,Kappa plane wave modes and continuous squeezing in quantum field theory,Phys. Rev. – 18 – D112(Jul, 2025) 025018

2025
[25]

Azizi,Phase-Induced Particle Creation in the Kappa-Gamma Vacuum,arXiv:2507.05299

A. Azizi,Phase-Induced Particle Creation in the Kappa-Gamma Vacuum,arXiv:2507.05299
[26]

Kubo,Statistical-Mechanical Theory of Irreversible Processes

R. Kubo,Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems,Journal of the Physical Society of Japan 12(1957), no. 6 570–586

1957
[27]

P. C. Martin and J. Schwinger,Theory of Many-Particle Systems. I,Phys. Rev.115(Sep,
[28]

W. G. Unruh and R. M. Wald,What happens when an accelerating observer detects a Rindler particle,Phys. Rev. D29(Mar, 1984) 1047–1056

1984
[29]

Louko and A

J. Louko and A. Satz,Transition rate of the Unruh-DeWitt detector in curved spacetime,Class. Quant. Grav.25(2008) 055012, [arXiv:0710.5671]

2008 arXiv
[30]

Svidzinsky, A

A. Svidzinsky, A. Azizi, J. S. Ben-Benjamin, M. O. Scully, and W. Unruh,Unruh and Cherenkov Radiation from a Negative Frequency Perspective,Phys. Rev. Lett.126(2021), no. 6 063603

2021
[31]

Doukas and L

J. Doukas and L. C. L. Hollenberg,Loss of spin entanglement for accelerated electrons in electric and magnetic fields,Phys. Rev. A79(May, 2009) 052109

2009
[32]

D. E. Bruschi, J. Louko, E. Martín-Martínez, A. Dragan, and I. Fuentes,Unruh effect in quantum information beyond the single-mode approximation,Phys. Rev. A82(Oct, 2010) 042332

2010
[33]

E. W. Aspling,Unruh-DeWitt Quantum Computing: Realizing Quantum Shannon Theory With Quantum Fields. PhD thesis, SUNY, Binghamton, 2024.arXiv:2407.13628

2024 arXiv
[34]

I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series, and Products. Academic Press, Amsterdam, 7th ed., 2014. – 19 –

2014

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [23]

Azizi,Kappa vacua: enhancing the Unruh temperature,JHEP07(2023) 064, [arXiv:2301.13672]

A. Azizi,Kappa vacua: enhancing the Unruh temperature,JHEP07(2023) 064, [arXiv:2301.13672]

arXiv 2023

[2] [1]

W. G. Unruh,Notes on black-hole evaporation,Phys. Rev. D14(Aug, 1976) 870–892

1976

[3] [2]

S. A. Fulling,Nonuniqueness of Canonical Field Quantization in Riemannian Space-Time, Phys. Rev. D7(May, 1973) 2850–2862

1973

[4] [3]

P. C. W. Davies,Scalar production in Schwarzschild and Rindler metrics,Journal of Physics A: Mathematical and General8(apr, 1975) 609

work page 1975

[5] [4]

S. W. Hawking,Black hole explosions?,Nature248(1974), no. 5443 30–31. – 17 –

work page 1974

[6] [5]

S. W. Hawking,Particle Creation by Black Holes,Commun. Math. Phys.43(1975) 199–220. [Erratum: Commun.Math.Phys. 46, 206 (1976)]

1975

[7] [6]

N. D. Birrell and P. C. W. Davies,Quantum Fields in Curved Space. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge, UK, 1982

1982

[8] [7]

R. M. Wald,Quantum Field Theory in Curved Space-Time and Black Hole Thermodynamics. Chicago Lectures in Physics. University of Chicago Press, Chicago, IL, 1994

1994