Space–time structure of new physics with polarized beams at the linear collider

We approach the issue of the discovery of new physics at high energies associated with the proposed International Linear Collider in the presence of longitudinal as well as transverse electron and positron beam polarization. We determine the beam polarization dependence and the angular distribution of a particle of arbitrary spin in a one-particle inclusive final state produced in e⁺e^- collisions through the interference of γ or Z amplitude with the amplitude from new interactions having arbitrary space–time structure. We thus extend the results of Dass and Ross, proposed at the time of the discovery of neutral currents, to beyond the standard model currents. We also extend the case of e⁺e^- annihilation in the s-channel to the production of bosons due to t- and u-channel processes. Our work provides an approach to model-independent determination of the space–time structure of beyond the standard model interactions. We briefly discuss applications of the framework to popular extensions of the standard model, and demonstrate that our framework is general enough to account for certain results in the minimal supersymmetric standard model.     

Dendrogramic Representation of Data: CHSH Violation vs. Nonergodicity

This paper is devoted to the foundational problems of dendrogramic holographic theory (DH theory). We used the ontic–epistemic (implicate–explicate order) methodology. The epistemic counterpart is based on the representation of data by dendrograms constructed with hierarchic clustering algorithms. The ontic universe is described as a p-adic tree; it is zero-dimensional, totally disconnected, disordered, and bounded (in p-adic ultrametric spaces). Classical–quantum interrelations lose their sharpness; generally, simple dendrograms are “more quantum” than complex ones. We used the CHSH inequality as a measure of quantum-likeness. We demonstrate that it can be violated by classical experimental data represented by dendrograms. The seed of this violation is neither nonlocality nor a rejection of realism, but the nonergodicity of dendrogramic time series. Generally, the violation of ergodicity is one of the basic features of DH theory. The dendrogramic representation leads to the local realistic model that violates the CHSH inequality. We also considered DH theory for Minkowski geometry and monitored the dependence of CHSH violation and nonergodicity on geometry, as well as a Lorentz transformation of data.     

Interacting Gravitational and Dirac Fields with Torsion

A general interaction scheme is formulated in a general space–time with torsion from the action principle by considering the gravitational, the Dirac, and the torsion field as independent fields. Some components of the torsion field come out to be automatically zero. Both the resulting Einstein-like and the Dirac-like fields equations contain nonlinear terms given by a self-interaction of the Dirac spinor and originally produced by torsion. The theory is specialized to the Robertson–Walker space–time without torsion. To solve he corresponding equations, that still have a complex structure, the spin coefficients have to be calculated explicitly from the tetrad employed. A solution, even if simple and elementary, is then determined.     

Generally Covariant Schrödinger Equation in Newton–Cartan Space–Time. Part II

Schrödinger equation in Newton–Cartan space–time can be obtained from Einstein equivalence principle, that is firstly one should obtain generally covariant Schrödinger's equation in Galilean space–time (using generally covariant Hamilton–Jacobi formalism and Schrödinger's Ansatz, as was previously shown) and get Schrödinger's equation in Newton–Cartan space–time with the help of equivalence principle. The equation possesses a gauge freedom f connected with phase transformation of the wave function. But absolute elements of the space–time possess a symmetry group and they depend on f. So, a natural problem arises: to find the gauge f in which absolute elements become invariant with respect to the group. In the paper the gauge f is found with the help of space–time properties, that is transformation rule of the wave function is obtained from the space–time structure (in Newton–Cartan space–time). The special form of f is found in the case when the space–time as a whole possesses a symmetry.     

Assessing Earthquake Forecast Performance Based on b Value in Yunnan Province,China

Many studies have shown that b values tend to decrease prior to large earthquakes. To evaluate the forecast information in b value variations, we conduct a systematic assessment in Yunnan Province, China, where the seismicity is intense and moderate–large earthquakes occur frequently. The catalog in the past two decades is divided into four time periods (January 2000–December 2004, January 2005–December 2009, January 2010–December 2014, and January 2015–December 2019). The spatial b values are calculated for each 5-year span and then are used to forecast moderate-large earthquakes (M ≥ 5.0) in the subsequent period. As the fault systems in Yunnan Province are complex, to avoid possible biases in b value computation caused by different faulting regimes when using the grid search, the hierarchical space–time point-process models (HIST-PPM) proposed by Ogata are utilized to estimate spatial b values in this study. The forecast performance is tested by Molchan error diagram (MED) and the efficiency is quantified by probability gain (PG) and probability difference (PD). It is found that moderate–large earthquakes are more likely to occur in low b regions. The MED analysis shows that there is considerable precursory information in spatial b values and the forecast efficiency increases with magnitude in the Yunnan Province. These results suggest that the b value might be useful in middle- and long-term earthquake forecasts in the study area.     

