On the Problem of the Amenability of the Gauge Group

Let G be one of the local gauge groups C(X, U(n)),C (X, U(n)), C(X, SU(n)) or C (X, SU(n)) where X is a compact Riemannian manifold. We observe that G has a nontrivial group topology, coarser than its natural topology, w.r.t. which it is amenable, viz. the relative weak topology of C(X, M(n)). This topology seems more useful than other known amenable topologies for G. We construct a simple fermionic model containing an action of G, continuous w.r.t. this amenable topology.     

On the relationship between the gradient and the bulk Richardson number for the atmospheric surface layer

Summary Semi-empirical formulations which have been proposed to describe the wind and potential temperature profiles are used to derive relationships between the gradient Richardson number, Ri, the finite-difference layer Richardson number, Ri_b, the surface layer Richardson number, Ri_s, and the bulk Richardson number,B, through the atmospheric surface layer. The theoretical analysis for stable conditions indicates that Ri (z ₃)=Ri_b, wherez ₃=(z ₂−z ₁)/ln(z ₂/z ₁), andz ₂;z ₁=upper and lower levels at which temperature and wind speed are specified. It is also found that, during stable conditions, the wind profile power law exponent,p, is computed at the heightz ₃, instead of the widely used geometric mean height,z _m, between top (z ₂) and bottom (z ₁) of the layer considered.     

From the Solution of the Tsarev System to the Solution of the Whitham Equations

We study the Cauchy problem for the Whitham modulation equations for increasing smooth initial data. The Whitham equations are a collection of one-dimensional quasi-linear hyperbolic systems. This collection of systems is enumerated by the genus g=0,1,2, ... of the corresponding hyperelliptic Riemann surface. Each of these systems can be integrated by the so-called hodograph transformation introduced by Tsarev. A key step in the integration process is the solution of the Tsarev linear overdetermined system. For each g>0, we construct the unique solution of the Tsarev system, which matches the genus g+1 and g–1 solutions on the transition boundaries.     

Spontaneous magnetization of the vacuum and the strength of the magnetic field in the hot Universe

Intergalactic magnetic fields are assumed to have been spontaneously generated at the reheating stage of the early Universe, due to vacuum polarization of non-Abelian gauge fields at high temperature. The fact that the screening mass of this type of fields has zero value was discovered recently. A procedure to estimate their field strengths, B(T), at different temperatures is here developed, and the value B(T _ew)∼10¹⁴ G at the electroweak phase transition temperature is derived by taking into consideration the present value of the intergalactic magnetic field strength, B ₀∼10⁻¹⁵ G, coherent on the ∼1 Mpc scale. As a particular case, the standard model is considered and the field scale at high temperature is estimated in this case. Model-dependent properties of the phenomena under investigation are briefly discussed, too.     

Confronting the MSSM and the NMSSM with the discovery of a signal in the two photon channel at the LHC

We confront the discovery of a boson decaying into two photons, as reported recently by ATLAS and CMS, with the corresponding predictions in the Minimal Supersymmetric Standard Model (MSSM) and the Next-to-Minimal Supersymmetric Standard Model (NMSSM). We perform a scan over the relevant regions of parameter space in both models and evaluate the MSSM and NMSSM predictions for the dominant Higgs production channel and the photon–photon decay channel. Taking into account the experimental constraints from previous direct searches, flavor physics, electroweak measurements as well as theoretical considerations, we find that a Higgs signal in the two photon channel with a rate equal to, or above, the SM prediction is viable over the full mass range 123?M _H ?127 GeV, both in the MSSM and the NMSSM. We find that besides the interpretation of a possible signal at about 125 GeV in terms of the lightest $\mathcal {CP}$ -even Higgs boson, both the MSSM and the NMSSM permit also a viable interpretation where an observed state at about 125 GeV would correspond to the second-lightest $\mathcal {CP}$ -even Higgs boson in the spectrum, which would be accompanied by another light Higgs with suppressed couplings to W and Z bosons. We find that a significant enhancement of the γγ rate, compatible with the signal strengths observed by ATLAS and CMS, is possible in both the MSSM and the NMSSM, and we analyse in detail different mechanisms in the two models that can give rise to such an enhancement. We briefly discuss also our predictions in the two models for the production and subsequent decay into two photons of a $\mathcal {CP}$ -odd Higgs boson.     

Effect of the configuration of the discharge chamber of the plasma focus on the neutron yield

Preliminary probe experiments on the Filippov-type plasma focus with the energy E = 70 kJ and a current of about 1 MA show significant stray currents flowing near the insulator. To suppress them and optimize the discharge circuit, the main discharge chamber elements, i.e., the insulator, anode and cathode liner, were changed. As a result, a 30-fold increase in the setup neutron yield to Y _n = 5· 10¹⁰ neutrons per pulse was detected.     

