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We consider Axion-like particle (ALP) model to construct numerical spatially homogeneous anisotropic Kantowski-Sachs cosmological model. We present various analytical and numerical results in this regard, discussing the evolution of various important cosmological parameters in this regard with ALP scalar field. We also present some general results for generic scalar field in a Kantowski-Sachs background.

Cascade multiplication is a common technique to enhance the sensitivity of photon detectors. In this study, we demonstrate novel cascade-amplified superconducting detectors utilizing arrays of Josephson junctions. The mutual coupling between junctions induces avalanche-like switching of multiple junctions upon photon absorption, leading to cascade amplification of the readout voltage. We present two prototypes featuring either low-Tc linear Nb/NbxSi1-x/Nb arrays, or high-Tc stacked intrinsic Josephson junctions. Both devices exhibit clear antenna effects in microwave directivities, indicating good impedance matching and absorption efficiency. The combination of high absorption efficiency and large cascade amplification has the potential to produce broadband THz sensors with sensitivity exceeding 10^13 V/W., Comment: 9 pages, 3 figures

The challenges of black box optimization arise due to imprecise responses and limited output information. This article describes new results on optimizing multivariable functions using an Order Oracle, which provides access only to the order between function values and with some small errors. We obtained convergence rate estimates for the one-dimensional search method (golden ratio method) under the condition of oracle inaccuracy, as well as convergence results for the algorithm on a "square" (also with noise), which outperforms its alternatives. The results obtained are similar to those in problems with oracles providing significantly more information about the optimized function. Additionally, the practical application of the algorithm has been demonstrated in maximizing a preference function, where the parameters are the acidity and sweetness of the drink. This function is expected to be convex or at least quasi-convex.

The lack of dense random-access memory is one of the main obstacles to the development of digital superconducting computers. It has been suggested that AVRAM cells, based on the storage of a single Abrikosov vortex, the smallest quantized object in superconductors, can enable drastic miniaturization to the nanometer scale. In this work, we present numerical modeling of such cells using time-dependent Ginzburg-Landau equations. The cell represents a fluxonic quantum dot containing a small superconducting island, an asymmetric notch for vortex entrance, a guiding track, and a vortex trap. We determine the optimal geometrical parameters for operation at zero magnetic field and the conditions for controllable vortex manipulation by short current pulses. We report ultra-fast vortex motion with velocities more than an order of magnitude faster than those expected for macroscopic superconductors. This phenomenon is attributed to strong interactions with the edges of a mesoscopic island, combined with the nonlinear reduction of flux-flow viscosity due to nonequilibrium effects in the track. Our results show that such cells can be scaled down to sizes comparable to the London penetration depth, 100 nm, and can enable ultrafast switching on the picosecond scale with ultra-low energy per operation, 0.1 aJ., Comment: 12 pages, 7 figures

The main aim of this paper is to simplify and popularise the construction from the 2013 paper by Apostolov, Calderbank, and Gauduchon, which (among other things) derives the Plebanski-Demianski family of solutions of GR using ideas of complex geometry. The starting point of this construction is the observation that the Euclidean versions of these metrics should have two different commuting complex structures, as well as two commuting Killing vector fields. After some linear algebra, this leads to an ansatz for the metrics, which is half-way to their complete determination. Kerr metric is a special 2-parameter subfamily in this class, which makes these considerations directly relevant to Kerr as well. This results in a derivation of the Kerr metric that is self-contained and elementary., Comment: 25 pages, no figures

Product search is uniquely different from search for documents, Internet resources or vacancies, therefore it requires the development of specialized search systems. The present work describes the H1 embdedding model, designed for an offline term indexing of product descriptions at e-commerce platforms. The model is compared to other state-of-the-art (SoTA) embedding models within a framework of hybrid product search system that incorporates the advantages of lexical methods for product retrieval and semantic embedding-based methods. We propose an approach to building semantically rich term vocabularies for search indexes. Compared to other production semantic models, H1 paired with the proposed approach stands out due to its ability to process multi-word product terms as one token. As an example, for search queries "new balance shoes", "gloria jeans kids wear" brand entity will be represented as one token - "new balance", "gloria jeans". This results in an increased precision of the system without affecting the recall. The hybrid search system with proposed model scores mAP@12 = 56.1% and R@1k = 86.6% on the WANDS public dataset, beating other SoTA analogues., Comment: 10 pages, 4 figures

