arXiv subjects

Fedor V. Kusmartsev

Publications and source records attributed to Fedor V. Kusmartsev.

10 recordsLinked to original sources

arXiv2026

On the Plebanski Formulation with Energy Momentum

In Plebanski's formulation the coupling of matter is less direct than in the metric formulation since the energy-momentum tensor $T_{μν}$ is symmetric, while the Plebanski variables are naturally valued in the self-dual/anti-self-dual Hodge decomposition of 2-forms. An explicit construction of the Plebanski matter source $T^i$ is obtained by lifting the trace-free energy-momentum tensor $\hat T_{μν}$ into the $(1,1)$ component of the algebraic curvature space using the Kulkarni-Nomizu product, and then extracting its chiral components. This construction reproduces the definition for $T^i$ in terms of the self-dual basis $Σ^i$ and $\hat T_{μν}$ introduced by Krasnov. We also verify that the matter-coupled chiral field equations imply the usual conservation law $\nabla_μT^{μν}=0$ through the chiral Bianchi identity $d^A F^i=0$. As an application, the construction is applied to a spherically symmetric electromagnetic stress-energy tensor, where the anti-self-dual part of the matter-coupled Plebanski field equations yields the Reissner-Nordström-de Sitter solution. The result gives a systematic prescription for translating metric matter sources into the anti-self-dual source terms required by the Plebanski field equations.

gr-qc↗

arXiv2026

Warped Product Einstein Manifolds in Four Dimensions

On four-dimensional (pseudo-)Riemannian manifolds $\mathcal{M}$ the curvature tensor (viewed as an endomorphism on 2-forms) admits a chiral $6 \times 6$ matrix representation which decomposes into four $3 \times 3$ blocks. $\mathcal{M}$ is Einstein if and only if the off-diagonal blocks vanish. If the manifold is a warped product $\mathcal{M} = F \times_f B$, then there exists an alternative matrix representation relative to the decomposition of the 2-forms into spaces induced by the exterior algebra on both the base and the fiber. These two representations are not independent and a similarity transformation can be found between them. We construct these matrices and associated transformations for $1+3$, $2+2$ and $3+1$ warped products, giving classifications for the Einstein limits from this algebraic perspective. Using this, one can easily Petrov classify the Einstein warped products for each case considered: $3+1$ are generically type-\RNum{1}, $2+2$ are type-D while $1+3$ are constrained to be type-O. In the closed Riemannian case, there are a number of topological restrictions on these manifolds that we discuss: in the half-conformally flat limit, each of these Einstein warped products must be flat.

gr-qc↗

arXiv2025

Encoding the Einstein Equations into an Algebraic Commutator Condition

We show that the structure of the Lorentz group in four dimensions is such that unimodular (trace-free) gravity can be consistently represented as an algebraic condition on the symmetric product space of 2-forms. This condition states that the commutator between the Riemann tensor and the Hodge dual must be equal to the commutator between the Kulkarni-Nomizu product of the energy-momentum and the metric with the Hodge dual; symbolically, $[\text{Riem}, \star] = 4π[T\KN g, \star]$. We show that this condition is equivalent to the trace-free field equations, that the right-hand-side vanishes if and only if the energy-momentum tensor vanishes (recovering the appropriate Einstein spacetime limit) and that this condition can be solved for electrovacuum in the spherically symmetric ansatz to yield Reissner-Nordström-de Sitter uniquely. This analysis suggests that the conceptual distinction between unimodular gravity and General Relativity is one of emphasis on how irreducible representations of the Riemann tensor are constrained by the existence of energy-momentum and the associated field equations.

gr-qc↗

arXiv2025

Topological Origin of Horizon Temperature via the Chern-Gauss-Bonnet Theorem

This paper establishes a connection between the Hawking temperature of spacetime horizons and global topological invariants, specifically the Euler characteristic of Wick-rotated Euclidean spacetimes. This is demonstrated for both de Sitter and Schwarzschild, where the compactification of the near-horizon geometry allows for a direct application of the Chern-Gauss-Bonnet theorem. For de Sitter, a simple argument connects the Gibbon-Hawking temperature to the global thermal de Sitter temperature of the Bunch-Davies state. This establishes that spacetime thermodynamics are a consequence of the geometrical structure of spacetime itself, therefore suggesting a deep connection between global topology and semi-classical analysis.

gr-qc↗

arXiv2024

Connecting 2-Forms, Conformal Transformations, Curvature Invariants and Topological Classes in Einstein Spacetimes

The unique Nature of the Lorentz group in four dimensions is the root cause of the many remarkable properties of the Einstein spacetimes, in particular their operational structure on the 2-forms. We show how this operational structure can be used for two ends. First, it allows for a simple generalization of the Birkhoff theorem to Schwarzschild (A)de-Sitter spacetime. Second, it provides the means to construct an Abelian endomorphism group on the space of 2-forms. It is observed that taking the trace over this group element-wise induces a further Abelian group which may be identified with a tensor representation of conformal transformations, giving Einstein spacetimes access to their own conformal equivalence class. A further trace over the group yields the curvature invariants of the spacetime. The Kretschmann scalar becomes the topological Euler density, which may be linked in a simple way to the Hawking temperature of horizons.

gr-qc↗

arXiv2021

Ionic liquid gating induced two superconductor-insulator phase transitions in spinel oxide Li$_{1 \pm x}$Ti$_2$O$_{4-δ}$

