Nonzero Length Research Articles

Penetration of arbitrary double potential barriers with probability unity: Implications for testing the existence of a minimum length

Quantum tunneling across double potential barriers is studied. With the assumption that the real space is a continuum, it is rigorously proved that large barriers of arbitrary shapes can be penetrated by low-energy particles with a probability of unity, i.e., realization of resonant tunneling (RT), by simply tuning the interbarrier spacing. The results are demonstrated by tunneling of electrons and protons, in which resonant and sequential tunneling are distinguished. The critical dependence of tunneling probabilities on the barrier positions not only demonstrates the crucial role of phase factors but also points to the possibility of ultrahigh accuracy measurements near resonance. By contrast, the existence of a nonzero minimum length puts upper bounds on the barrier size and particle mass, beyond which effective RT ceases. A scheme is suggested for dealing with the practical difficulties arising from the delocalization of particle position due to the uncertainty principle. This work opens a possible avenue for experimental tests of the existence of a minimum length based on atomic systems. Published by the American Physical Society 2024

Applicability of the Névot-Croce factor in analysis of X-ray reflection from a rough surface

Usability of the Névot-Croce (NC) formula for calculation of the reflectivity from a surface with high-frequency roughness is critically analyzed. First, the necessary conditions of the NC factor applicability are identified quantitatively in the limiting case of vanishingly small correlation length of roughness. Second, the conditions are established, when the nonzero correlation length of real surface roughness can be reckoned as vanishingly small. Third, basing on available in literature experimental data, these conditions are compared with the experimental values of the correlation length of high-frequency roughness. The final conclusions concerning applicability of the NC formula for hard X-ray to extreme ultraviolet radiation are formulated.

Monodisperse Molecular Models for the sp Carbon Allotrope Carbyne; Syntheses, Structures, and Properties of Diplatinum Polyynediyl Complexes with PtC20Pt to PtC52Pt Linkages.

Extended conjugated polyynes provide models for the elusive sp carbon polymer carbyne, but progress has been hampered by numerous synthetic challenges. Stabilities appear to be enhanced by bulky, electropositive transition-metal endgroups. Reactions of trans-(C6F5)(p-tol3P)2Pt(C≡C)nSiEt3 (n = 4-6, PtCxSi (x = 2n)) with n-Bu4N+F-/Me3SiCl followed by excess tetrayne H(C≡C)4SiEt3 (HC8Si) and then CuCl/TMEDA and O2 give the heterocoupling products PtCx+8Si, PtCx+16Si, and sometimes higher homologues. The PtCx+16Si species presumably arise via protodesilylation of PtCx+8Si under the reaction conditions. Chromatography allows the separation of PtC16Si, PtC24Si, and PtC32Si (from n = 4), PtC18Si and PtC26Si (n = 5), or PtC20Si and PtC28Si (n = 6). These and previously reported species are applied in similar oxidative homocouplings, affording the family of diplatinum polyynediyl complexes PtCxPt (x = 20, 24, 28, 32, 36, 40 in 96-34% yields and x = 44, 48, 52 in 22-7% yields). These are carefully characterized by 13C NMR, UV-visible, and Raman spectroscopy and other techniques, with particular attention to behavior as the Cx chain approaches the macromolecular limit and endgroup effects diminish. The crystal structures of solvates of PtC20Pt, PtC24Pt, and PtC26Si, which feature the longest sp chains structurally characterized to date, are analyzed in detail. All data support a polyyne electronic structure with a nonzero optical band gap and bond length alternation for carbyne.

Deterministic n-person shortest path and terminal games on symmetric digraphs have Nash equilibria in pure stationary strategies

We prove that a deterministic n-person shortest path game has a Nash equlibrium in pure and stationary strategies if it is edge-symmetric (that is (u, v) is a move whenever (v, u) is, apart from moves entering terminal vertices) and the length of every move is positive for each player. Both conditions are essential, though it remains an open problem whether there exists a NE-free 2-person non-edge-symmetric game with positive lengths. We provide examples for NE-free 2-person edge-symmetric games that are not positive. We also consider the special case of terminal games (shortest path games in which only terminal moves have nonzero length, possibly negative) and prove that edge-symmetric n-person terminal games always have Nash equilibria in pure and stationary strategies. Furthermore, we prove that an edge-symmetric 2-person terminal game has a uniform (subgame perfect) Nash equilibrium, provided any infinite play is worse than any of the terminals for both players.

