Investigation of zero-frequency solutions to the pion dispersion equation

The instability of nuclear matter is considered for the case where it is generated by the vanishing of the frequencies of collective excitations belonging to specific types (specifically, excitations that have the pion quantum numbers J ^π = 0^?). The behavior of zero-frequency solutions to the pion dispersion equation is analyzed versus the strength G′ of spin—isospin particle—hole interaction. It is shown that there exists a strength value G′_tr (|G′_tr| ? 1) such that, for G′ < G′_tr, zero-frequency solutions are excitations of the ω _P type, while, for G′ ≥ G′_tr, such solutions are excitations of the ω _c type. Excitations of the ω _P type for G′ < ?1 describe the instability of nuclear matter against small density fluctuations (Pomeranchuk’s instability), while excitations of the ω _c type are responsible for the instability associated with pion condensation at G′ ≈ 2. For stable nuclear matter, the solutions ω _P(κ) and ω _c (κ) lie on unphysical sheets of the complex plane of frequency.     

Neutral Particle Motion around a Schwarzschild Black Hole in Modified Gravity

We investigate circular motion of neutral test particles on equatorial plane near a black hole in scalar-tensor-vector gravity. We consider three cases (i) α < G/G_N (ii) α = G/G_N and (iii) α > G/G_N to find the regions where motion can exist. The corresponding effective potential, energy, angular momentum and center of mass energy are evaluated. Further, we define four different cases for α > G/G_N and identify stable and unstable regions of circular orbits. It is found that circular orbits having zero angular momentum exist at r = αGNM due to repulsive gravity effects. We conclude that the structure of stable regions for α < G/G_N as well as α = G/G_N case is completely different from that of α > G/G_N.     

Magnetic catalysis of stability of quark matter in the Nambu-Jona-Lasinio model

The effect of an external magnetic field H on the stability of quark matter is studied on the basis of the Nambu-Jona-Lasinio model. It is shown that, at H = 0, droplets of quark matter are stable only in the case where the coupling constant G is greater than some value G_bag. If H ≠ 0, stable multiquark formations may exist even for G ≤ G_bag (magnetic catalysis of stability). For G > G_bag, a magnetic field facilitates the formation of stable quark matter.     

Applications of a unique group embedding of internal symmetry groups andSU(2): spin-extensions for G2 and for the Sp(6)-Trion model

A recently proposed method of embeddingSU (2) and an internal symmetry groupG into a bigger groupG is applied to construct a spin extension ofG ₂ andSp (6). BecauseG ₂ andSp (6) possess a generalized quark model the embedding group can be proved to be unique and to be given bySp (14) resp.O (12) forG ₂ resp.Sp (6). For a particle classification splittings are calculated and tabulated forSp (14) ↓G ₂ xSU (2) andO (12) ↓Sp (6) xSU (2). The identification of low dimensional irreducible representations ofO (12) is quite satisfactory whereas an unreasonable number of unobserved particles are needed to fill up the supermultiplets of the spin extensionSp (14) of G₂.     

Local Geometry of the <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript> Moduli Space

We consider deformations of torsion-free G ₂ structures, defined by the G ₂-invariant 3-form φ and compute the expansion of \({\ast \varphi }\) to fourth order in the deformations of φ. By considering M-theory compactified on a G ₂ manifold, the G ₂ moduli space is naturally complexified, and we get a Kähler metric on it. Using the expansion of \({\ast \varphi }\), we work out the full curvature of this metric and relate it to the Yukawa coupling.     

On double polarization asymmetries in the elastic electron-proton scattering

Double polarization asymmetry D_p^(M) for the process of elastic electroweak scattering of the longitudinally polarized electrons by polarized proton target is considered with account of anapole G_1p and electric dipole moment (EDM) G_2p proton form factors. This asymmetry is only due to T-parity violating form factor G_2p, but does not directly depend on it, and having a significant value, allows to confirm the existence of the EDM of the proton.     

