arXiv subjects

Andrei Galiautdinov

Publications and source records attributed to Andrei Galiautdinov.

At least 19 recordsLinked to original sources

arXiv2026

Emergent vacua and stability constraints on black hole solutions in higher-dimensional $f(R)$ gravity

We investigate static spherically symmetric vacuum solutions in higher-dimensional $f(R)$ gravity, beginning with the five-dimensional Starobinsky model governed by the action $f(R) = R + αR^2 - 2Λ$. By enforcing the ghost-free stability criterion $f'(R) > 0$ on constant scalar curvature spacetimes, we show that a stable effective cosmological constant cannot be dynamically generated from pure $R^2$ geometric corrections in five dimensions; its existence is inextricably tied to a bare cosmological constant. Generalizing this analysis to arbitrary dimensions $D$ and single-term curvature corrections $f(R) = R + αR^n$ with a vanishing bare cosmological constant, we derive a universal stability bound, $n > D/2$, required for the existence of stable emergent vacua. Finally, we demonstrate that expanding the gravitational action to a multi-term polynomial hierarchy circumvents this strict limitation. By including curvature corrections up to $\mathcal{O}(R^3)$, the extended geometric degrees of freedom simultaneously satisfy the trace constraint and the stability criterion. Furthermore, we establish the exact parameter space boundaries that ensure not only asymptotic vacuum stability but strict global stability ($f'(R) > 0$ for all $R$), allowing for the dynamical generation of exact, globally ghost-free vacuum spacetimes in $D \ge 5$ purely from higher-order geometric terms. The scalaron mass requirement, $m_s^2>0$ is not imposed in full in our analysis. A detailed investigation of its implications on the models considered in this work are left for future study.

gr-qc↗

arXiv2026

Strongly anisotropic Rytova-Keldysh interaction and the ground state of 2D excitons

The classic Rytova-Keldysh potential describes the non-local dielectric screening of Coulomb interactions in ultrathin two-dimensional (2D) materials. Recently, the corresponding potential for arbitrary in-plane anisotropy was derived in integral form, with numerical studies suggesting that an effective isotropic approximation remains robust for highly directional systems. In this paper we provide the analytical foundation for these observations by mapping the complete spatial landscape of the strongly anisotropic Rytova-Keldysh interaction. By applying the method of steepest descent and momentum-space coordinate scaling to the exact one-dimensional integral representation, we derive closed-form asymptotic expressions for the potential across all spatial regimes. We find that the intermediate-range screening exhibits a non-trivial amplitude scaling driven by the direction of weakest polarizability, while the short-range limit produces an anisotropic logarithmic well governed by the geometric mean of the principal polarizabilities. Finally, utilizing this short-range confinement, we implement an anisotropic Gaussian variational ansatz to solve the Wannier equation, providing a closed-form analytical expression for the exciton ground-state binding energy that explicitly captures the competition between the effective mass and dielectric tensors.

cond-mat.mes-hall↗

arXiv2026

Logarithmically enhanced hyperbolic square-root deformation of Starobinsky inflation

We propose an enhanced hyperbolic square-root (HSQRT) deformation of the Starobinsky model in the context of $f(R)$ gravity. The original HSQRT construction provided a globally regular modification of $R^2$ inflation, curing the strong-coupling singularity at negative curvatures while preserving the exponential slow-roll plateau at large positive curvatures. Motivated by recent cosmological data (ACT DR6 and DESI), we introduce a structurally minimal, rational-logarithmic enhancement. This enhancement modifies the deep UV asymptotic regime while preserving global tachyon-free stability, ghost freedom, and the recovery of general relativity at low curvatures. In the Einstein frame, the scalaron dynamics is described by a globally defined, Padé-regulated effective potential, $V_{\text{Padé}}(ϕ) = V_{\text{Staro}}(ϕ) \left(1+ \frac{4β}{\frac{2}{3}κ^2ϕ^2 + 1}\right)^{-1} + \frac{1}{4ακ^2} \left[1 - \left( 1 + \sqrt{\frac{2}{3}}κϕ\right) e^{-\sqrt{\frac{2}{3}}κϕ} \right] e^{-\sqrt{\frac{2}{3}}κϕ}$, which exhibits the inverse-power asymptotic form at high curvatures, $V(ϕ) \simeq \frac{1}{8ακ^2} \left( 1 - \frac{6β}{κ^2ϕ^2} \right)$, with the strength of the deviation from the baseline HSQRT geometry governed by dimensionless parameter $β$. We derive analytic expansions for the slow-roll observables, yielding a leading-order spectral index $n_s \simeq 1 - 3/(2N)$ and a tensor-to-scalar ratio $r \simeq 2\sqrt{3β}/N^{3/2}$. For standard e-fold durations ($N \in [50, 60]$), this model drives the spectral index directly into the newly favored observational window ($n_s \simeq 0.970\text{--}0.975$) and predicts an exceptionally small spectral running $α_s \simeq -3/(2N^2) \in [-0.00060, -0.00042]$, establishing a viable target for next-generation CMB observatories.

