Unquenching the Quark-Antiquark Green’s Function

We propose a nonperturbative resummation scheme for the four-point connected quark-antiquark Greens function G⁴ that shows how the Bethe-Salpeter equation may be unquenched with respect to quark-antiquark loops. This mechanism allows to dynamically account for hadronic meson decays and multiquark structures whilst respecting the underlying symmetries. An initial approximation to the four-point Schwinger-Dyson equation – suitable for phenomenological application – is examined numerically in a couple of aspects. It is demonstrated that this approximation explicitly maintains the correct asymptotic limits and contains the physical resonance structures in the near timelike region in the quark-antiquark channel.This work was performed under grant no. COSY 41139452     

SNA’s in the Quasi-Periodic Quadratic Family

We rigorously show that there can exist Strange Nonchaotic Attractors (SNA) in the quasi-periodically forced quadratic (or logistic) map

Dynamics of the Earth’s radiation belts

In this article, we provide a short review of the current state of the field of the radiation belts of the Earth. The main attention is given to the variations of energetic particle fluxes during geomagnetic storms. Electron and proton acceleration mechanisms in the terrestrial magnetosphere are discussed. The possibility of predicting various space weather parameters using the data on relativistic electrons of the outer radiation belt is discussed.     

Elastic Properties of Graphene-Like Compounds: the Keating’s and Harisson’s Models

Physics of the Solid State - The third-order elastic constants, the pressure dependences of the second-order elastic constants, the Kleinman and Grüneisen parameters, and the thermal expansion...     

Consciousness and the Wigner’s Friend Problem

It is generally agreed that decoherence theory is, if not a complete answer, at least a great step forward towards a solution of the quantum measurement problem. It is shown here however that in the cases in which a sentient being is explicitly assumed to take cognizance of the outcome the reasons we have for judging this way are not totally consistent, so that the question has to be considered anew. It is pointed out that the way the Broglie–Bohm model solves the riddle suggests a possible clue, consisting in assuming that even very simple systems may have some sort of a proto-consciousness, but that their “internal states of consciousness” are not predictive. It is, next, easily shown that if we imagine the systems get larger, in virtue of decoherence their internal states of consciousness progressively gain in predictive value. So that, for macro-systems, they may be identified (in practice) with the predictive states of consciousness on which we ground our observational predictions. The possibilities of carrying over this idea to standard quantum mechanics are then investigated. Conditions of conceptual consistency are considered and found rather strict, and, finally, two solutions emerge, differing conceptually very much from one another but in both of which the, possibly non-predictive, generalized internal states of consciousness play a crucial role.     

Cosmic rays in the Earth’s atmosphere

This paper presents a brief historical overview of studies of cosmic rays in the Earth’s atmosphere, which were initiated and led by S.N. Vernov for over 50 years. The main results of these studies that were obtained in recent decades are given. They include the study of the processes of generation and propagation of solar cosmic rays, the modulation of galactic cosmic rays in the heliomagnetosphere, and the role of cosmic rays in atmospheric processes.     

Thermodynamic theory of the Tolman’s length

There still exists controversy on the sign and magnitude of the Tolman’s length and the Tolman’s gap.Further experimental,computational and theoretical investigations on them are needed to solve this problem.In 2006,Blokhuis and Kuipers obtained a rigorous relationship between the Tolman’s length and other thermodynamic quantities for the single-component liquid-vapour system.In the present paper,we derive two general relationships between the Tolman’s length and other thermodynamic quantities for the single-component liquid-vapour system.The relationship derived by Blokhuis and Kuipers and an earlier result turn out to be two special cases of our results.     

Ramanujan’s ‘‘Lost Notebook’’ and the Virasoro Algebra

By using the theory of vertex operator algebras, we gave a new proof of the famous Ramanujans modulus 5 modular equation from his Lost Notebook (p. 139 in [R]). Furthermore, we obtained an infinite list of q-identities for all odd moduli; thus, we generalized the result of Ramanujan.Acknowledgements It was indeed hard to trace all the known proofs of (1.1), (1.2) and (1.3). We apologize if some important references are omitted. We would like to thank Jim Lepowsky for conversations on many related subjects. A few years ago Lepowsky and the author were trying to relate classical Rogers-Ramanujan identities and Zhus work [Z]. We also thank Bruce Berndt for pointing us to [BrO] and Steve Milne for bringing [Mi] to our attention.     

New Analytical Solution of the Equilibrium Ampere’s Law Using the Walker’s Method: a Didactic Example

This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere’s law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker’s generating function in details without omitting any step. The Walker’s generating function g(ζ) is written in a new way as the tangent of an unspecified function K(ζ). In this trend, the general solution of the GS equation is expressed as exp(??2Ψ) =?4|K ^′(ζ)|²/cos²[K(ζ) ? K(ζ ^?)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris’s solution as a test, in this case K(ζ) = arctan(exp(i ζ)). In summary, one of the article purposes is to present a review of the Harris’s solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g(ζ) = tan(K(ζ)). We also present a new analytical solution to the equilibrium Ampere’s law using g(ζ) = cosh(b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.     

