abstract

A transformation method is applied to the second order ordinary differential equation satisfied by orthogonal polynomials to construct a family of exactly solvable quantum systems in any arbitrary dimensional space. Using the properties of orthogonal polynomials, the method transforms polynomial differential equation to \(D\)-dimensional radial Schrodinger equation which facilitates construction of exactly solvable quantum systems. The method is also applied using associated Laguerre and hypergeometric polynomials. The quantum systems generated from other polynomials are also briefly highlighted.

abstract

Semiclassical wave functions based on the Maslov–Fedoriuk approach and satisfying the Dirichlet boundary conditions are constructed in the rational polygon billiards. They are defined on classical objects called skeletons which are the billiard generalization of Arnold’s tori. The skeletons, which are considered, are built of periodic trajectories. In the phase space, these skeletons are represented by Lagrange surfaces which have forms of cylinder-like or Möbius-like bands. Semiclassical solutions constructed on these surfaces are exact making the Lagrange surface billiard-like. Projected on the rational polygon billiards these exact solutions become again semiclassical taking the forms of the superscars of Bogomolny and Schmit [Phys. Rev. Lett. 92, 244102(2004)]. This allows us to consider the exact solutions on the Lagrange surfaces as the resonant states for the rational billiards which manifest themselves in the form of superscars in the high energy limit. It is shown that the superscar states can be found also in the chaotic deformations of the polygon billiards such as the Bunimovich or Sinai ones.

abstract

We analyze the annihilation cross section of the Dark Matter which interacts with the Standard Model sector over the scalar unparticle propagator. We observe that the annihilation cross section of the dark matter pair is sensitive to the dark matter mass and the scaling dimension of scalar unparticle. We estimate a range for the dark matter mass and the scaling dimension of scalar unparticle by using the current dark matter abundance.

abstract

Some distributions of the \(\mu ^-\) in the top-quark pair production reaction \(pp \rightarrow b u\bar {d}\;\bar {b} \mu ^-\bar {\nu }_{\mu }\) at the LHC are calculated to leading order in the presence of the anomalous \(Wtb\) coupling with operators of dimension up to five. The distributions in the transverse momentum, rapidity and cosine of the \(\mu ^-\) angle with respect to the beam in the laboratory frame and with respect to the reversed momentum of the \(b\)-quark in the rest frame of \(W\)-boson are changed rather moderately by the anomalous \(Wtb\) coupling. The distributions computed with the full set of leading order Feynman diagrams practically do not differ from those computed with the \(t\bar t\) production diagrams, with typical acceptance cuts. This demonstrates very little effect of the off-resonance background contributions.

abstract

Parameters of widely used nuclear rms charge radius formulas have been refitted based on the latest experimental data for about 900 nuclei. It has been seen that the new parameters in the formulas give better results than the previous ones. Besides, an \(N^{1/3}\)-dependent formula has been proposed and discussed. This formula gives effective results for rms charge radius. The standard deviation in all formulas with new parameters are concentrated between \(-\)0.1 and 0.1. In other words, for about 90% of nuclei, the differences of charge radii from experimental values are lower than 0.1 fm.

abstract

Articular cartilage is an extraordinary tribochemical device designed by nature. Yet, a long-standing debate exists as to the mechanisms by which its interfacial properties facilitate lubrication toward very low static and kinetic frictional coefficients. We postulate the physiologic emergence of proton channels in amphiphile-water sub-systems undergoing mesoscopic Smoluchowski-type dynamics as a governing mechanism toward nanoscale articular cartilage lubrication. We argue that an enthalpic interplay between geometric and electrostatic confinement and the associated entropic counterpart is characteristic of proton channel crowding rather than of proton drift. A proton-wave inversion effect also supported by quantum mechanical evaluation is demonstrated such that the wave plays a beneficial role in nanoscale lubrication driven by local free-energy gradients. These findings have practical implications for the treatment of damaged articular cartilage as exemplified by the physiochemical scalpel used in modern tissue rescue interventions as a wound healing biomimic facilitating articular cartilage lesion recovery. Amphiphile proton channels also provide a mechanism for surface active phospholipid self-assembly supportive of their efficacy as an occasional sacrificial layer designed to mitigate certain perturbation events. This behavior remains a necessary requisite to reconstitute normal bearing surfaces after therapeutic tissue rescue.