gr-qc↗

arXiv2026

Globally stable, ghost-free hyperbolic square-root deformation of the Starobinsky model

We propose an exact, analytic deformation of the Starobinsky model governed by the strictly positive derivative of its Lagrangian, $f'(R) = αR + \sqrt{α^2 R^2 + 1}$, with $α> 0$. This geometric hyperbolic square-root ansatz is designed to eliminate the well-known strong-coupling singularity that arises in quadratic $f(R)$ gravity when $f'(R)=0$. The construction seamlessly recovers general relativity at low curvatures and preserves the successful slow-roll inflationary plateau at extreme positive curvatures. In the limit $R \to -\infty$, the derivative $f'(R)$ asymptotes to zero strictly from above, removing the pathological branch associated with the vanishing of $f'(R)$. This guarantees that the only admissible constant-curvature ($R=A$) solutions correspond to standard Einstein spaces with an effective cosmological constant $Λ_{\text{eff}} \equiv A/4$. The first and second derivatives of the action, as well as the scalaron mass squared, remain strictly positive globally, ensuring a perfectly ghost-free and tachyon-free cosmological evolution across the entire spacetime manifold. In the Einstein frame, the dynamics of the scalaron is governed by the globally defined potential $V(ϕ) = \frac{1}{8α} [ 1 - (1 + 2\sqrt{2/3}ϕ) \exp(-2\sqrt{2/3}ϕ) ] + Λ\exp(-2\sqrt{2/3}ϕ)$, which naturally establishes an impenetrable energetic wall as $ϕ\to -\infty$, offering a robust, globally stable mechanism for non-singular bouncing cosmologies. For $N = 60$ inflationary e-folds, the model predicts a scalar spectral index of $n_s \simeq 0.967$ and a strongly suppressed tensor-to-scalar ratio of $r \simeq 0.00083$, which position the proposed theory within the observationally favored parameter space of the Planck and BICEP/Keck Array baseline constraints.

gr-qc↗

arXiv2026

Exotic spherically-symmetric Lambda-vacuum in the four-dimensional Starobinsky model

We introduce an exact, two-parameter family of static, spherically-symmetric, constant-curvature $Λ$-vacuum solutions within the four-dimensional Starobinsky $f(R)=R+αR^2+2Λ$ model. When the bare cosmological constant is precisely fine-tuned to $Λ= 1/(8α)$, the scalar curvature is rigidly fixed such that the derivative $f'(R)=1+2αR$ identically vanishes. Because this derivative acts as the effective multiplier for the standard curvature terms in the modified field equations, its global vanishing mathematically erases the normal rules of gravitational dynamics, demonstrating that the family represents a pathological boundary to the space of viable physical geometries. This exact decoupling of the field equations permits the existence of a fundamentally unconstrained $1/r^2$ integration constant in the metric, which functions as a purely geometric Reissner-Nordstrom hair mimicker. However, any infinitesimal classical deviation from this exact boundary instantaneously destroys the degeneracy, rigorously forcing the geometric hair to vanish and discontinuously collapsing the spacetime back into the standard, dynamical Schwarzschild-de Sitter solution. We provide the exact derivation of this spacetime and methodically highlight its physical pathologies, including the identically vanishing Wald entropy of the associated black hole horizons, the strict divergence of the effective gravitational coupling, the complete breakdown of the test-particle approximation, and the onset of severe ghost instabilities. Ultimately, this exact solution functions as a ``do not enter'' sign within the Starobinsky model, pedagogically illustrating the extreme fragility and physical hostility of degenerate, purely mathematical solutions in highly non-linear $f(R)$ gravity theories.

