Legendre Transformation for Regularizable Lagrangians in Field Theory

Hamilton equations based not only upon the Poincaré–Cartan equivalent of a first-order Lagrangian, but also upon its Lepagean equivalent are investigated. Lagrangians which are singular within the Hamilton–De Donder theory, but regularizable in this generalized sense are studied. Legendre transformation for regularizable Lagrangians is proposed and Hamilton equations, equivalent with the Euler–Lagrange equations, are found. It is shown that all Lagrangians affine or quadratic in the first derivatives of the field variables are regularizable. The Dirac field and the electromagnetic field are discussed in detail.     

Second-Order Subexponential Sequences and the Asymptotic Behavior of Their De Pril Transform

Suppose that { f(n), n N ₀ } is a sequence of positive real numbers and suppose that the sequence { a(n), n N ₀ } is given by a(0) = 0, and, for n 1, by the convolution equation nf(n) = a* f(n). The resulting sequence is denoted by a(n) = _f (n) and is called the De Pril transform of { f(n), n N ₀ } . In this paper, we consider first- and second-order asymptotic behavior of { _{f (n), n N 0} } for a large class of subexponential sequences { f(n), n N ₀ } . We also discuss some applications.     

A one-dimensional lattice model for a quantum mechanical free particle

Two types of particles, A and B with their corresponding antiparticles, are defined in a onedimensional cyclic lattice with an odd number of sites. In each step of time evolution, each particle acts as a source for the polarization field of the other type of particle with nonlocal action but with an effect decreasing with the distance: . It is shown that the combined distribution of these particles obeys the time evolution of a free particle as given by quantum mechanics.     

Charge exchange collisions of H<Superscript>+</Superscript>/D<Superscript>+</Superscript> ions with alkaline Earth atoms (Ca,Mg)

The Classical Trajectory Monte Carlo (CTMC) Method has been used to calculate the differential, partial and total single electron capture cross sections for the collision of H⁺/D⁺ with Ca and Mg atoms in the energy range of 1–100 keV. The differential cross sections at angles near the diffraction limit (<0.1^○) in both systems show a forward peak followed by an asymptotic fall at higher angles. Total and partial capture cross sections are found to be in good agreement with the experimental observations. Oscillations in the partial capture cross sections have been explained due to the swapping of the field electron. Isotope effect in the electron transfer is reported to be negligible.     

Magnetohydrodynamic properties of incompressible Meissner fluids

We consider a superconducting material that exists in the liquid state, more precisely, in which the Meissner-Ochsenfeld effect persists in the liquid state. First, we investigate how the shape of such a hypothetical Meissner liquid will adapt to accomodate for an applied external field. In particular, we analyse the case of a droplet of Meissner fluid, and compute the elongation of the droplet and its quadrupole frequency as a function of the applied field. Next, the influence of an applied field on the flow of the liquid is studied for the case of a surface wave. We derive the dispersion relation for surface waves on an incompressible Meissner fluid. We discuss some candidate realizations of the Meissner fluids and for the case of a superconducting colloid discuss which regime of wave lengths would be most affected by the Meissner effect.     

Low Dimension Dynamics in the EPRB Experiment with Random Variable Analyzers

The Einstein–Podolsky–Rosen–Bohm (EPRB) experiment performed with random variable and spatially separated analyzers is a milestone test in the controversy between Objective Local Theories (OLT) and Quantum Mechanics (QM). Only a few OLT are still possible. Some of the surviving OLT (specifically, the so called non-ergodic theories) would be undetectable in the averaged statistical values, but they may leave their trace in the time dynamics. For, while QM predicts random processes, the OLT of this kind predict the existence of regularities that may be revealed as a low dimensional object in the phase space. We perform a numerical analysis of the time-resolved data recorded in that experiment to unveil any hypothetical low dimensional dynamics that may be present. We find no consistent indication of such dynamics except for one data file, the longest of all in the real time. The possible causes of these dynamics are discussed.      

Klein,Einstein, and Five-Dimensional Unification

I examine the changing attitudes of Oskar Klein (1894–1977) and Albert Einstein (1879–1955) toward the notion of extending general relativity by an extra dimension with the aim of encompassing electromagnetism and gravitation in a unified field theory. I show how Klein developed his model of five-dimensional unification with the goal of explaining the discreteness of atomic energy levels, and how Einstein later embraced that goal. By examining the correspondence between Klein and Einstein, some of which was relayed through Paul Ehrenfest (1880–1933), I speculate that Klein’s work helped motivate Einstein to explore deterministic five-dimensional theories as a potential alternative to probabilistic quantum mechanics. Finally, I consider the contributions of Wolfgang Pauli (1900–1958) to the subject and elucidate his role in convincing Klein and Einstein that their models were not viable. Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. He currently is a member of the Executive Committee of the Forum on the History of Physics of the American Physical Society.     

Implications of the nuclear EMC effect

The discovery more than twenty years ago, by the EMC Collaboration, that the deep-inelastic-scattering DIS structure functions are influenced by the nuclear environment stunned the nuclear physics community and brought quarks and gluons into the field with great impact. A great length of time has passed, but despite a semi-infinite number of papers on the subject, there is no explanation that is universally accepted. Many models (related in one way or another to QCD) have been successful in reproducing data for deep inelastic scattering on nuclear targets, but fewer have described both the DIS and nuclear Drell-Yan experiments. Although there are some positive indications, no model has been used to predict correctly and unambiguously new independent phenomena. We review the history and discuss the best experimental prospects for future discovery.     

Precision measurement of vector and tensor analyzing powers in elastic deuteron-proton scattering

High-precision vector and tensor analyzing powers of elastic deuteron-proton ( d + p) scattering have been measured at intermediate energies to investigate effects of three-nucleon forces. Angular distributions in the range of 70^°-120^° in the center-of mass frame for incident-deuteron energies E _d ^lab = 130 and 180 MeV were obtained using the RIKEN facility. The beam polarization was unambiguously determined by measuring the ^12C (d, α)^10B(2⁺) reaction at 0^°. Results of the measurements are compared with state-of-the-art three-nucleon calculations. The present modeling of nucleon-nucleon forces and its extension to the three-nucleon system is not sufficient to describe the high-precision data consistently and requires, therefore, further investigation.