Freezing of Energy of a Soliton in an External Potential

In this paper we study the dynamics of a soliton in the generalized NLS with a small external potential ?V of Schwartz class. We prove that there exists an effective mechanical system describing the dynamics of the soliton and that, for any positive integer r, the energy of such a mechanical system is almost conserved up to times of order ?^?r. In the rotational invariant case we deduce that the true orbit of the soliton remains close to the mechanical one up to times of order ?^?r.     

Intergroup azimuthal correlations of secondary particles in the interaction between <Superscript>56</Superscript>Fe nuclei of momentum 2.5 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon and photoemulsion nuclei

Angular correlations between secondary particles emitted in the interaction between ⁵⁶Fe nuclei of momentum 2.5 GeV/c per nucleon and photoemulsion nuclei were measured. These secondaries are partitioned into four groups: s, g, b, and f. For particles from each pair of the above groups, the average values of the collinearity factor and of the asymmetry parameter, as well as the parameter η of the function α(1+η cos ε) approximating the distribution of azimuthal-angle differences ε, were calculated.     

Random time averaged diffusivities for Lévy walks

We investigate a Lévy walk alternating between velocities ±v ₀ with opposite sign. The sojourn time probability distribution at large times is a power law lacking its mean or second moment. The first case corresponds to a ballistic regime where the ensemble averaged mean squared displacement (MSD) at large times is ?x ²? ∝ t ², the latter to enhanced diffusion with ?x ²? ∝ t ^ν, 1 < ν < 2. The correlation function and the time averaged MSD are calculated. In the ballistic case, the deviations of the time averaged MSD from a purely ballistic behavior are shown to be distributed according to a Mittag-Leffler density function. In the enhanced diffusion regime, the fluctuations of the time averages MSD vanish at large times, yet very slowly. In both cases we quantify the discrepancy between the time averaged and ensemble averaged MSDs.     

On the theory of the resonant interaction of electrons with a high-frequency electric field in one-dimensional two-barrier nanostructures with symmetric barriers of finite height and width

The theory of the interaction of electrons with a high-frequency electric field in one-dimensional two-barrier nanostructures with symmetric barriers of finite height and widths was developed. An exact solution to the Schrödinger equation was found for electrons in this nanostructure in the absence of high-frequency electric field. An analytical expression for the direct current I ₀ induced in this structure by an incident electron flux with energy ε differing slightly from the resonant level energy ε _r (|ε ? ε _r | << ε _r ) was derived. In the small-signal approximation, the active (field-phased) component I _c of the alternating electric current was calculated. At ε > ε _r , the current I _c is negative in the entire frequency range, which suggests the possibility of ac electric field amplification and generation in the two-barrier resonant-tunneling structure with the barriers of finite height and width. Within the applicability of the theory (?ω << ε _r ), the frequency at which amplification and generation of the ac electric field are possible reaches ω ? 10¹³ s ^?1; the power transferred by electrons to the field is ～1 W/cm².     

Meson Effect in the Proto Neutron Star PSR J0348+0432

The effect of mesons f ₀(975) (named as f), ?(1020) (named as ?) and δ on the moment of inertia of the PNS PSR J0348+0432 is examined in the framework of the relativistic mean field theory considering the baryon octet. It is found that the energy density ε and pressure p will increase considering the mesons δ whereas will decrease as the mesons f and ? being considered. When the mesons f,? and δ are considered, the energy density and pressure will all decrease. It is also found that the contribution of mesons f, ? and δ to the central energy density is only the central energy density’s 0.06 ～0.6% whereas the contribution of mesons f, ? and δ to the central pressure is the central pressure’s 4 ～7%. For the radius, it will decrease when the contributions of mesons f, ? and δ are considered. The moment of inertia I will increase considering the mesons δ whereas will decrease as the mesons f and ? being considered. When the mesons f, ? and δ are all considered, the moment of inertia will decrease. It is found that the contribution of mesons f and ? to moment of inertia is 4 ～9 times larger than that of mesons δ. Our results show that the mesons f, ? and δ contribute to the moment of inertia’s 2 ～5%.     