An SU(2) structure in four dimensions can be described as a triple of 2-forms Sigma^i in Lambda^2(M), i=1,2,3 satisfying Sigma^i wedge Sigma^j ~ delta^{ij}. Such a triple defines a Riemannian signature metric on M. An SU(2) structure is said to be integrable if the holonomy of this Riemannian metric is contained in SU(2). It is well-known that this is the case if and only if the 2-forms are closed dSigma^i=0. The main purpose of the paper is to analyse the second order in derivatives diffeomorphism invariant action functionals that can be constructed for an SU(2) structure. The main result is that there is a unique such action functional if one imposes an additional requirement that the action is also SU(2) invariant, with SU(2) acting on the triple Sigma^i as in its vector representation. This action functional has a very simple expression in terms of the intrinsic torsion of the SU(2) structure. We show that its critical points are SU(2) structures whose associated metric is Einstein. The action we describe has also a first order in derivatives version, and we show how this is related to what in the physics literature is known as Plebanski formalism for GR., Comment: 18 pages, no figures

The most natural first-order PDE's to be imposed on a Cayley 4-form in eight dimensions is the condition that it is closed. As is known, this implies integrability of the Spin(7) structure defined by the Cayley form, as well as Ricci-flatness of the associated metric. We address the question as to what the most natural second-order in derivatives set of conditions is. We start by constructing the most general diffeomorphism invariant second order in derivatives Lagrangian that is quadratic in the perturbations of the Cayley form. We find that there is a one-parameter family of such Lagrangians. We then describe a non-linear completion of the linear story. To this end, we parametrise the intrinsic torsion of a Spin(7) structure by a 3-form, and show that this 3-form is completely determined by the exterior derivative of the Cayley form. We construct an action functional, which depends on the Cayley 4-form and and auxiliary 3-form as independent variables. There is a unique functional whose Euler-Lagrange equation for the auxiliary 3-form states that it is equal to the torsion 3-form. There is, however, a more general one-parameter family of functionals that can be constructed, and we show how the linearisation of these functionals reproduces the linear story. For any member of our family of theories, the Euler-Lagrange equations are written only using the operator of exterior differentiation of forms, and do not require the knowledge of the metric-compatible Levi-Civita connection. Geometrically, there is a preferred member in the family of Lagrangians, and we propose that its Euler-Lagrange equations are the most natural second-order equations to be satisfied by Cayley forms. Our construction also leads to a natural geometric flow in the space of Cayley forms, defined as the gradient flow of our action functional., Comment: 25 pages, no figures

Magnetoconvection in a tall vertical box with vertical hot and cold walls, and an imposed steady uniform magnetic field perpendicular to the temperature gradient, is analyzed numerically. The geometry and the values of the non-dimensional parameters - the Prandtl number of 0.025, the Rayleigh number of $7.5 \times 10^5$, and the Hartmann number between 0 and 798 - match those of an earlier experiment. A parametric study of the effect of wall electric conductivity, across a wide range of conductance ratio values, on flow properties is performed. Two configurations of electric boundary conditions are explored. In one configuration, all walls have finite electric conductivity, while in the other, only the walls with constant temperature are electrically conducting. The flows are analyzed using their integral properties and distributions of velocity, temperature, and electric currents. It is found that, in general, the convection flow is suppressed by the magnetic field. However, this effect is strongly modified by the wall's electric conductivity and is markedly different for the two wall configurations. The associated changes in flow structure, rate of heat transfer, and flow's kinetic energy are revealed. It is also shown that the assumption of quasi-two-dimensionality may not be valid under some conditions, even at high Hartmann numbers., Comment: The following article has been submitted to Physics of Fluids. After it is published, it will be found at https://publishing.aip.org/resources/librarians/products/journals/