Young’s modulus and the Poisson’s ratio of planar and nanotubular supracrystalline structures

A method has been proposed for calculating the two-dimensional Young??s modulus and the Poisson??s ratio for planar and nanotubular structures through the components of the two-dimensional elastic rigidity tensor obtained by numerical methods. The method has been tested for graphene and two-dimensional supracrystalline sheets.     

Chevalley’s theorem for the complex crystallographic groups

Abstract

We prove that, for the irreducible complex crystallographic Coxeter group W , the following conditions are equivalent:

• a) W is generated by reflections;

• b) the analytic variety X/W is isomorphic to a weighted projective space.

The result is of interest, for example, in application to topological conformal field theory. We also discuss the status of the above statement for other types of complex crystallographic group W and certain generalizations of the statement.     

Metallic layer in the Earth’s lower mantle

We predict the insulator-metal-insulator transitions for the temperature and pressure of the lower mantle with the metal layer thickness Δh ≈ 400 km at the depth of 1400–1800 km. The insulator-metal transition has the Mott-Hubbard origin, while the second transition from metal to insulator results from spin crossover of the Fe²⁺ ions from high spin S = 2 to low spin S = 0 state. The conductivity in the metal layer may attain 250 S/m. The depth profile of the conductivity is also suggested.     

New experimental tests of the photon’s indivisibility

We consider the old foundational problem of quantum/classical optics ?C indivisibility of photon. Quantum theory predicts that in experiments on coincidence detection double clicks are impossible (up to noise); on the other hand, the known semiclassical and classical models predict a relatively high rate of coincidence. We present a model of the classical (random) wave type which predicts that in the same way as in quantum optics coincidence of clicks is a rare event. However, this model has a new prediction compared to quantum optics, namely, that the rate of double clicks depends substantially on the discrimination threshold of a detector. We propose to perform new detailed tests to check the discrimination threshold dependence predicted by our model. In experiments on coincidence detection performed to date, for example, the Grangier experiment does not contain statistical data on the threshold dependence.     

On the CHSH Form of Bell’s Inequalities

A common mistake present in the derivation of the usually known as the CHSH form of Bell’s inequalities is pointed out. References and comments to the correct approach are given. This error does not alter the final result and only affects the logical consistency of the derivation, but since it seems to be a widespread misconception regarding the roll and interpretation of the of use of hidden variables in Bell’s theorem it is considered to be of general interest.     

Neutron interference in the Earth’s gravitational field

This work relates to the famous experiments, performed in 1975 and 1979 by Werner et al., measuring neutron interference and neutron Sagnac effects in the earth’s gravitational field. Employing the method of Stodolsky in its weak field approximation, explicit expressions are derived for the two phase shifts, which turn out to be in agreement with the experiments and with the previously obtained expressions derived from semi-classical arguments: these expressions are simply modified by relativistic correction factors.     

Registering Jovian electrons in the Earth’s orbit

The results from observing Jovian electrons in the vicinity of the Earth are discussed. Variations in Jovian electron flows are observed during 14 rotations of the Sun in 2007–2008. The results are analyzed by assuming the existence of magnetic traps in the space between the Sun and Jupiter that are filled with electrons near Jupiter, and are then registered when the traps pass by the Earth. The average period of variation in the Jovian electron flow during the 14 solar rotations is 26.2 days instead of the expected synodic period of the Sun–Earth system equal to 27.3 days. An explanation for this phenomenon is proposed.     

On Zurek’s Derivation of the Born Rule

Recently, W. H. Zurek presented a novel derivation of the Born rule based on a mechanism termed environment-assisted invariance, or envariance [W. H. Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and identify fundamental assumptions that have implicitly entered into it, emphasizing issues that any such derivation is likely to face.     

Maxwell’s Equations as the One-Photon Quantum Equation

Maxwell's equations (the Faraday and Ampère-Maxwell laws) can be presented as a three-component equation in a way similar to the two-component neutrino equation. However, in this case, the electric and magnetic Gauss laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have also shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable and well understood quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum theories.     

Beyond the LAN: Ethernet’s Evolution into the Public Network

This article details the evolution of Ethernet into Gigabit Ethernet and how this LAN-based technology has undergone major transformations over time. From its data rates and distances to supported media and functionality, Ethernet has greatly improved, enabling it to surmount many of its former limitations and in so doing to expand beyond the LAN into the MAN and now even the WAN. In this article, Pioneer Consulting explores the evolution further by focusing on some of the major technological directions in the Ethernet equipment industry.     

On the theory of temperature distribution over the Earth’s atmosphere

The steady-state temperature distribution over the Earth’s atmosphere is described in terms of the law of degradation of energy (or the principle of entropy increase). The distribution is in satisfactory agreement with meteorological measurements. Using constructed dissipative function \(\dot Q\), a nonlinear differential equation is rigorously derived that describes the synergetics of the steady-state temperature distribution over the atmosphere, from troposphere to exosphere. A detailed analysis of solutions of this equation makes it possible to qualitatively explain nontrivial dependence T(z) over an atmospheric area inhomogeneous in chemical composition. This fact substantiates the correctness of formal introduction and necessity to consider interaction between blackbody radiation and convective stream. It is argued that hard gamma quanta far from the violet part of the spectrum are responsible for heat radiation coming from the Sun.