Effect of Torsion in Dirac Equation for Coulomb Potential in Robertson–Walker Space–Time

The Dirac equation with Coulomb-like potential and self-interaction term, that originates from torsion, is studied in the Robertson–Walker space–time. It is shown that the angular dependence of the equation can be separated also in presence of nonlinear terms. Under reasonable physical assumptions, the time dependence is also separated. An extended perturbative calculation can then be applied qualitatively. The conclusion is that the perturbation of the energy levels of the system, as consequence of the self-interacting term, is not relevant on physical grounds.     

Computer Simulations for Some One-Dimensional Models of Random Walks in Fluctuating Random Environment

We report some results of computer simulations for two models of random walks in random environment (rwre) on the one-dimensional lattice for fixed space–time configuration of the environment (“quenched rwre”): a “Markov model” with Markov dependence in time, and a “quasi stationary” model with long range space–time correlations. We compare with the corresponding results for a model with i.i.d. (in space time) environment. In the range of times available to us the quenched distributions of the random walk displacement are far from gaussian, but as the behavior is similar for all three models one cannot exclude asymptotic gaussianity, which is proved for the model with i.i.d. environment. We also report results on the random drift and on some time correlations which show a clear power decay     

On Waylen's Regular Axisymmetric Similarity Solutions

We review the similarity solutions proposed by Waylen for a regular time–dependent axisymmetric vacuum space–time, and show that the key equation introduced to solve the invariant surface conditions is related by a Bäcklund transform to a restriction on the similarity variables. We further show that the vacuum space–times produced via this path automatically possess a (possibly homothetic) Killing vector, which may be time–like.     

Coulomb scattering for scalar field in Schrödinger picture

The scattering of a charged scalar field on Coulomb potential on de Sitter space–time is studied using the solution of the free Klein–Gordon equation. We find that the scattering amplitude is independent of the choice of the picture and in addition the total energy is conserved in the scattering process.     

Unusual Surface Latent Heat Flux Variations and Their Critical Dynamics Revealed before Strong Earthquakes

We focus on the possible thermal channel of the well-known Lithosphere–Atmosphere–Ionosphere Coupling (LAIC) mechanism to identify the behavior of thermal anomalies during and prior to strong seismic events. For this, we investigate the variation of Surface Latent Heat Flux (SLHF) as resulting from satellite observables. We demonstrate a spatio-temporal variation in the SLHF before and after a set of strong seismic events occurred in Kathmandu, Nepal, and Kumamoto, Japan, having magnitudes of 7.8, 7.3, and 7.0, respectively. Before the studied earthquake cases, significant enhancements in the SLHF were identified near the epicenters. Additionally, in order to check whether critical dynamics, as the signature of a complex phenomenon such as earthquake preparation, are reflected in the SLHF data, we performed a criticality analysis using the natural time analysis method. The approach to criticality was detected within one week before each mainshock.     

中低能速度能区离子与H,He原子碰撞中的经典电子俘获截面

Bohr-Lindhard模型被用来描述中低能速度能区离子—原子碰撞中的经典电子俘获过程。根据离子与原子的作用时间与碰撞参数的关系,建立俘获几率对碰撞参数的依赖性,碰撞参数范围被限定在俘获半径之内。在该模型的框架内,人们试图通过电子的空间分布函数来研究所有碰撞参数的贡献,但存在较为复杂的数值计算。基于Bohr-Lindhard模型,本工作提出通过简单的指数衰减函数来描述电子俘获几率对碰撞参数的依赖性,计算了Aq+(q = 2~6)-H碰撞中的单电子俘获截面和Aq+(q = 3~6)-He碰撞中的双电子俘获截面,计算结果与已有实验数据符合很好,很好地描述了低能和中能区的电子俘获截面随能量和电荷态的变化,该工作还可计算其他不同电荷态离子与He和H靶的电子俘获截面。     

Vertex Algebras in Higher Dimensions and Globally Conformal Invariant Quantum Field Theory

We propose an extension of the definition of vertex algebras in arbitrary space–time dimensions together with their basic structure theory. A one–to–one correspondence between these vertex algebras and axiomatic quantum field theory (QFT) with global conformal invariance (GCI) is constructed.     