Current-biased Josephson junctions can act as detectors of electromagnetic radiation. At optimal conditions, their sensitivity is limited by fluctuations causing stochastic switching from the superconducting to the resistive state. This work provides a quantitative description of a stochastic switching current detector, based on an underdamped Josephson junction. It is shown that activation of a Josephson plasma resonance can greatly enhance the detector responsivity in proportion to the quality factor of the junction. The ways of tuning the detector for achieving optimal operation are discussed. For realistic parameters of Nb/AlOx/Nb tunnel junctions, the sensitivity and noise-equivalent power can reach values of $S\simeq 2\times10^{13}$ (V/W) and $NEP\simeq 5\times10^{-24}$ (WHz$^{-1/2}$), respectively. These outstanding characteristics facilitate both bolometric and single-photon detection in microwave and terahertz ranges., Comment: 9 pages, 4 Figures

Frequently, the burgeoning field of black-box optimization encounters challenges due to a limited understanding of the mechanisms of the objective function. To address such problems, in this work we focus on the deterministic concept of Order Oracle, which only utilizes order access between function values (possibly with some bounded noise), but without assuming access to their values. As theoretical results, we propose a new approach to create non-accelerated optimization algorithms (obtained by integrating Order Oracle into existing optimization "tools") in non-convex, convex, and strongly convex settings that are as good as both SOTA coordinate algorithms with first-order oracle and SOTA algorithms with Order Oracle up to logarithm factor. Moreover, using the proposed approach, we provide the first accelerated optimization algorithm using the Order Oracle. And also, using an already different approach we provide the asymptotic convergence of the first algorithm with the stochastic Order Oracle concept. Finally, our theoretical results demonstrate effectiveness of proposed algorithms through numerical experiments.

Area metrics are an intriguing generalization of length metrics which appears in several quantum-gravity approaches. We describe the space of diffeomorphism-invariant area-metric actions quadratic in fluctuations and derivatives. A general theory is found to be specified by four parameters, two of which are mass parameters for the non-length degrees of freedom. We find that a two-parameter subclass of theories exhibits an additional shift symmetry of the kinetic term, and leads to a ghost-free graviton propagator for the effective theory obtained after integrating out the non-length degrees of freedom. One of the two parameters determines the strength of parity violations, the other defines a mass parameter for the non-length degrees of freedom. The same type of action has been found to appear from modified Plebanski theory and in the continuum limit of (effective) spin foams. We moreover find that area-metric actions in Lorentzian (but not in Euclidean) signature feature wrong-sign kinetic and mass terms for the non-length degrees of freedom. Nevertheless, despite a coupling of these degrees of freedom to the length metric, the linearized dynamics turns out to be stable for the above subclass of actions., Comment: v1: 22 pages; v2: minor modifications, content matches version published in PRD

We propose and develop a new method to classify orbits of the spin group ${\rm Spin}(2d)$ in the space of its semi-spinors. The idea is to consider spinors as being built as a linear combination of their pure constituents, imposing the constraint that no pair of pure spinor constituents sums up to a pure spinor. We show that this leads to a simple combinatorial problem that has a finite number of solutions in dimensions up to and including fourteen. We call each distinct solution a combinatorial type of an impure spinor. We represent each combinatorial type graphically by a simplex, with vertices corresponding to the pure constituents of a spinor, and edges being labelled by the dimension of the totally null space that is the intersection of the annihilator subspaces of the pure spinors living at the vertices. We call the number of vertices in a simplex the impurity of an impure spinor. In dimensions eight and ten the maximal impurity is two. Dimension twelve is the first dimension where one gets an impurity three spinor, represented by a triangle. In dimension fourteen the generic orbit has impurity four, while the maximal impurity is five. We show that each of our combinatorial types uniquely corresponds to one of the known spinor orbits, thus reproducing the classification of spinors in dimensions up to and including fourteen from simple combinatorics. Our methods continue to work in dimensions sixteen and higher, but the number of the possible distinct combinatorial types grows rather rapidly with the dimension., Comment: 20 pages, some diagrams embedded in the text