Design and Synthesis of the Gravity Compensator with a Non-zero Length Spring

Design and Synthesis of the Gravity Compensator with a Non-zero Length Spring

Dual CFT on a dyonic Kerr-Sen black hole and its gauged and ultraspinning counterparts

We demonstrate that rotating dyonic black holes in Einstein-Maxwell-Dilaton-Axion (EMDA) theory is holographically dual with 2D conformal field theory. We first investigate the duality on dyonic Kerr-Sen black hole with non-vanishing dilaton and axion charges. The near-horizon geometry of extremal dyonic Kerr-Sen spacetime possesses the $SL(2,R) \times U (1)$ isometry allowing to employ the asymptotic symmetry group method to find the corresponding central charge. We find two different branches of the mass which correspond to CFT with two different central charges $c_L=12am_+$ and $c_L=12am_-$. The exact agreement between the Bekenstain-Hawking entropy and entropy from CFT is then found also in two different branches of extremal entropy. Furthermore, we demonstrate that this duality is robust insofar for non-zero AdS length. We show that the duality holds for both dyonic Kerr-Sen-AdS black hole and its ultraspinning counterpart. In both cases, we obtain the expected entropy from CFT which matches exactly with the Bekenstein-Hawking entropy. Since dyonic and axion charges are proportional to $1/m$, we note that there are possibly more than two branches of the central charge for non-zero AdS length in terms of mass. When we turn off dyonic charge, the axion charge vanishes showing the results of Kerr-Sen-AdS black hole. Moreover, when we assume the equal electromagnetic charges, it recovers the results when the dilaton charge vanishes. In the end, we compare the results of dyonic Kerr-Sen-AdS black hole and its ultraspinning counterpart to those of the dyonic Kerr-Newman-AdS black hole and the ultraspinning counterpart. Depending on the dyonic charge parameters, it is found that extremal ultraspinning dyonic Kerr-Sen-AdS black hole is not always superentropic.

Generalized uncertainty principle and burning stars

Gamow’s theory of the implications of quantum tunneling for star burning has two cornerstones: quantum mechanics and the equipartition theorem. It has been proposed that both of these foundations are affected by the existence of a non-zero minimum length, which usually appears in quantum gravity scenarios and leads to the generalized uncertainty principle (GUP). Mathematically, in the framework of quantum mechanics, the effects of the GUP are considered as perturbation terms. Here, generalizing the de Broglie wavelength relation in the presence of a minimal length, GUP corrections to the Gamow temperature are calculated, and in parallel, an upper bound for the GUP parameter is estimated.

Constraining the generalized uncertainty principle with neutron interferometry

The non-zero minimal length arises in various theories of gravity, leading to the so-called generalized uncertainty principle (GUP). In this short paper we analyze the GUP effects on neutron interferometry, showing that the obtained phase shifts depend on the mass and velocity of the particle. New upper bounds on the dimensionless GUP parameter have been found that are in agreement with the literature.

Magnonic skin effect and magnon valve effect in an antiferromagnetically coupled heterojunction

We theoretically study the scattering behavior of spin waves (SWs) at the interface of an antiferromagnetically coupled (AFMC) heterojunction. It is shown that the SWs passing through the interface are evanescent and the incident waves are all reflected back, demonstrating a magnetization-dependent magnon blocking effect in this structure. We also analytically derive the expressions for the decay length of the evanescent waves (EWs). The theoretical result indicates that with the increase of the spin-wave (SW) frequency, the decay length decreases and the EWs are more concentrated at the interface, showing a magnonic skin effect (MSE) which is similar to the skin effect of electromagnetic waves. Furthermore, a positive magnonic Goos-H\"anchen shift (MGHS) of the reflected waves is also predicted. It can be understood by an effective reflection interface shift induced by the nonzero decay length of the EWs. The results of micromagnetic simulations are consistent well with all the theoretical findings. Based on the above findings, we also propose a magnon valve without spacers, which shows 100% on-off ratio for magnons. Our work provides insights into SW transmissions in the system of AFMC heterostructures and will serve as a promising tool for future magnonic devices.