The associations between emergent physical phenomena (e.g., superconductivity) and orbital, charge, and spin degrees of freedom of $3d$ electrons are intriguing in transition metal compounds. Here, we successfully manipulate the superconductivity of spinel oxide Li$_{1\pm x}$Ti$_2$O$_{4-δ}$ (LTO) by ionic liquid gating. A dome-shaped superconducting phase diagram is established, where two insulating phases are disclosed both in heavily electron-doping and hole-doping regions. The superconductor-insulator transition (SIT) in the hole-doping region can be attributed to the loss of Ti valence electrons. In the electron-doping region, LTO exhibits an unexpected SIT instead of a metallic behavior despite an increase in carrier density. Furthermore, a thermal hysteresis is observed in the normal state resistance curve, suggesting a first-order phase transition. We speculate that the SIT and the thermal hysteresis stem from the enhanced $3d$ electron correlations and the formation of orbital ordering by comparing the transport and structural results of LTO with the other spinel oxide superconductor MgTi$_2$O$_4$, as well as analysing the electronic structure by first-principles calculations. Further comprehension of the detailed interplay between superconductivity and orbital ordering would contribute to the revealing of unconventional superconducting pairing mechanism.

cond-mat.supr-con↗

arXiv2020

Optical Transistor for an Amplification of Radiation in a Broadband THz Domain

We propose a new type of optical transistor for a broadband amplification of THz radiation. It is made of a graphene--superconductor hybrid, where electrons and Cooper pairs couple by Coulomb forces. The transistor operates via the propagation of surface plasmons in both layers, and the origin of amplification is the quantum capacitance of graphene. It leads to THz waves amplification, the negative power absorption, and as a result, the system yields positive gain, and the hybrid acts like an optical transistor, operating with the terahertz light. It can, in principle, amplify even a whole spectrum of chaotic signals (or noise), that is required for numerous biological applications.

physics.app-ph↗

arXiv2019

High-throughput investigation of tunable superconductivity in FeSe films

There is an ongoing debate about the relative importance of structural change versus doping charge carriers on the mechanism of superconductivity in Fe-based materials. Elucidating this issue is a major challenge since it would require a large number of samples where structure properties or the carrier density is systematically varied. FeSe, with its structural simplicity, is an ideal platform for addressing this question. It has been demonstrated that the superconductivity in this material can be controlled through crystal lattice tuning, as well as electronic structure manipulation. Here, we apply a high-throughput methodology to FeSe to systematically delineate the interdependence of its structural and electronic properties. Using a dual-beam pulsed laser deposition, we have generated FeSe films with a marked gradient in the superconducting transition temperature (below 2 K < Tc < 12 K) across 1 cm width of the films. The Tc gradient films display ~ 1% continuous stretch and compression in the out-of-plane and in-plane lattice constants respectively, triggering the continuous enhancement of superconductivity. Combining transport and angular-resolved photoemission measurements on uniform FeSe films with tunable Tc from 3 K to 14 K, we find that the electron carrier density is intimately correlated with Tc, i.e., it increases by a factor of 6 and ultimately surpasses the almost constant hole concentration. Our transmission electron microscope and band structure calculations reveal that rather than by shifting the chemical potential, the enhanced superconductivity is linked to the selective adjustment of the dxy band dispersion across the Fermi level by means of reduced local lattice distortions. Therefore, such novel mechanism provides a key to understand discrete superconducting phases in FeSe.

cond-mat.supr-con↗

arXiv2019

Anomalies of upper critical field in the spinel superconductor LiTi$_2$O$_{4-δ}$

High-field electrical transport and point-contact tunneling spectroscopy were used to investigate superconducting properties of the unique spinel oxide, LiTi$_2$O$_{4-δ}$ films with various oxygen content. We find that the upper critical field $B_\mathrm{c2}$ gradually increases as more oxygen impurities are brought into the samples by carefully tuning the deposition atmosphere. It is striking that although the superconducting transition temperature and energy gap are almost unchanged, an astonishing isotropic $B_\mathrm{c2}$ up to $\sim$ 26 Tesla is observed in oxygen-rich sample, which is doubled compared to the anoxic sample and breaks the Pauli limit. Such anomalies of $B_\mathrm{c2}$ were rarely reported in other three dimensional superconductors. Combined with all the anomalies, three dimensional spin-orbit interaction induced by tiny oxygen impurities is naturally proposed to account for the remarkable enhancement of $B_\mathrm{c2}$ in oxygen-rich LiTi$_2$O$_{4-δ}$ films. Such mechanism could be general and therefore provides ideas for optimizing practical superconductors with higher $B_\mathrm{c2}$.

cond-mat.supr-con↗

arXiv2016

Applications of statistical physics distributions to several types of income

This paper explores several types of income which have not been explored so far by authors who tackled income and wealth distribution using Statistical Physics. The main types of income we plan to analyze are income before redistribution (or gross income), income of retired people (or pensions), and income of active people (mostly wages). The distributions used to analyze income distributions are Fermi-Dirac distribution and polynomial distribution (as this is present in describing the behavior of dynamic systems in certain aspects). The data we utilize for our analysis are from France and the UK. We find that both distributions are robust in describing these varieties of income. The main finding we consider to be the applicability of these distributions to pensions, which are not regulated entirely by market mechanisms.

physics.soc-ph↗