On the asymptotic behavior of the solutions of the Caldirola-Kanai equation

We study in this Letter the asymptotic behavior, as t+, of the solutions of the one-dimensional Caldirola-Kanai equation for a large class of potentials satisfying the condition V(x)+ as |x|. We show, first of all, that if I is a closed interval containing no critical points of V, then the probability P _t (t) of finding the particle inside I tends to zero as t+. On the other hand, when I contains critical points of V in its interior, we prove that P _t (t) does not oscillate indefinitely, but tends to a limit as t+. In particular, when the potential has only isolated critical points x ₁, ..., x _N our results imply that the probability density of the particle tends to in the sense of distributions.Supported by Fulbright-MEC grant 85-07391.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

Extracting the wavefunction of the LSP at the LHC

We consider associated production of squarks and gluinos with the lightest supersymmetric particle (LSP), or states nearly degenerate in mass with it. Though sub-dominant to pair production of color SU(3)-charged superpartners, these processes are directly sensitive to the wavefunction composition of the lightest neutralinos. Exploiting event-shape variables - including some introduced here for the first time - we are able to identify the composition of the LSP by selecting events involving a single high-pT jet recoiling against missing transverse energy. We illustrate the proposed technique on a set of benchmark cases and propose methods for applying these results in more realistic experimental environments.     

Effect of the frustration to the ground state energy and entropy of the spin-glass in the random bond Ising model on the square lattice

The energies and the entropies of the spin-glass state and the paramagnetic state at T = 0 of the random-bond Ising mixture of the ferromagnetic bond (concentration p) and the antiferromagnetic bond (concentration 1 ? p) on the square lattice are calculated by the method of the square approximation in the simple version. A self-consistent relation that the partial trace of the normalized density matrix of the square cluster is equal to that of the vertex ($\text{tr}\text{(}{}_{\mathrm{jkl}}\text{?}\text{?}{}^{\mathrm{(4)}}\text{(i,j,k,l) =}\text{?}\text{?}{}^{\mathrm{(1)}}\text{(i)}$) leads to an integral equation for the distribution function of the effective fields, and it is solved exactly at T = 0. The symmetric solution of the integral equation contains the paramagnetic state and two spin-glass states, SG1 and SG2. The energies and the entropies of these states are obtained as functions of the concentration p. The values of the energies per spin at $\text{p =}\text{1}\text{2}$ are -0.75|E_F|, -0.72746|E_F|, -0.72543|E_F|, and correspond to a minimum, a saddle point, and a maximum, respectively, and the values of the entropies are 0, 0.082886k_B, and 0.054457k_B, respectively. The present results are compared with those of the pair approximation and discussed.     

On the Thermodynamics of the q-Particles

Since the grand partition function Zq for the so-called q-particles (i.e., quons), q∈(−1,1), cannot be computed by using the standard 2nd quantisation technique involving the full Fock space construction for q=0, and its q-deformations for the remaining cases, we determine such grand partition functions in order to obtain the natural generalisation of the Plank distribution to q∈[−1,1]. We also note the (non) surprising fact that the right grand partition function concerning the Boltzmann case (i.e., q=0) can be easily obtained by using the full Fock space 2nd quantisation, by considering the appropriate correction by the Gibbs factor 1/n! in the n term of the power series expansion with respect to the fugacity z. As an application, we briefly discuss the equations of the state for a gas of free quons or the condensation phenomenon into the ground state, also occurring for the Bose-like quons q∈(0,1).     

About the Stability of the Dodecatoplet

A new investigation is done of the possibility of binding the “dodecatoplet”, a system of six top quarks and six top antiquarks, (t ⁶ t̄ ⁶), using the Yukawa potential mediated by Higgs exchange. A simple variational method gives a upper bound close to that recently estimated in a mean-field calculation. It is supplemented by a lower bound provided by identities among the Hamiltonians describing the system and its subsystems.     

On the purity of the limiting gibbs state for the Ising model on the Bethe lattice

We give a proof that for the Ising model on the Bethe lattice, the limiting Gibbs state with zero effective field (disordered state) persists to be pure for temperature below the ferromagnetic critical temperatureT _c ^F until the critical temperatureT _c ^SG of the corresponding spin-glass model. This new proof revises the one proposed earlier.     

Calculation of the dependence of the centrifugal constants of the molecule H2O on the quantum number v2 on the basis of the Morse oscillator

An explanation is given in this paper for the anomalous dependence of the centrifugal distortion in flexible molecules of the type H₂O on the bending quantum number v₂ on the basis of the Morse oscillator. A computation of the dependence of the rapidly varying rotational, quartic, sextic constants of the molecule H₂O on v₂ describes the experimental behavior of these constants well.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 93–96, August, 1982.     