Propagation of electromagnetic waves in hot magnetoactive plasma

The paper derives the general form of the tensor of dielectric permittivity? _ij(ω,k), Eq. (15), of non-relativistic hot magnetoactive collisionless plasma taking into consideration the influence of spatial dispersion. The general form of the tensor? _ij(ω,k) is used to express the tensorε _ij(ω,k) in the region of weak and strong spatial dispersion and in some special cases. A general dispersion equation (30) is derived and an analysis is made of the waves propagating in hot magnetoactive plasma. The expressions derived are used to investigate the damping of a right-handed circularly polarized wave propagating in hot magnetoactive plasma in the direction of the magnetic field.     

Analysis of the production of Higgs boson pairs at the one-loop level in the minimal supersymmetric standard model

Within theminimal supersymmetric standardmodel, the amplitudes and total cross sections for the processes e ⁺ e ^? → hh, e ⁺ e ^? → hH, e ⁺ e ^? → HH, and e ⁺ e ^? → AA are calculated in the first order of perturbation theory with allowance for a complete set of one-loop diagrams in the m _e → 0 approximation. Analytic expressions are obtained for the quantities under consideration; numerical results are presented in a graphical form. It is shown that the cross section for the process e ⁺ e ^? → hh is larger than those for the other processes (and is on the same order of magnitude as the cross section for the corresponding processes in the Standard Model). In the case of the collision energy equal to √s = 500 GeV, an integrated luminosity in the region ∫ ? ≥ 500 fb^?1, and a longitudinal polarization of the e ⁺ e ? beams used, 520, 320, and 300 production events are possible in the processes e ⁺ e ^? → hh (at M _h = 115 GeV), e ⁺ e ^? → HH, and e ⁺ e ^? → AA (at M _H,A = 120 GeV), respectively. Even at M _H,A ≈ 500 GeV and √s = 1.5 TeV, not less than 200 events for each of the processes can be accumulated. The cross section for the process e ⁺ e ^? → hH is small (about 10^?2 fb), which complicates the detection of the sought signal significantly.     

On the binding of atoms with antiatoms

The stability of X⁺Y⁺X^?Y^? Coulomb molecules consisting of X⁺Y^? atoms and X^?Y⁺ antiatoms to dissociation is studied. On the basis of multiparameter variational calculations, it is found that such molecules are stable to dissociation into X⁺X^? atoms and Y⁺Y^? antiatoms if the mass ratio of particles X and Y lies in the range 0.4710<m _X /m _Y <2.1231. The e⁺e⁺e^?e^?, π⁺μ⁺π^?μ^?, t⁺d⁺t^?d^?, p⁺K⁺p^?K^?, and d⁺p⁺d^?p^? molecules satisfy this condition.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

Pseudo-ε-expansion and the two-dimensional Ising model

The pseudo-ε-expansions for the coordinate of the fixed point g^*, the critical exponents, and the sextic effective coupling constant g₆ are determined for the two-dimensional Ising model on the basis of the five-loop renormalization group series. It is found that the pseudoe-expansions for the coordinate of the fixed point g^*, the inverse exponent γ^?1, and the constant g₆ possess a remarkable property, namely, the higher terms of these series are so small that reliable numerical results can be obtained without invoking Borel summation.     

Energy and momentum losses of a magnetized plasma via familon emission

Familon emission from a dense magnetized plasma in the processes e^? → e^?φ and e^? → μ^?φ is investigated. The contribution of these processes to the energy losses of a supernova remnant is calculated. It is shown that, at a late stage of the cooling of a supernova remnant, the energy loss of a plasma via familon emission may become commensurate with the loss via neutrino emission. It is found that, because of asymmetry of familon emission in the process e^? → gm^?φ, there arises a force acting on the plasma.     