Oscillatory behaviour analysis of a liquid rise in cylindrical capillaries

We conduct a rigorous mathematical analysis of an oscillatory behaviour during the capillary flow. Our investigation concerns a nonlinear ODE modelling rise in a narrow vertical tube. This equation has been proposed by many authors as a generalization and improvement over the classical Lucas-Washburn model. The extension includes components related to a non-zero immersion length and to a discontinuous variable describing the exit/entrance effect at the bottom of the tube. We propose an arbitrarily accurate regularization of the non-smooth component in order to prove several results concerning dynamical behaviour of the exact solution: existence and uniqueness, estimates, and switch of the behaviour from monotone to oscillatory. We have found that the latter is independent of the chosen regularization which makes the model robust. Furthermore, we applied the Lyapunov stability analysis to deliver a comprehensive description of the asymptotic behaviour of trajectories

Consultation length and no-show prediction for improving appointment scheduling efficiency at a cardiology clinic: A data analytics approach

BackgroundThe observed consultation length at specialty clinics, such as cardiology care, is represented by two underlying groups - one with zero service time due to patient no-shows, and the other characterized by positive values with high variance. This inconstancy affects the scheduler’s ability to accurately estimate consultation length, which, in turn, hinders effective utilization of the clinic’s resources and timely access to care. The objectives of this study were to: (i) predict the consultation length by accounting for its semicontinuous nature (i.e., zero in case of no-shows and positive otherwise), using machine learning (ML) algorithms, (ii) identify important features for predicting no-shows and non-zero consultation length, and (iii) assess the impact of integrating the ML-based prediction with the appointment scheduling system. MethodsWe used two-years of data extracted from the electronic medical records of a cardiology clinic. By leveraging 16 predictors pertaining to the patient, appointment, and doctor, a two-part ML-based approach was developed to handle the semicontinuous consultation length. Supervised classification models were employed to predict no-shows (i.e., categorize the consultation length as zero or positive), and regression algorithms were developed for estimating non-zero consultation lengths. Three algorithms, namely, random forests, stochastic gradient boosting, and deep neural networks, were individually employed for both no-show classification and positive consultation length prediction. Finally, the best performing classification and regression models were combined to establish the complete two-part model, and its prediction error on new data is benchmarked against the clinic’s current performance. The evaluation metrics for classification models were area under the receiver operating characteristic curve (AUC-ROC) and area under the precision-recall curve (AUC-PR). The prediction performance of regression algorithms was evaluated by mean absolute error (MAE), root mean squared error (RMSE), and mean absolute percentage error (MAPE). A simulation modeling approach was adopted to ascertain the effectiveness of using ML-based prediction for scheduling decisions as opposed to the clinic’s current strategy. ResultsAmong the classification models tested, stochastic gradient boosted classification tree (SGBCT) demonstrated best performance (AUC-ROC = 0.85, AUC-PR = 0.64). For positive consultation length prediction, deep neural network regressor (DNNR) resulted in lowest prediction error (MAE = 8.55, RMSE = 6.88, MAPE = 12.24). The complete two-part model (SGBCT + DNNR) outperformed the clinic’s approach to consultation length estimation by achieving 50 % and 52 % reduction in RMSE and MAE, respectively. Further adopting it for appointment scheduling could reduce the patient waiting time and doctor idle time by 56 % and 52 %, respectively. Besides, several clinical insights, along with critical features for no-show and consultation length prediction, were also identified from our proof-of-concept study. ConclusionThis study demonstrates that routine clinical tasks such as estimation of consultation length and no-shows can be accurately predicted using ML algorithms, and subsequently integrated into the clinical scheduling system to improve resource utilization and reduce patient waiting time.

One-dimensional harmonic oscillator problem and its hidden SU(1,1) symmetry in the presence of a minimal length

The one-dimensional harmonic oscillator in the presence of a minimal length possesses a hidden SU(1,1) symmetry. This symmetry makes it possible to construct the deformed canonical coherent states. These states turn out to be ground states of the deformed dipolar coupling. Indeed, the coupling to the external field may be considered as a dipolar coupling of a charged dipole to an electric field in one dimension. The spectrum is constructed algebraically. The wave functions in the momentum space are then reported. We have found that the momentum probability density of order n possesses n+1 vertices and these vertices of excited states disappear from n−1 when the deformation parameter increases. So, the particle in these states loses its point nature and can even explore space. The Heisenberg uncertainty relation involving a non-zero minimal length induces then a finite lower bound to spatial localisation.