Cross-spectral purity of the Stokes parameters

We extend the concept of cross-spectral purity from the spectral density to the polarization properties of electromagnetic fields by considering the polarization Stokes parameters. We show that purity conditions similar to those in the case of electromagnetic cross-spectral purity can be derived for all the Stokes parameters. Furthermore, we introduce a situation of strict cross-spectral purity which leads to the equality of the degrees of coherence for electromagnetic fields in the space–time and space–frequency domains.     

Black Hole Entropy: Membrane Approach

The wall contribution character of the Bekenstein–Hawking entropy in the brick-wall model leads us to propose a new method of computing the entropy of a black hole. In our model, the entropy is attributed to the dynamical degrees of the field covering the two dimensional membranes just outside the horizon. A cutoff different from the model of 't Hooft is necessarily introduced. It can be treated as an increase in horizon because of the space–time fluctuations. It is also shown that our method can be applied to the nonstatic case, such as Vaidya–deSitter space–time, and the final result relies on a time-dependent cutoff different from the brick-wall model.     

Spinning Particles in NUT–Reissner–Nordstrom Space–Time

We study the geodesic motion of pseudo-classical spinning particles in the NUT–Reissner–Nordstrom space–time. We investigate the generalized Killing equations for spinning space and derive the constants of the motion in terms of the solutions of these equations. We give an analysis of the motion on a cone and on a plane.     

Phase recovery from fringe patterns using the continuous wavelet transform

Interferometry is well established as an optical technique in which a measurand is encoded as the phase of a periodically varying intensity pattern. In view of the inherent accuracy of interferometry, many methods have been developed to retrieve the phase from images of the fringe pattern. Our focus in this paper is one such technique—the continuous wavelet transform (CWT). We begin by reviewing the CWT and the space–spatial–frequency localisation properties of wavelets. We show that a path which follows the maximum modulus of the CWT (the wavelet ridge) gives the instantaneous fringe frequency as a function of spatial displacement. The phase is automatically and trivially obtained, without discontinuities, by integration. Examples of practical wavelets are given and algorithms to isolate the wavelet ridge reviewed.     

Geodesic connectedness and conjugate points in GRW space–times

Given two points of a generalized Robertson–Walker space–time, the existence, multiplicity and causal character of geodesics connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional space–times and to GRW space–times satisfying the timelike convergence condition are also found.     

Dirac Equation in Space–Time with Torsion

The Dirac equation in a curved space–time endowed with compatible affine connection is reconsidered. After a detailed decomposition of the total action, the equation is obtained by varying with respect to the Dirac spinor and the torsion field. The result is a known Dirac-like equation with constraints that can be interpreted as the equation of a self-interacting spin 1/2 particle in curved space–time. The scheme is then translated into the language of the 2-spinor formalism of curved space–time based on the choice of a null tetrad frame. The spinorial equation so obtained coincides with the standard one in case of no torsion, while in general it remains a nonlinear equation describing a self-interacting spin 1/2 particle. The nonlinearity is produced by the interaction of the particle with its own current that remains conserved as in the free torsion case.     

Information Processing in the Brain as Optimal Entropy Transport: A Theoretical Approach

We consider brain activity from an information theoretic perspective. We analyze the information processing in the brain, considering the optimality of Shannon entropy transport using the Monge–Kantorovich framework. It is proposed that some of these processes satisfy an optimal transport of informational entropy condition. This optimality condition allows us to derive an equation of the Monge–Ampère type for the information flow that accounts for the branching structure of neurons via the linearization of this equation. Based on this fact, we discuss a version of Murray’s law in this context.