gr-qc↗

arXiv2026

Comment on "Multidimensional arrow of time" (arXiv:2601.14134)

In a recent preprint [arXiv:2601.14134v1], Rubin argues that the arrow of time originates from the monotonic growth of the volume of extra dimensions. While the identification of a geometric origin for time's arrow is compelling in the case of brane-world models, we point out a possible tension between the proposed volume growth and the observational stability of the effective four-dimensional Newton's gravitational constant, G, that may arise in Kaluza-Klein (KK) theory. In standard KK approaches, such volume growth induces a time-variation of G that exceeds Big Bang Nucleosynthesis (BBN) and Lunar Laser Ranging (LLR) bounds by many orders of magnitude. To resolve this tension while preserving the author's key insight in the Kaluza-Klein case, we propose an extension: the "shape-dynamic arrow of time". By utilizing the scale-invariant monotonicity of Perelman's nu-entropy under normalized Ricci flow, we demonstrate how an arrow of time can emerge from the geometric smoothing of extra dimensions at fixed volume, thereby satisfying observational constraints on fundamental constants.

gr-qc↗

arXiv2026

Comment on "Application of the three-dimensional telegraph equation to cosmic-ray transport" (arXiv:1606.08272)

In a recent publication [R. C. Tautz and I. Lerche, Res. Astron. Astrophys. 16, 162 (2016); arXiv:1606.08272], the authors present a derivation of the Green's function for the three-dimensional telegraph equation (also known as the heat wave equation, or relativistic heat conduction equation). We demonstrate that the closed-form expression derived in their Appendix A is incorrect. Specifically, the published solution lacks a Dirac delta term representing the ballistic wavefront and contains an algebraic error in the prefactor of the wake term. These omissions arise from the neglect of distributional derivatives when differentiating a Heaviside step function. We provide a rigorous derivation of the Green's function using the Fourier transform method, verify the correct limiting behavior as the damping vanishes, and pinpoint the exact mathematical step where the original derivation failed.

astro-ph.IM↗

arXiv2026

Quantum deliberating machines

Within the familiar circuit-based quantum computational setting, we introduce and analyze a toy model of a quantum physical device capable of internal, self-referential deliberation. The key idea is to represent ``deliberation'' as a coherent iterative branching process, in which competing branch-dependent system evolutions are maintained in superposition, with additional control and memory registers recording branch histories, and the policy register adaptively biasing subsequent development. We provide explicit quantum circuit realizations and carry out detailed step-by-step derivations of the entangled control--memory--system--policy dynamics. We carefully distinguish between internally adaptive and internally reinforced deliberations, proposing the architectures for both, and briefly discuss categorical and controlled--Stinespring reformulations, as well as their conceptual implications. The primary construction models a memory-driven deliberation where the policy update depends on which actions were taken, not on their results. We also present a simple extension that allows for minimalistic, outcome-driven policy updates, implementing a coherent feedback loop that steers the system toward a target state regardless of initial branch-dependent evolution. This loop can be interpreted as a quantum autopilot or search-and-rescue mechanism, illustrating how a device can autonomously correct and optimize its internal strategy in superposition. Finally, we briefly consider various implementations of a dialogue that may take place between two deliberating machines. Taken together, this frames the proposed model as a plausible setting for exploring how such devices may maintain multiple alternatives in parallel, while performing an internal decision-making process through coherent branching, entanglement, adaptive policy updates, and policy-driven self-modifying unitary dynamics.