Low-temperature contribution to the resonant tunneling conductance of a disordered N–I–N junction

A formula for the contribution ΔG ^res(T) to the resonant tunneling conductance of the N–I–N junction (where N is a normal metal and I is an insulator) with a weak (low impurity concentrations) structural disorder in the I layer from the low-temperature “smearing” electron Fermi surfaces in its N shores is obtained. It is shown that the temperature dependence ΔG ^res(T) in such a “dirty” junction qualitatively differs from the corresponding dependence ΔG ₀(T) in a “pure” (without resonant impurities in the I layer) junction: ΔG ^res(T) < 0, d(ΔG ^res)/dT < 0; ΔG ₀(T) > 0, d(ΔG ₀)/dT > 0, which can serve as an experimental test of the presence of impurity tunneling resonances in the disordered I layer.     

Amplitude of Aharonov-Bohm oscillations in a small semiconductor ring interferometer in the tunneling regime

The amplitude g_AB of Aharonov-Bohm oscillations in a small semiconductor ring interferometer is studied as a function of the average conductance G_AV. Experimentally, it is found that, in the tunneling regime, the relative amplitude g_AB/G_AV of h/e oscillations is constant in the rings under investigation and smaller than unity. The small value of g_AB/G_AV in ring interferometers in the tunneling regime at low temperatures is explained by the difference in the amplitudes of the interfering electron waves.     

Diffraction enhancement effect and new possibilities of measuring the electric charge of the neutron and its inertial-to-gravitational mass ratio

Diffraction enhancement of small effects affecting a neutron undergoing Laue diffraction at Bragg angles θ _B close to 90° is predicted and experimentally observed. The enhancement is due to the delay of the neutron inside the crystal during diffraction and is proportional to tan² θ _B. As a result, the diffraction enhancement factor may be as large as ～10⁸–10⁹. On this basis, a new method is proposed for searching for the electric charge of the neutron and for measuring the ratio of its inertial mass m _i to the gravitational mass m _G . It is shown that the accuracy of the neutron charge measurement can be improved by more than two orders of magnitude in relation to the present-day accuracy and that the ratio m _i /m _G can be measured to an precision of σ(m _i /m _G ) ～ 10^?6.     

Comparison of theK ± p scattering data with the forward dispersion relations

The dispersion relations forK ^± p forward scattering were evaluated in order to test the compatibility with the experimental data and to obtain an estimation of the effective coupling constantG ^2/4π=(G _Λ ² +G _Σ ² )/4π.     

Impact of pairing on the heat capacity of systems with an isolated level bunch near the Fermi surface

Canonical heat capacity vs. the temperature for systems with an isolated level bunch near the Fermi surface is calculated using exact eigenvalues of the effective Bardeen–Cooper–Schrieffer Hamiltonian (H _BCS). Two degenerate levels separated by energy spacing Δε in spherical systems can produce two maxima in C at low values of G/Δε, where G is the pairing strength of H _BCS. These two maxima become one as G/Δε grows and the system deforms.     

Bad communities with high modularity

In this paper we discuss some problematic aspects of Newman and Girvan’s modularity function Q _N . Given a graph G, the modularity of G can be written as Q _N = Q _f ? Q ₀, where Q _f is the intracluster edge fraction of G and Q ₀ is the expected intracluster edge fraction of the null model, i.e., a randomly connected graph with same expected degree distribution as G. It follows that the maximization of Q _N must accomodate two factors pulling in opposite directions:Q _f favors a small number of clusters and Q ₀ favors many balanced (i.e., with approximately equal degrees) clusters. In certain cases the Q ₀ term can cause overestimation of the true cluster number; this is the opposite of the well-known underestimation effect caused by the “resolution limit” of modularity. We illustrate the overestimation effect by constructing families of graphs with a “natural” community structure which, however, does not maximize modularity. In fact, we show there exist graphs G with a “natural clustering” V of G and another, balanced clustering U of G such that (i) the pair (G, U) has higher modularity than (G, V) and (ii) V and U are arbitrarily different.     

Fluctuations of orientational order in a uniaxial nematic liquid crystal with biaxial molecules and its response to an external field

Homogeneous thermal fluctuations of the orientational order parameters S and G of biaxial molecules in a uniaxial nematic liquid crystal are investigated in the framework of the molecular-statistical theory. It is demonstrated that the molecular biaxiality significantly affects the order parameters S and G, their temperature dependences in the nematic phase, the amplitude and the temperature dependence of the order parameter fluctuations in the nematic and isotropic phases, and the character of the transition from the nematic phase to the isotropic liquid phase. It is established that the fluctuations of the parameters S and G in the nematic phase are related to the temperature dependences of S and G and the susceptibilities χ_S and χ_G of the nematic liquid crystal to external fields, which leads to a change in the parameters S and G at a fixed director orientation. Explanations are offered for the known experimental data on the orientational ordering of biaxial molecules under the action of external fields in the isotropic phase of nematic liquid crystals.     