Long Time,Large Scale Limit of the Wigner Transform for a System of Linear Oscillators in One Dimension

We consider the long time, large scale behavior of the Wigner transform W _? (t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile et al. in Phys. Rev. Lett. 96 (2006) to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile et al. in Arch. Rat. Mech. 195(1):171–203 (2009). In the present paper we prove that in the unpinned case there exists γ ₀>0 such that for any γ∈(0,γ ₀] the weak limit of W _? (t/? ^3/2γ ,x/? ^γ ,k), as ??1, satisfies a one dimensional fractional heat equation \(\partial_{t} W(t,x)=-\hat{c}(-\partial_{x}^{2})^{3/4}W(t,x)\) with \(\hat{c}>0\). In the pinned case an analogous result can be claimed for W _? (t/? ^2γ ,x/? ^γ ,k) but the limit satisfies then the usual heat equation.     

Tests of discrete symmetries with the neutral kaon system at the KLOE and KLOE-2 experiments

The KLOE-2 experiment continues and extends the program of its predecessor KLOE in the field of discrete symmetry tests with the K meson system, among other studies which comprise light meson spectroscopy, dark matter searches and γγ physics. Together, KLOE and KLOE-2 have recorded the largest sample (almost 8 fb^??1) of e⁺e^? collisions at the energy equal to ? meson mass, amounting to 2.4 × 10¹⁰ of produced ? mesons. We report on the latest results and ongoing analyses of KLOE and KLOE-2 concerning discrete symmetry tests and measurements of symmetry-violating observables. A measurement of the CPT violation sensitive asymmetry in semileptonic decays of K˙S with 1.7 fb^??1 of KLOE data will be presented, which improves the sensitivity w.r.t. previous measurements about twice. Moreover, status of direct tests of T and CPT in transitions of neutral kaons performed with the ? →K˙SK˙L → πeν, 3π⁰(2π) processes will be reported, followed by the search of the CP-violating decay K˙S → 3π⁰ using the data recently acquired by KLOE-2.     

Application of the hidden local symmetry effective chiral Lagrangian to evaluation of the <Emphasis Type="Italic">ω</Emphasis>(782), <Emphasis Type="Italic">ϕ</Emphasis>(1020) → 5<Emphasis Type="Italic">π</Emphasis> decay widths

The amplitudes obtained from the effective chiral Lagrangian with anomalous terms based on hidden local symmetry are applied to the evaluation of the partial widths of the decays ω → 2π⁺2π^?π⁰ and ω → π⁺π^?3π⁰. Combining the Okubo-Zweig-Iizuka rule, applied to the five-pion final state, with the Adler condition of vanishing of the amplitude at the vanishing of four-momentum of any final pion in the chiral limit, the ? → 2π⁺2π^?π⁰ and ? → π⁺π^?3π⁰ decay amplitudes are also calculated. The partial widths of the above decays are evaluated, and the resonance excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the free parameters characterizing the anomalous terms of the Lagrangian. The evaluated branching ratios \(Br_{\phi \to \pi + \pi - 3\pi ^0 } \approx 2 \times 10^{ - 7} \) and \(Br_{\phi \to 2\pi + 2\pi - \pi ^0 } \approx 5 \times 10^{ - 7} \) are such that with the luminosity L = 500 pb^?1, attained at the DAΦNE ? factory, one may already possess about 1340 events of the decays ? → 5π.     

Pentaquark search in the NA49 experiment

The NA49 experiment has found narrow peaks in the Ξ^? π ^?, Ξ^? π ⁺ (and antiparticle) spectra at 1862 MeV/c ². These states were identified with the predicted pentaquark cascades. We have searched for other decay channels of the pentaquark cascades. No signal was observed in the ΛK ^? and ΛK _S ⁰ spectra. Based on systematic inconsistencies in the experimental values of the reported Θ⁺, we tried to look for other possible pentaquark states, but observed no signal beyond statistical fluctuations.     