On the physical interpretation and the mathematical structure of the combinatorial hierarchy

The combinatorial hierarchy model for basic particle processes is based on elementary entities; any representation they may have is discrete and two-valued. We call themSchnurs to suggest their most fundamental aspect as concatenating strings. Consider a definite small number of them. Consider an elementary creation act as a result of which two different Schnurs generate a new Schnur which is again different. We speak of this process as a discrimination. By this process and by this process alone can the complexity of the universe be explored. By concatenations of this process we create more complex entities which are themselves Schnurs at a new level of complexity. Everything plays a dual role in which something comes in from the outside to interact, and also serves as a synopsis or concatenation of such a process. We thus incorporate the observation metaphysic at the start, rejecting Bohr's reduction to the haptic language of common sense and classical physics. Since discriminations occur sequentially, our model is consistent with a fixed past-uncertain future philosophy of physics. We demonstrate that this model generates four hierarchical levels of rapidly increasing complexity. Concrete interpretation of the four levels of the hierarchy (with cardinals 3,7,127,2¹²⁷-110³⁸) associates the three levels which map up and down with the three absolute conservation laws (charge, baryon number, lepton number) and the spin dichotomy. The first level represents +, –, and ± unit charge. The second has the quantum numbers of a baryon-antibaryon pair and associated charged meson (e.g.,n¯n,p¯n,p¯p,n¯p, ⁺ , ⁰, ^– ). The third level associates this pair, now including four spin states as well as four charge states, with a neutral lepton-antilepton pair (e¯e orv¯v), each pair in four spin states (total, 64 states)—three charged spinless, three charged spin-1, and a neutral spin-1 mesons (15 states), and a neutral vector boson associated with the leptons; this gives 3+15+3×15=63 possible boson states, so a total correct count of 63+64=127 states. Something likeSU ₂×SU ₃ and other indications of quark quantum numbers can occur as substructures at the fourth (unstable) level. Breaking into the (Bose) hierarchy by structures with the quantum numbers of a fermion, if this is an electron, allows us to understand Parker-Rhodes' calculation ofm _p /m _e =1836.1515 in terms of our interpretation of the hierarchy. A slight extension gives us the usual static approximation to the binding energy of the hydrogen atom, ² m _e c ² . We also show that the cosmological implications of the theory are in accord with current experience. We conclude that we have made a promising beginning in the physical interpretation of a theory which could eventually encompass all branches of physics.Work supported by the Department of Energy under contract number EY-76-C-03-051.     

On the calculation of the two-point function for the thirring-model by the method of functional integration

By the method of functional integration the two-point functionS _F for the spinor model with the interaction\( - \lambda (\bar \psi \psi )^2 \) is calculated in a two-dimensional space-time. After Fourier-transformationS _F (p) results as a power series with respect to 1/√λ. If we change the order of terms, we get a series in powers of γp. Each coefficient is a series in powers of 1/√λ. The first terms of this series are considered as a good approximation for bigλ. By reasons of convergence of the integrals we must displace the expansion centre of the series in powers ofγ p fromp ²=0 top ²=a ².     

Contribution of the correlations of the director fluctuations to the neutron diffraction in the nematic phase

The intermolecular part of the nematic phase coherent neutron structure factor,S_inter(Q), including the correlations of the preferred molecular orientations, is calculated.     

Dynamics of the thermocline in the equatorial region of the Pacific ocean

This paper is devoted to the subsurface current dynamics in equatorial regions, where the hallmark of a strong stratification is a sharp interface (thermocline), separating two layers of different density, and whose depth is dependent upon the strength of the winds above the ocean's surface. We give here a few monotonicity results concerning the dynamics of the thermocline in the equatorial region. The most important one asserts that the level of the thermocline decreases as the strength of the wind at ten meters above the ocean surface, denoted |U_w|, increases. Moreover, the strength of the current at the thermocline decreases as |U_w| increases.     

Constraining the anisotropy of the Universe with the Pantheon supernovae sample

We test the possible dipole anisotropy of the Finslerian cosmological model and the other three dipole-modulated cosmological models, i.e. the dipole-modulated ΛCDM, wCDM and Chevallier–Polarski–Linder (CPL) models, by using the recently released Pantheon sample of SNe Ia. The Markov chain Monte Carlo (MCMC) method is used to explore the whole parameter space. We find that the dipole anisotropy is very weak in all cosmological models used. Although the dipole amplitudes of four cosmological models are consistent with zero within the \begin{document}$1\sigma$\end{document} uncertainty, the dipole directions are close to the axial direction of the plane of the SDSS subsample in Pantheon. This may imply that the weak dipole anisotropy in the Pantheon sample originates from the inhomogeneous distribution of the SDSS subsample. A more homogeneous distribution of SNe Ia is necessary to constrain the cosmic anisotropy.