On the Geometry of Closed G<Subscript>2</Subscript>-Structures

We give an answer to a question posed in physics by Cveti? et al. [9] and recently in mathematics by Bryant [3], namely we show that a compact 7-dimensional manifold equipped with a G ₂-structure with closed fundamental form is Einstein if and only if the Riemannian holonomy of the induced metric is contained in G ₂. This could be considered to be a G ₂ analogue of the Goldberg conjecture in almost Kähler geometry and was indicated by Cveti? et al. in [9]. The result was generalized by Bryant to closed G ₂-structures with too tightly pinched Ricci tensor. We extend it in another direction proving that a compact G ₂-manifold with closed fundamental form and divergence-free Weyl tensor is a G ₂-manifold with parallel fundamental form. We introduce a second symmetric Ricci-type tensor and show that Einstein conditions applied to the two Ricci tensors on a closed G ₂-structure again imply that the induced metric has holonomy group contained in G ₂.     

Partial pseudospin polarization,latticetronics and Fano resonances in quantum dots based in graphene ribbons: a conductance spectroscopy

In this work we study, as a function of the height V and width L _b of the potentialbarriers, the transport of Dirac quasi-particles through quantum dots in graphene ribbons.We observed, as we increase V, a partial polarization (PP) of the pseudospin due to the participation of the hyperbolic bands. This generates polarizations in the sub-lattices A or B outside the dot regions for single, coupled, and open dots. Thus for energies around the Dirac point, the conductance G at both sides of the dot shows a latticetronics of conductances G _A and G _B as a function ofV and L _b . This fact can be used as a PPspectroscopy which associates hole-type waves with the latticetronics. A periodic enhancement of PP is obtained with the increase of V in dots formed bybarriers that completely occupy the nanoribbon width. For this case, a direct correspondence between G(V) and PP(V) exists. On the other hand, for the open dots, the PP(V) and the G(V) show a complex behavior that exhibit higher intensities when compared to the previous case. In the Dirac limit we have no backscattering signs, however when we move slightly away from this limit the firstsigns of confinement appear in the PP(V) (it freezes in a given sub-lattice). In the last case the backscattering fingerprints are obtained directly fromthe conductance (splittings). The open quantum dots are very sensible to their opening w _d and this generatesFano line-shapes of difficult interpretation around the Dirac point. The PP spectroscopy used here allows us to understand the influence of w _d in the relativistic analogues and to associate electron-type waves with the observed Fano line-shapes.     

Photoconduction and photocontrolled collective effects in the Peierls conductor TaS<Subscript>3</Subscript>

Light illumination of thin crystals of CDW conductor TaS₃ is found to result in dramatic changes of both linear (G) and nonlinear conduction. The increase of G is accompanied by suppression of the collective conduction, growth of the threshold field E _T , and appearance of the switching and hysteretic behavior in the nonlinear conduction. The effects in the nonlinear conduction are associated with increase of CDW elasticity due to illumination that leads, in particular, to the appearance of a relation E _T ∝ G^1/3 expected for the one-dimensional pinning.     

Low energy frontier: Physics with polarized cold neutrons

Recent developments in investigations of beta decay of the free neutron are discussed. Measurements of the neutron lifetime τ _n and the electron emission asymmetry A _n are a classic source of determination of the Standard Model parameters G _v , G _A and λ _n . Combined with the results of the muon decay experiments, the nuclear superallowed 0→0 transitions and decays of particles containing heavy quarks, they provide tests of the SM assumptions: the unitarity of the CKM matrix, the number of the neutrino families, or the CVC hypothesis. In contrast, more complex correlations between the spins and the momenta of the emitted particles, (e.g. B _n , D _n , R _n or G _n ), are uniquely sensitive to the so called “Physics beyond the Standard Model”. Thus the question of the right handed bosons, the admixture of the scalar or tensor interaction, with or without time reversal violating terms, may be addressed separately in a dedicated, single experiment. Further development of powerful beams of polarized cold neutrons and sources of ultracold neutrons is imperative for progress in these studies.     