Effect of FCNC mediated <Emphasis Type="Italic">Z</Emphasis> boson on lepton flavor violating decays

We study the three body lepton flavor violating (LFV) decays μ ^?→e ^? e ⁺ e ^?, \(\tau^{-} \to l_{i}^{-} l_{j}^{+} l_{j}^{-}\) and the semileptonic decay τ→μφ in the flavor changing neutral current (FCNC) mediated Z boson model. We also calculate the branching ratios for LFV leptonic B decays, B _d,s →μe, B _d,s →τe, B _d,s →τμ and the conversion of muon to electron in Ti nucleus. The new physics parameter space is constrained by using the experimental limits on μ ^?→e ^? e ⁺ e ^? and τ ^?→μ ^? μ ⁺ μ ^?. We find that the branching ratios for τ→eee and τ→μφ processes could be as large as \({\sim}{\mathcal{O}}(10^{-8})\) and \(\mathrm{Br}(B_{d,s} \to \tau \mu,~ \tau e) \sim {\mathcal{O}}(10^{-10})\). For other LFV B decays the branching ratios are found to be too small to be observed in the near future.     

Zur Theorie der Vorwärtsasymmetrie bei der Photospaltung des Deuterons

The forward asymmetry in the differential cross section for the photo disintegration of the deuteron has been calculated on the basis of a phenomenological theory for energies up to 80 MeV. The formulas for this asymmetry, which come from theE1-E2-andM1-M2-interference, are given, assuming the validity ofSiegert's theorem. TheE2-andM2-amplitudes are calculated approximately, using the Hulthén wavefunction with a 4% D-state admixture for the ground state and scattered waves determined by the phase shifts given by Marshak for the final states. The contribution of theM1-M2-interference turns out to be unimportant for the asymmetry, theE1-E2-interference giving the main effect. In the differential cross section,dσ/dΩ=a + b sin ² ? + c cos ? + d cos ? sin ² ?, we have obtained a very low value forc and the ratioc/d is approximately equal toa/3b. This is in contradiction to the assumptionc/d=a/b made in the previous analysis of the experimental data. This ratio seems to be insensitive to the value of the D-state admixture. For the lover energiesE _γ=10 MeV andE _γ=20 MeV the theoretical values for “d” are in agreement with the experimental ones. For the energies 54 and 80 MeV we have made a comparison of the theoretical differential cross sectiondσ/dΩ, taking into account the values for “a” and “b”, obtained in a former work ie, with the measureddσ/dΩ.     

Weak radiative hyperon decays in the quark model

Weak radiative hyperon decays are considered on the basis of the quark model including one-quark transitions associated with the effective sdγ vertex and two-quark processes s + u → u + d + γ induced by W-boson exchange. The phenomenological model proposed in this study gives values that describe experimental data well and makes predictions for the asymmetry of the decays Λ → n + γ and ξ^? → Σ^? + γ.     

Many-electron model of band structure and metal-insulator transition under pressure in FeBO<Subscript>3</Subscript>

A many-electron model is proposed for the band structure of FeBO₃ with regard to strong electron correlations in the d⁴, d⁵, and d⁶ configurations. Under normal conditions, FeBO₃ is characterized by a dielectric charge-transfer gap in the strong correlation regime U?W. With increasing pressure, not only does the d-band W width grow but simultaneously the effective Hubbard parameter U_eff sharply drops, which is due to the crossover of high-spin and low-spin ground state terms of the Fe²⁺, Fe³⁺, and Fe⁴⁺ ions. It is predicted that a transition from the semiconducting antiferromagnetic state to the metallic paramagnetic state will occur in the high-pressure phase with increasing temperature.     

Probable Decay Modes at Limits of Nuclear Stability of the Superheavy Nuclei

The modes of decay for the even–even isotopes of superheavy nuclei of Z = 118 and 120 with neutron number 160 ≤ N ≤ 204 are investigated in the framework of the axially deformed relativistic mean field model. The asymmetry parameter η and the relative neutron–proton asymmetry of the surface to the center (R _η ) are estimated from the ground state density distributions of the nucleus. We analyze the resulting asymmetry parameter η and the relative neutron–proton asymmetry R _η of the density play a crucial role in the mode(s) of decay and its half-life. Moreover, the excess neutron richness on the surface, facets a superheavy nucleus for β^? decays.