quant-ph↗

arXiv2025

Modified Fronsdal coordinates for maximally extended Schwarzschild spacetime

We introduce a coordinate system that complements the Kruskal--Szekeres extension. Like the standard construction, it covers the maximally extended Schwarzschild manifold in its entirety, while offering an additional advantage of expressing the areal radius as an explicit function of the new coordinates. Its main limitation, however, is that radial null geodesics are no longer represented as 45-degree lines in the Kruskal plane, making the causal structure more difficult to interpret. Nevertheless, the new system offers a compelling aesthetic trade-off: among all known maximally extended systems - including those of Kruskal-Szekeres, Israel, Fronsdal, Novikov, and Synge - it exhibits the highest degree of symmetry with respect to Schwarzschild's original r- and t-coordinate lines. It trades the regular pattern of Kruskal's light cones for a symmetric nesting arrangement of the two-dimensional spheres. The proposed extension sheds new light on the closely related Fronsdal's six-dimensional embedding construction, and clarifies the deep connection that exists between the most important implicit (Kruskal-Szekeres) and explicit (Israel's) procedures for maximal extension of the Schwarzschild geometry that is well known to those working in the field but rarely presented in textbooks on general relativity.

gr-qc↗

arXiv2025

Canonical quantization of the dark positive-energy Dirac field and time asymmetry

We perform canonical quantization of the single-component, spin-zero field that was introduced by Dirac in 1971 and recently suggested as a candidate for dark matter by Bogomolny. The massive and massless cases are treated separately. Since in the massive case only positive-frequency modes are normalizable and regarded as physical, the mode expansion for the field involves annihilation operators only, making the quantization procedure particularly simple. The corresponding Hamiltonian turns out to be unambiguous, with no need for normal ordering. The positive-energy requirement imposed on the second-quantized system leads to equally acceptable Bose and Fermi choices for particle statistics. This suggests a simple extension of original Dirac's theory in which Bose and Fermi single-component positive-energy Dirac fields are combined into a doublet whose members can transform into each other. The model includes a Landau-Anderson-Higgs type potential that allows spontaneous selection of the direction in the internal bose-fermi space. The bosonic sector of the theory hints at the possibility of a dark, background spacetime condensate that could endow the universe with its cosmological temporal asymmetry. In the massless case of Dirac's original theory, we explore the possibility of allowing the field expansion to involve both positive- and negative-frequency modes. This leads to the anticommutation relations for creation and annihilation operators associated with the negative energy solutions, resulting in supersymmetric behavior of the single-component field in the ultrarelativistic limit. Finally, we speculate on the possibility for the positive-energy Dirac particles to obey some exotic (such as non-abelian, Clifford) statistics in which the particles are neither created nor destroyed.

gr-qc↗

arXiv2024

Simulating kaon mixing with Josephson phase qubits

Superconducting circuits with Josephson junctions distinguish themselves from other types of quantum computing architectures by having easily controllable metastable computational states (the so-called phase qubits) with a very large ratio of their respective lifetimes. In this pedagogical note I describe how we can use this remarkable property of the phase qubits to further test the validity of the superposition principle in the macroscopic quantum regime by simulating the kaon mixing mechanism of particle physics.

quant-ph↗

arXiv2024

Positive-energy Dirac particles in cosmology

We provide general relativistic treatment of the single-component field described by Dirac's positive-energy wave equation of 1971. It is motivated by Bogomolny's proposal to regard that field as a possible candidate for dark matter. Our emphasis is on standard (flat) Friedmann-Robertson-Walker cosmology. The early universe is not considered, though there is a strong indication that the field may play a role in internally driven generation of cosmic anisotropy.