Mathematical Modeling in the Study of the Ricci Operator on Four-Dimensional Locally Homogeneous (Pseudo)Riemannian Manifolds with Isotropic Weyl Tensor

It is known that a locally homogeneous manifold can be obtained from a locally conformally homogeneous (pseudo)Riemannian manifolds by a conformal deformation if the Weyl tensor (or the Schouten-Weyl tensor in the three-dimensional case) has a nonzero squared length. Thus, the problem arises of studying (pseudo)Riemannian locally homogeneous and locally conformally homogeneous manifolds, the Weyl tensor of which has zero squared length, and itself is not equal to zero (in this case, the Weyl tensor is called isotropic).
 One of the important aspects in the study of such manifolds is the study of the curvature operators on them, namely, the problem of restoring a (pseudo)Riemannian manifold from a given Ricci operator.
 The problem of the prescribed values of the Ricci operator on 3-dimensional locally homogeneous Riemannian manifolds has been solved by O. Kowalski and S. Nikcevic. Analogous results for the one-dimensional and sectional curvature operators were obtained by D.N. Oskorbin, E.D. Rodionov, and O.P Khromova.
 This paper is devoted to the description of an example of studying the problem of the prescribed Ricci operator for four-dimensional locally homogeneous (pseudo) Riemannian manifolds with a nontrivial isotropy subgroup and isotropic Weyl tensor.

Viscometric functions and rheo-optical properties of dilute polymer solutions: Comparison of FENE-Fraenkel dumbbells with rodlike models

Rigid macromolecules or polymer chains with persistence length on the order of the contour length (or greater) have traditionally been modelled as rods or very stiff springs. The FENE-Fraenkel-spring dumbbell, which is finitely extensible about a non-zero natural length with tunable harmonic stiffness, is one such model which has previously been shown to reproduce bead–rod behaviour in the absence of hydrodynamic interactions. The force law for the FENE-Fraenkel spring reduces to the Hookean or FENE spring force law for appropriately chosen values of the spring parameters. It is consequently possible to explore the crossover region between the limits of bead–spring and bead–rod behaviour by varying the parameters suitably. In this study, using a semi-implicit predictor–corrector Brownian dynamics algorithm, the FENE-Fraenkel spring is shown to imitate a rod with hydrodynamic interactions when spring stiffness, extensibility and simulation timestep are chosen carefully. By relaxing the spring stiffness and extensibility, the FENE-Fraenkel spring can also reproduce spring-like behaviour, such as a crossover from −1∕3 to −2∕3 power-law scaling in the viscosity with shear rate, and a change from positive to negative second normal stress difference. Furthermore, comparisons with experimental data on the viscosity and linear dichroism of high aspect ratio, rigid macromolecules shows that the extensibility and stiffness of the FENE-Fraenkel spring allows for equal or improved accuracy in modelling inflexible molecules compared to rodlike models.

More on the regularized big bang singularity

The big bang singularity of the expanding-universe Friedmann solution of the Einstein gravitational field equation can be regularized by the introduction of a degenerate metric and a nonzero length scale $b$. The result is a nonsingular bounce of the cosmic scale factor with a contracting prebounce phase and an expanding postbounce phase. The corresponding maximum values of the curvature and the energy density occur at the moment of the bounce and are proportional to powers of $1/b$. This article presents a detailed calculation of the dynamics of such a nonsingular bounce. In addition, a comparison is made between this nonsingular bounce and the bounces of loop quantum cosmology and string cosmology.

Modified Anti Snyder Model with Minimal Length, Momentum Cutoff and Convergent Partition Function

In this paper we consider the possible modification of the anti Snyder model so that it have the non-zero minimal length, momentum cutoff and the convergent partition function. For the modified anti Snyder model we discuss the representations, eigenstates of position operator, momentum wave function, one dimensional box problem, and harmonic oscillator problem. We extend this model into D-dimensional case so that it also may guarantee the convergent partition function. Using this partition function we discuss the thermodynamics of the free particle system and cosmological constant problem.