On the Exact Evaluation of the Face-Centred Cubic Lattice Green Function

The mathematical properties of the lattice Green function

Open image in new window

are investigated, where w=w ₁+iw ₂ lies in a complex plane which is cut from w=?1 to w=3, and {? ₁,? ₂,? ₃} is a set of integers with ? ₁+? ₂+? ₃ equal to an even integer. In particular, it is proved that G(2n,0,0;w), where n=0,1,2,…, is a solution of a fourth-order linear differential equation of the Fuchsian type with four regular singular points at w=?1,0,3 and ∞. It is also shown that G(2n,0,0;w) satisfies a five-term recurrence relation with respect to the integer variable n. The limiting function

$G^{-}(2n,0,0;w_1)\equiv\lim_{\epsilon\rightarrow0+}G(2n,0,0;w_1-\mathrm{i}\epsilon) =G_{\mathrm{R}}(2n,0,0;w_1)+\mathrm{i}G_{\mathrm {I}}(2n,0,0;w_1) ,\nonumber $

where w ₁∈(?1,3), is evaluated exactly in terms of ₂ F ₁ hypergeometric functions and the special cases G ^?(2n,0,0;0), G ^?(2n,0,0;1) and G(2n,0,0;3) are analysed using singular value theory. More generally, it is demonstrated that G(? ₁,? ₂,? ₃;w) can be written in the form

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where Open image in new window are rational functions of the variable ξ, K(k _?) and E(k _?) are complete elliptic integrals of the first and second kind, respectively, with

$k_{-}^2\equiv k_{-}^2(w)={1\over2}- {2\over w} \biggl(1+{1\over w} \biggr)^{-{3\over2}}- {1\over2} \biggl(1-{1\over w} \biggr ) \biggl(1+{1\over w} \biggr)^{-{3\over2}} \biggl(1-{3\over w} \biggr)^{1\over2}\nonumber $

and the parameter ξ is defined as

$\xi\equiv\xi(w)= \biggl(1+\sqrt{1-{3\over w}} \,\biggr)^{-1} \biggl(-1+\sqrt{1+{1\over w}} \,\biggr) .\nonumber $

This result is valid for all values of w which lie in the cut plane. The asymptotic behaviour of G ^?(2n,0,0;w ₁) and G(2n,0,0;w ₁) as n→∞ is also determined. In the final section of the paper a new ₂ F ₁ product form for the anisotropic face-centred cubic lattice Green function is given.

     

Zur Frage des Grundzustandes im Tb I-Spektrum

Analysis of the optical spectrum of Tb I confirms the conclusion reached byBender, Penselin andSchlüpmann from atomic beam magnetic resonance observations, that the lowest multiplet in the 4f ⁸5d6s ² configuration is⁸ G. The lowest level, however, is not⁸ G _15/2, but⁸ G _13/2, which is the true ground level of the Tb atom, provided the determination of the relative position of 4f ⁹6s ^{2 6} H _15/2 with respect to 4f ⁸5d6s ^{2 8} G _15/2 byBender c. s. is correct.     

Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas

Traveling wave solution of the Gardner equation is studied analytically by using the two dependent (G^′/G,1/G)-expansion and (1/G^′)-expansion methods and direct integration. The exact solutions of the Gardner equations are obtained. Our analytic solutions are applied to the unmagnetized four-component and dusty plasma systems consisting of hot protons and electrons to investigate dynamical features of the solitons and shock waves produced in these systems. A wide variety of parameters of the plasma is used, and the basic features of the Gardner solitons that are beyond the existing study in literature are found. It is observed that the analytic solutions from (G^′/G,1/G)-expansion and (1/G^′)-expansion methods only produce shock waves but the solitary waves are found from the analytic solutions derived from the direct integration. It is also noted that the superhot electrons and relative mass density of the electrons significantly effect the soliton’s amplitude, width, and position. We have also numerically proved that the combination of every value of nomalized density μ₁ or temperature ratio σ₁ with the other sets of plasma parameters creates a region where the solutions have similar physical properties. The time-dependent behavior of the soliton is also studied, and a periodic motion of soliton along the phase variable η is found during the evolution. The investigations and the limits presented in this study may be helpful for studying and understanding the nonlinear properties of the solitary and shock waves seen in various physical and astrophysical plasma systems.