gr-qc↗

arXiv2023

Feynman's method in chiral nanorod-based metamaterial nanoplasmonics

We propose a theoretical approach to some of the nanorod-based metamaterial implementations that does not depend on macroscopic electrodynamics. The approach is motivated by the fact that in actual experiments the incident electromagnetic wave encounters a metamaterial structure which is planar in its shape, contains a layer or two of artificially created building blocks, and therefore cannot be regarded as a three-dimensional continuous medium. This leads to a theoretical framework in which the phenomenological concept of refractive index loses its principled meaning, and the deeper concept of scattering is taking center stage. Our proposal and its mathematical realization rely heavily on Feynman's explanation of the physical origin of the index of refraction and on his formula for the field of a plane of oscillating charges. We provide a complete proof of Feynman's formula, filling in some steps that were missing in the original derivation, and then generalize it to the case of a finite disk, which may be relevant to the actual experiments involving laser beams. We then show how the formula can be applied to metamaterial nanoplasmonics by considering some subtle interference effects in narrow laser beams striking metamaterial plates. The first two effects use a single layer of aligned plasmonic nanorods, while the third uses a single layer of gyrotropic elements that may conveniently be described by the celebrated Born-Kuhn oscillator model. The considered effects can potentially be used in the development of quality standards for various metamaterial devices.

physics.optics↗

arXiv2023

Derivation of the Lorentz transformation without the use of Einstein's second postulate

Derivation of the Lorentz transformation without the use of Einstein's Second Postulate is provided along the lines of Ignatowsky, Terletskii, and others. This is a write-up of the lecture first delivered in PHYS 4202 E&M class during the Spring semester of 2014 at the University of Georgia. The main motivation for pursuing this approach was to develop a better understanding of why the faster-than-light neutrino controversy (OPERA experiment, 2011) was much ado about nothing.

physics.class-ph↗

arXiv2019

Anisotropic Keldysh interaction

We generalize the classic calculations by Rytova and Keldysh of screened Coulomb interaction in semiconductor thin films to systems with anisotropic permittivity tensor. Explicit asymptotic expressions for electrostatic potential energy of interaction in the weakly anisotropic case are found in closed analytical form. The case of strong in-plane anisotropy, however, requires evaluation of the inverse Fourier transform of $1/(k+Ak_x^2+Bk_y^2)$, which, at present, remains unresolved.

cond-mat.mes-hall↗

arXiv2018

Quantum Zeno effect: A possible resolution to the leakage problem in superconducting quantum computing architectures

We propose to use the continuous version of the quantum Zeno effect to eliminate leakage to higher energy states in superconducting quantum computing architectures based on Josephson phase and flux qubits. We are particularly interested in the application of this approach to the single-step Greenberger-Horne-Zeilinger (GHZ) state protocol described in [A. Galiautdinov and J. M. Martinis, Phys. Rev. A 78, 010305(R) (2008)]. While being conceptually appealing, the protocol was found to be plagued with a number of spectral crowding and leakage problems. Here we argue that by coupling the qubits to a measuring device which continuously monitors leakage to higher energy states (say, to a very lossy resonator of frequency omega = E3(qubit)-E1(qubit), with 1 labeling the ground state of the qubit), we could potentially restrict the multi-qubit system's evolution to its computational subspace, thus circumventing the above mentioned problems.

quant-ph↗

arXiv2017

Ground state of an exciton in a three-dimensional parabolic quantum dot: convergent perturbative calculation

Working in the effective-mass approximation, we apply a powerful convergent perturbative technique of Turbiner's to the calculation of the ground state energy and the wave function of an exciton confined to a three-dimensional parabolic quantum dot. Unlike the usual Rayleigh-Schrodinger perturbation theory, Turbiner's approach works well even in the regime of strong coupling and does not require the knowledge of the full solution to the undisturbed problem. The second-order convergent calculation presented below is in excellent agreement with the results of exact numerical simulations for a wide range of system's confinement parameters.

cond-mat.mes-hall↗

arXiv2017

Post-Newtonian celestial mechanics in scalar-tensor cosmology

Applying the recently developed dynamical perturbation formalism on cosmological background to scalar-tensor theory, we provide a solid theoretical basis and a rigorous justification for phenomenological models of orbital dynamics that are currently used to interpret experimental measurements of the time-dependent gravitational constant. We derive the field equations for the scalar-tensor perturbations and study their gauge freedom associated with the cosmological expansion. We find a new gauge eliminating a prohibitive number of gauge modes in the field equations and significantly simplifying post-Newtonian equations of motion for localized astronomical systems in the universe with time-dependent gravitational constant. We identify several new post-Newtonian terms and calculate their effect on secular cosmological evolution of the osculating orbital elements.

gr-qc↗