Vacuum fluctuations are a fundamental and irremovable property of a quantized electromagnetic field. These fluctuations are the cause of the Casimir effect -- mutual attraction of two electrically neutral metallic plates in vacuum in the absence of any other interactions. For most geometries and materials, Casimir effect is strictly attractive, leading to the only stable equilibrium configuration with merged plates. Recent observation showed, however, that this unavoidable vacuum-induced attraction can be mitigated by the presence of electrostatic repulsion produced by the formation of double electric layers, and a stable equilibrium between two charged metallic plates in a solution of an organic salt can be reached. Here, we study theoretically in details equilibrium configurations and their dynamical behavior in the system of two parallel metallic films coupled by the Casimir and electrostatic interactions. We analyze the effect of various parameters of the system -- such as the salt concentartion and temperature -- on the equilibrium cavity thicknesses, inspect resonant properties of the resulting an-harmonic optomechanical system near equilibrium, and examine its stochastic dynamics under the influence of thermal fluctuations of the environment.

We revisit the problem of determining the zero modes of the Dirac operator on the Eguchi-Hanson space. It is well known that there are no normalisable zero modes, but such zero modes do appear when the Dirac operator is twisted by a $U(1)$ connection with $L^2$ normalisable curvature. The novelty of our treatment is that we use the formalism of spin-$c$ spinors (or spinors as differential forms), which makes the required calculations simpler. In particular, to compute the Dirac operator we never need to compute the spin connection. As a result, we are able to reproduce the known normalisable zero modes of the twisted Eguchi-Hanson Dirac operator by relatively simple computations. We also collect various different descriptions of the Eguchi-Hanson space, including its construction as a hyperk\"ahler quotient of $\mathbb{C}^4$ with the flat metric. The latter illustrates the geometric origin of the connection with $L^2$ curvature used to twist the Dirac operator. To illustrate the power of the formalism developed, we generalise the results to the case of Dirac zero modes on the Ricci-flat K\"ahler manifolds obtained by applying Calabi's construction to the canonical bundle of $\mathbb{C} P^n $.

We employ a linear stability analysis and direct numerical simulations to study the characteristics of wall-modes in thermal convection in a rectangular box under strong and inclined magnetic fields. The walls of the convection cell are electrically insulated. The stability analysis assumes periodicity in the spanwise direction perpendicular to the plane of the homogeneous magnetic field. Our study shows that for a fixed vertical magnetic field, the imposition of horizontal magnetic fields results in an increase of the critical Rayleigh number along with a decrease in the wavelength of the wall modes. The wall modes become tilted along the direction of the resulting magnetic fields and therefore extend further into the bulk as the horizontal magnetic field is increased. Once the modes localized on the opposite walls interact, the critical Rayleigh number decreases again and eventually drops below the value for onset with a purely vertical field. We find that for sufficiently strong horizontal magnetic fields, the steady wall modes occupy the entire bulk and therefore convection is no longer restricted to the sidewalls. The above results are confirmed by direct numerical simulations of the nonlinear evolution of magnetoconvection., Comment: 25 pages, 18 figures

We examine a single-file chain of ammonia molecules in a carbon nanotube. To this end, we use i) molecular dynamics simulations (combined with the charges for ammonia nitrogen and hydrogen obtained from quantum chemistry) and ii) lattice-model calculations [M.~Druchok {\it et al.}, J. Chem. Phys. {\bf 158}, 104304 (2023)]. Our findings demonstrate the occurrence of the orientational quasiorder of the ammonia dipoles, which become parallel to the tube axis, at intermediate temperatures below $100$~K., Comment: 12 pages, 12 figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:2302.09362

