A note on the Holst action, the time gauge, and the Barbero–Immirzi parameter

In this note, we review the canonical analysis of the Holst action in the time gauge, with a special emphasis on the Hamiltonian equations of motion and the fixation of the Lagrange multipliers. This enables us to identify at the Hamiltonian level the various components of the covariant torsion tensor, which have to be vanishing in order for the classical theory not to depend upon the Barbero–Immirzi parameter. We also introduce a formulation of three-dimensional gravity with an explicit phase space dependency on the Barbero–Immirzi parameter as a potential way to investigate its fate and relevance in the quantum theory.     

The Schrödinger Equation,the Zero-Point Electromagnetic Radiation,and the Photoelectric Effect

A Schrödinger type equation for a mathematical probability amplitude Ψ(x,t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V(x). The particle phase space probability density is denoted Q(x,p,t), and the entire system is immersed in the “vacuum” zero-point electromagnetic radiation. We show, in the first part of the paper, that the generalized Liouville equation is reduced to a simpler Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. This leads us to a simpler Liouville equation that will facilitate the calculations in the second part of the paper. Within this second part, we address ourselves to the following task: Since the Schrödinger equation depends on \(\hbar \), and the zero-point electromagnetic spectral distribution, given by \(\rho _{0}{(\omega )} = \hbar \omega ^{3}/2 \pi ^{2} c^{3}\), also depends on \(\hbar \), it is interesting to verify the possible dynamical connection between ρ₀(ω) and the Schrödinger equation. We shall prove that the Planck’s constant, present in the momentum operator of the Schrödinger equation, is deeply related with the ubiquitous zero-point electromagnetic radiation with spectral distribution ρ₀(ω). For simplicity, we do not use the hypothesis of the existence of the L. de Broglie matter-waves. The implications of our study for the standard interpretation of the photoelectric effect are discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunneling phenomenon and the Compton’s effect.     

Ions,bubbles, and vortices at the superfluid λ-transition

A vortex-ring theory of the superfluid -transition is reviewed, and new results are presented for the vortex density and for the superfluid density of helium in confined geometries. Possible experiments using ion probes to detect the thermally excited vortices are discussed. It appears that the usual helium ions are not suitable for this purpose, and that larger ion complexes such as multielectron bubbles will need to be employed. An experiment to stably trap multielectron bubbles with acoustic standing waves is outlined.     

The Repulsive Lattice Gas, the Independent-Set Polynomial, and the Lovász Local Lemma

We elucidate the close connection between the repulsive lattice gas in equilibrium statistical mechanics and the Lovász local lemma in probabilistic combinatorics. We show that the conclusion of the Lovász local lemma holds for dependency graph G and probabilities {p_x} if and only if the independent-set polynomial for G is nonvanishing in the polydisc of radii {p_x}. Furthermore, we show that the usual proof of the Lovász local lemma – which provides a sufficient condition for this to occur – corresponds to a simple inductive argument for the nonvanishing of the independent-set polynomial in a polydisc, which was discovered implicitly by Shearer⁽⁹⁸⁾ and explicitly by Dobrushin.^(37,38) We also present some refinements and extensions of both arguments, including a generalization of the Lovász local lemma that allows for soft dependencies. In addition, we prove some general properties of the partition function of a repulsive lattice gas, most of which are consequences of the alternating-sign property for the Mayer coefficients. We conclude with a brief discussion of the repulsive lattice gas on countably infinite graphs.     

Einstein,Incompleteness, and the Epistemic View of Quantum States

Does the quantum state represent reality or our knowledge of reality? In making this distinction precise, we are led to a novel classification of hidden variable models of quantum theory. We show that representatives of each class can be found among existing constructions for two-dimensional Hilbert spaces. Our approach also provides a fruitful new perspective on arguments for the nonlocality and incompleteness of quantum theory. Specifically, we show that for models wherein the quantum state has the status of something real, the failure of locality can be established through an argument considerably more straightforward than Bell’s theorem. The historical significance of this result becomes evident when one recognizes that the same reasoning is present in Einstein’s preferred argument for incompleteness, which dates back to 1935. This fact suggests that Einstein was seeking not just any completion of quantum theory, but one wherein quantum states are solely representative of our knowledge. Our hypothesis is supported by an analysis of Einstein’s attempts to clarify his views on quantum theory and the circumstance of his otherwise puzzling abandonment of an even simpler argument for incompleteness from 1927.     