Изотропный тензор Вейля на четырехмерных локально однородных псевдоримановых многообразиях

The locally homogeneous (pseudo)Riemannian manifolds are studied by many mathematicians. The more general cases of these manifolds are spaces where conformal transformations act transitively. They are also called the locally conformally homogeneous (pseudo)Riemannian manifolds. It is worth noting that such manifolds were investigated both for the case of Riemannian metric, and for the case of pseudo-Riemannian metric. The work of E.D. Ro dionov, V.V. Slavskii, and L.N. Chibrikova claims that if there is a Weyl tensor with the non-zero squared length for a manifold of dimension n ≥ 4, then a locally homogeneous space can be obtained from a locally conformally homogeneous (pseudo)Riemannian space by means of a conformal deformation. Hence, there should be a naturally arisen problem to investigate such (pseudo)Riemannian locally conformally homogeneous and locally homogeneous manifolds for which the squared length of the Weyl tensor equals to zero, but the tensor itself is not equal to zero (such a Weyl tensor is also called isotropic). In this paper, we describe a step-by-step algorithm to solve the problem of classification of four-dimensional locally homogeneous pseudo-Riemannian manifolds with an isotropic Weyl tensor and a non-trivial isotropy subgroup.

The role of behavioral changes and prompt treatment in the control of STIs.

In this paper, we study general recovery functions and treatment in the dynamics of an model for sexually transmitted infections with nonzero partnership length. It is shown how partnership dynamics influences the predicted prevalence at the steady state and the basic reproduction number. Sobol's indices are used to evaluate the contribution of model parameters to the overall variance of . The recovery functions studied here take into account that society's capacity to provide treatment is limited when the number of infected individuals is large. Bifurcation analysis is used to establish a relationship between an alert level of prevalence and the minimum recovery time that guarantees the eradication of the disease. We also show that a backward bifurcation can occur when there are delays in the treatment of infected individuals.

Jeans-type instability of a complex self-interacting scalar field in general relativity

We study the gravitational instability of a general relativistic complex scalar field with a quartic self-interaction in an infinite homogeneous static background. This quantum relativistic Jeans problem provides a simplified framework to study the formation of the large-scale structures of the Universe in the case where dark matter is made of a scalar field. The scalar field may represent the wave function of a relativistic self-gravitating Bose-Einstein condensate. Exact analytical expressions for the dispersion relation and Jeans length $\lambda_J$ are obtained from a hydrodynamical representation of the Klein-Gordon-Einstein equations. When relativistic effects are fully accounted for, we find that the perturbations are stabilized at very large scales of the order of the Hubble length $\lambda_H$. Numerical applications are made for ultralight bosons without self-interaction (fuzzy dark matter), for bosons with a repulsive self-interaction, and for bosons with an attractive self-interaction (QCD axions and ultralight axions). We show that the Jeans instability is inhibited in the ultrarelativistic regime (early Universe and radiationlike era) because the Jeans length is of the order of the Hubble length ($\lambda_J\sim\lambda_H$), except when the self-interaction of the bosons is attractive. By contrast, structure formation can take place in the nonrelativistic regime (matterlike era) for $\lambda_J\le \lambda\le \lambda_H$. Since the scalar field has a nonzero Jeans length due to its quantum nature (Heisenberg uncertainty principle or quantum pressure due to the self-interaction of the bosons), it appears that the wave properties of the scalar field can stabilize gravitational collapse at small scales, providing halo cores and suppressing small-scale linear power. This may solve the CDM crisis such as the cusp problem and the missing satellite problem.

Исследование четырехмерных локально однородных (псевдо)римановых многообразий с изотропным тензором Схоутена — Вейля

Локально однородные (псевдо)римановы многообразия изучались в работах многих математиков. Их обобщением являются локально конформно однородные (псевдо)римановы пространства, на которых транзитивно действуют конформные преобразования. Такие многообразия также ранее исследовались как в римановом случае, так и в псевдоримановом.В работе Е.Д. Родионова, В.В. Славского и Л.Н. Чибриковой было доказано, что из локально конформно однородного (псевдо)риманова пространства можно с помощью конформной деформации получить локально однородное пространство, если тензор Вейля (или тензор Схо-утена — Вейля в трехмерном случае) имеет ненулевой квадрат длины. Таким образом возникает задача об изучении (псевдо)римановых локально однородных и локально конформно однородных многообразий, тензор Схоутена — Вейля которых имеет нулевой квадрат длины, а сам не равен нулю.В данной работе приводится алгоритм, с помощью которого можно решить задачу о классификации четырехмерных локально однородных (псевдо)римановых многообразий с нетривиальной подгруппой изотропии и изотропным тензором Схоутена — Вейля.DOI 10.14258/izvasu(2018)4-14