We discuss the effects of nonhomogeneous magnetic fields in liquid metal flows in two different configurations. In the first configuration, we briefly report the impact of fringing magnetic fields in a turbulent Rayleigh-B{\'e}nard convection setup, where it was shown that the global heat transport decreases with an increase of fringe-width. The convective motion in regions of strong magnetic fields is confined near the sidewalls. In the second configuration, we numerically study the effects of an oscillating magnetic obstacle with different frequencies of oscillation on liquid metal flow in a duct. The Reynolds number is low such that the wake of the stationary magnetic obstacle is steady. The transverse oscillation of the magnet creates a sinusoidal time-dependent wake reminiscent of the vortex shedding behind solid obstacles. We examine the behavior of the streamwise and spanwise components of the Lorentz forces as well as the work done by the magnets on the fluid. The frequency of the oscillation of the streamwise component of Lorentz force is twice that of the spanwise component as in the case of lift and drag on solid cylindrical obstacles. The total drag force and the energy transferred from the magnets to the fluid show a non-monotonic dependence on the frequency of oscillation of the magnetic obstacle indicative of a resonant excitation of the sinusoidal vortex shedding., Comment: 6 pages, 5 figures

A photonic crystal microcavity with the liquid crystal resonant layer tunable by heating has been implemented. The multiple vanishing resonant lines corresponding to optical bound states in the continuum are observed. The abrupt behaviour of the resonant linewidth near the vanishing point can be used for temperature sensing.

Heavy Neutral Leptons are popular hypothetical particles, first introduced as a way to explain neutrino oscillations, and since then extensively studied in relation to many other aspects of physics beyond the Standard Model. They also serve as viable targets for direct experimental searches, being effectively described only by HNL mass and mixing with each neutrino flavor. Motivated by this, we study the lower theoretical boundary for mixing with a specified flavor in two and three HNLs cases. We find the connection of this limit with the effective neutrino mass appearing in neutrinoless double beta decay (and similar expressions for mixing with muon and tau neutrino). In two HNLs case, there is a rather strict relation between mixing of different HNLs with the same neutrino flavor. We find that existing exclusion regions and their expected expansions in the near future are all described by a certain limit. We call that limit pseudodegenerate and find its relation to the symmetrical limit, already studied in the literature. We also study pseudodegenerate limit and conditions under which it is achieved in three HNLs case., Comment: 27 pages, 13 figures

Cayley 4-form Phi on an 8-dimensional manifold M is a real differential form of a special algebraic type, which determines a Riemannian metric on M as well as a unit real Weyl spinor. It defines a Spin(7) structure on M, and this Spin(7) structure is integrable if and only if Phi is closed. We introduce the notion of a complex Cayley form. This is a one-parameter family of complex 4-forms Phi_tau on M of a special algebraic type. Each Phi_tau determines a real Riemannian metric on M, as well as a complex unit Weyl spinor psi_tau. The subgroup of GL(8,R) that stabilises Phi_tau, tau not=0 is SU(4), and Phi_tau defines on $M$ an SU(4) structure. We show that this SU(4) structure is integrable if and only if Phi_tau is closed. We carry out a similar construction for the split signature case. There are now two one-parameter families of complex Cayley forms. A complex Cayley form of one type defines an SU(2,2) structure, a form of the other type defines an SL(4,R) structure on M. As in the Riemannian case, these structures are integrable if and only of the corresponding complex Cayley forms are closed. Our central observation is that there exists a special member of the second one-parameter family of complex Cayley forms, which we call the Lorentzian Cayley form. This 4-form has the property that it is calibrated by Lorentzian 4-dimensional subspaces H,H^perp. In particular, in a basis adapted to such a calibration, the Lorentzian Cayley form is built from the complex self-dual 2-forms for H,H^perp. We explain how these observations solve a certain puzzle that existed in the context of 4-dimensional Lorentzian geometry., Comment: 32 pages, no figures