Analysis of the common characteristics of the Hartmann,Ronchi, and Shack–Hartmann tests

An overview of the settings of the planes for the filters and observed patterns in the Hartmann and Ronchi tests is presented. Also a new set of filters for both test were developed. In a similar way, it is easy to extend this analysis to the Shack–Hartmann test, and to propose a new Null Shack–Hartmann filter.     

Qweak, N → Δ, and physics beyond the standard model

The data-taking phase of the Qweak experiment ended in May of 2012 at the Thomas Jefferson National Accelerator Facility. Qweak aims to measure the weak charge of the proton, Q _W ^p , via parity-violating elastic electron-proton scattering. The expected value of Q _W ^p is fortuitously suppressed, which leads to an increased sensitivity to physics beyond the Standard Model.     

String vertices,overlap equations, τ functions and the Hirota equation

String vertices,V, are shown to satisfy a new type of overlap equation of the form as well as corresponding equations forA _n andB _n cycles. A special case of such an equation, when integrated, is shown to be the Hirota equation for the K–P hierarchy.     

Effects of the 3d transition metal doping on the structural,electronic, and magnetic properties of BeO nanotubesEffects of the 3d transition metal doping on the structural,electronic, and magnetic properties of BeO nanotubesEffects of the 3d transition metal doping on the structural,electronic, and magnetic properties of BeO nanotubes

First-principles calculations have been performed on the structural, electronic, and magnetic properties of seven 3d transition-metal （TM） impurities （V, Cr, Mn, Fe, Co, Ni, and Cu） doped armchair （5,5） and zigzag （8,0） beryllium oxide nanotubes （BeONTs）. The results show that there exists a structural distortion around the 3d TM impurities with respect to the pristine BeONTs. The magnetic moment increases for V- and Cr-doped BeONTs and reaches a maximum for Mn-doped BeONT, and then decreases for Fe-, Co-, Ni-, and Cu-doped BeONTs successively, consistent with the predicted trend of Hund＇s rule to maximize the magnetic moments of the doped TM ions. However, the values of the magnetic moments are smaller than the predicted values of Hund＇s rule due to the strong hybridization between the 2p orbitals of the near O and Be ions of BeONTs and the 3d orbitals of the TM ions. Furthermore, the V-, Co-, and Ni-doped （5,5） and （8,0） BeONTs with half-metal ferromagnetism and thus 100% spin polarization character are good candidates for spintronic applications.     

The first Brillouin zone of the hexagonal close-packed structure and study on the properties of vacancies and phonon dispersions by the improved ones of the modified analytic embedded atom method potentials for Ru,Sc, Ti,Y, and Zr

ABSTRACT

We studied the first Brillouin zone of the hexagonal close-packed (HCP) structure and the improved ones of the modified analytical embedded atom method (EAM) potentials were adopted to calculate the properties of the mono- and bi-vacancies and the phonon dispersions for HCP transition metals Ru, Sc, Ti, Y, and Zr. The agreements with the experimental data showed that the improved potentials for the HCP transition metals are available.     

Existence,regularity, and asymptotic behavior of the solutions to the Ginzburg-Landau equations on ℝ3

This paper studies the solutions of the Ginzburg-Landau equations on ³ in the presence of an arbitrarily distributed external magnetic field. The existence and regularity of the solutions at the lowest energy level are established. The solutions found are in the Coulomb gauge. If the external field is sufficiently regular, the solutions are shown to have nice asymptotic decay properties at infinity.     

W-algebras and the equivalence of bihamiltonian,Drinfeld–Sokolov and Dirac reductions

We prove that the classical $W$-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld–Sokolov or Dirac reductions. We conclude that the classical $W$-algebra depends only on the nilpotent orbit but not on the choice of a good grading or an isotropic subspace. In addition, using this result we prove again that the transverse Poisson structure to a nilpotent orbit is polynomial and we better clarify the relation between classical and finite $W$-algebras.     

The ζ-Determinant and the Additivity of the η-Invariant on the Smooth, Self-Adjoint Grassmannian

In this paper we discuss the existence of the ‘-determinant of a Dirac operator \Dd\Dd on a compact manifold with boundary. We show that the determinant is well defined in the case of the operator \Dd\Dd with a domain determined by a boundary condition from the smooth, self-adjoint Grassmannian \Grass_￥^*(\Dd)\Grass_{\infty}^*(\Dd) discussed in the papers [5, 13, 29]. We prove a generalization of a pasting formula for the m-invariant (see [34]). The results of the paper are used in the recent proof of the projective equality of the ‘-determinant and Quillen determinant on \Grass_￥^*(\Dd)\Grass_{\infty}^*(\Dd) (see [30, 31]).     

Truncated Gamow functions, α-decay and the exponential law

For a quantum mechanical two-bodys-wave resonance we prove that the evolution of square integrable approximations of the Gamow function is outgoing and exponentially damped. An error estimate is given in terms of resonance energy and explicity. We obtain the Breit-Wigner form. The results are used in an -decay model to prove general validity of the exponential decay law for periods of several lifetimes.     

MAP,MAC, and vortex-rings configurations in the Weinberg–Salam model

We report on the presence of new axially symmetric monopoles, antimonopoles and vortex-rings solutions of the SU(2)×U(1) Weinberg–Salam model of electromagnetic and weak interactions. When the ?$?$-winding number n=1$n=1$, and 2, the configurations are monopole–antimonopole pair (MAP) and monopole–antimonopole chain (MAC) with poles of alternating sign magnetic charge arranged along the z$z$-axis. Vortex-rings start to appear from the MAP and MAC configurations when the winding number n=3$n=3$. The MAP configurations possess zero net magnetic charge whereas the MAC configurations possess net magnetic charge of 4πn/e$4\pi n/e$.     

Einstein–Cartan gravity,Asymptotic Safety,and the running Immirzi parameter

In this paper we analyze the functional renormalization group flow of quantum gravity on the Einstein–Cartan theory space. The latter consists of all action functionals depending on the spin connection and the vielbein field (co-frame) which are invariant under both spacetime diffeomorphisms and local frame rotations. In the first part of the paper we develop a general methodology and corresponding calculational tools which can be used to analyze the flow equation for the pertinent effective average action for any truncation of this theory space. In the second part we apply it to a specific three-dimensional truncated theory space which is parametrized by Newton’s constant, the cosmological constant, and the Immirzi parameter. A comprehensive analysis of their scale dependences is performed, and the possibility of defining an asymptotically safe theory on this hitherto unexplored theory space is investigated. In principle Asymptotic Safety of metric gravity (at least at the level of the effective average action) is neither necessary nor sufficient for Asymptotic Safety on the Einstein–Cartan theory space which might accommodate different “universality classes” of microscopic quantum gravity theories. Nevertheless, we do find evidence for the existence of at least one non-Gaussian renormalization group fixed point which seems suitable for the Asymptotic Safety construction in a setting where the spin connection and the vielbein are the fundamental field variables.     

Regular Bouncing Solutions,Energy Conditions,and the Brans—Dicke Theory

JETP Letters - In general, to avoid a singularity in cosmological models involves the introduction of exotic kind of matter fields, for example, a scalar field with negative energy density. In...     

Optical Möbius strips, twisted ribbons, and the index theorem

The twist numbers of circular optical M?bius strips and twisted ribbons are shown to obey the index theorem under rotation of the plane of observation, and under change in the radius of the path.