Abe homotopy classification of topological excitations under the topological influence of vortices

Topological excitations are usually classified by the nth homotopy group πn. However, for topological excitations that coexist with vortices, there are cases in which an element of πn cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of πn corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of π₁ on πn. In this paper, we show that topological excitations coexisting with vortices are classified by the Abe homotopy group κn. The nth Abe homotopy group κn is defined as a semi-direct product of π₁ and πn. In this framework, the action of π₁ on πn is understood as originating from noncommutativity between π₁ and πn. We show that a physical charge of a topological excitation can be described in terms of the conjugacy class of the Abe homotopy group. Moreover, the Abe homotopy group naturally describes vortex-pair creation and annihilation processes, which also influence topological excitations. We calculate the influence of vortices on topological excitations for the case in which the order parameter manifold is Sn/K, where Sn is an n-dimensional sphere and K is a discrete subgroup of SO(n+1). We show that the influence of vortices on a topological excitation exists only if n is even and K includes a nontrivial element of O(n)/SO(n).     

The Lorentz-Lorenz function of five gaseous and liquid saturated hydrocarbons

The refractive indices of compressed gaseous and liquid ethane, propane,n-butane,n-pentane, and liquidn-hexane were measured on up to seven isotherms at temperatures between 290 K and 500 K. Densities ranged from 0.2 g/cm³ to 0.7 g/cm³ at pressures up to 170 bar. The refractive index valuesn were combined with simultaneously measured density values ?, to compute the Lorentz-Lorenz function LL =(n ²-1)M/(n ²+2) ?=A _n+B_n(?/M), whereM is the molar mass andA _n andB _n are the first and second refractive index virial coefficients. Additionally, the functions LL/z (z=pV/nRT is the compressibility factor) of ethane, propane, andn-butane were computed to determine the second refractive index virial coefficientsB _n(T). The relative uncertainty of the measured LL functions is 0.1% in most cases. At constant temperature (LL?A _n)/A_n is ≦5·10^?3 for ethane, propane, andn-butane and ≦0.02 forn-pentane andn-hexane. The greatest deviations of the LL functions from theA _n value were measured at the temperatures near the critical points. TheA _n-values show a temperature dependence which increases with increasing molar mass (maximum value: ΔA _n/ΔT=0.0044 cm³/mol · K). The slopes of the LL-function become lower and the LL maxima become smaller with increasing distance of the temperature from the critical point. TheB _n values increase linearly with reciprocal temperature.     

Universal Covering Group of U(n) and Projective Representations

Using fiber bundle theory, we construct the universal covering group of U(n),U(n), and show that U(n) is isomorphic to the semidirect product SU(n) ∝.We give a bijection between the set of projective representations of U(n) and theset of equivalence classes of certain unitary representations of SU(n) ∝.Applying Bargmann's theorem, we give explicit expressions for the liftings ofprojective representations of U(n) to unitary representations of SU(n) ∝. Forcompleteness, we discuss the topological and group theoretic relations betweenU(n), SU(n), U(t), and Z _n .     

Structural, electronic and magnetic properties of Mn, Co, Ni in Gen for (n=1-13)

The structural, electronic and magnetic properties of TMGe_n (TM=Mn, Co, Ni; n=1-13) have been investigated using spin polarized density functional theory. The transition metal (TM) atom prefers to occupy surface positions for n<9 and endohedral positions for n≥9. The critical size of the cluster to form endohedral complexes is at n=9, 10 and 11 for Mn, Co and Ni respectively. The binding energy of TMGe_n clusters increases with increase in cluster size. The Ni doped Ge_n clusters have shown higher stability as compared to Mn and Co doped Ge_n clusters. The HOMO-LUMO gap for spin up and down electronic states of Ge_n clusters is found to change significantly on TM doping. The magnetic moment in TMGe_n is introduced due to the presence of TM. The magnetic moment is mainly localized at the TM site and neighbouring Ge atoms. The magnetic moment is quenched in NiGe_n clusters for all n except for n=2, 4 and 8.     

A general multi-secret visual cryptography scheme

In a (k, n) visual cryptography scheme (VCS), a secret image is encoded into n shadow images that are distributed to n participants. Any k participants can reveal the secret image by stacking their shadow images, and less than k participants have no information about the secret image. In this paper we consider the case when the secret image is more than one, and this is a so-called multi-secret VCS (MVCS). The previous works on MVCS are all the simple 2-out-of-2 cases. In this paper, we discuss a general (k, n)-MVCS for any k and n. This paper has three main contributions: (1) our scheme is the first general (k, n)-MVCS, which can be applied on any k and n, (2) we give the formal security and contrast conditions of (k, n)-MVCS and (3) we theoretically prove that the proposed (k, n)-MVCS satisfies the security and contrast conditions.     

A Level 1 Large-Deviation Principle for the Autocovariances of Uniquely Ergodic Transformations with Additive Noise

A large-deviation principle (LDP) at level 1 for random means of the type $$M_n \equiv \frac{1}{n}\sum\limits_{j = 0}^{n - 1} {Z_j Z_{j + 1} ,{\text{ }}n = 1,2,...}$$ is established. The random process {Z _n} _n≥0 is given by Z _n = Φ(X _n) + ξ _n , n = 0, 1, 2,..., where {X _n} _n≥0 and {ξ _n} _n≥0 are independent random sequences: the former is a stationary process defined by X _n = T ⁿ(X ₀), X ₀ is uniformly distributed on the circle S ¹, T: S ¹ → S ¹ is a continuous, uniquely ergodic transformation preserving the Lebesgue measure on S ¹, and {ξ_n} _n≥0 is a random sequence of independent and identically distributed random variables on S ¹; Φ is a continuous real function. The LDP at level 1 for the means M _n is obtained by using the level 2 LDP for the Markov process {V _n = (X _n, ξ _n , ξ _n+1)} _n≥0 and the contraction principle. For establishing this level 2 LDP, one can consider a more general setting: T: [0, 1) → [0, 1) is a measure-preserving Lebesgue measure, $\Phi :\left[ {0,\left. 1 \right)} \right. \to \mathbb{R}$ is a real measurable function, and ξ _n are independent and identically distributed random variables on $\mathbb{R}$ (for instance, they could have a Gaussian distribution with mean zero and variance σ²). The analogous result for the case of autocovariance of order k is also true.     

Image potential eigenstates and resonances on the (110) surfaces of noble metals: Energies and lifetimes

The energies and lifetimes of the image potential resonances at the ? point on the Cu(110), Ag(110), and Au(110) surfaces are studied, and the energies of the image potential states on the Pd(110) surface are analyzed. It is shown that every quantum number n corresponds to a pair of image potential states (resonances) n ⁺ and n ^? at the ? point. The average energy of a pair of eigenstates (resonances) at n ≥ 2 is well described by the formula ē _n = (E _n+ + E _n?) = E ₀ ? (0.85 eV)/(n + δ)², where δ is the quantum defect, E ₀ = (1/2m _e )(?π/a)², and a is the lattice parameter. The splitting energy of a pair of eigenstates (resonances) obeys the law ΔE _n = E _n+ — E _n? ∝ n ^?3. The lifetimes τ _n± of image potential resonances are proportional to n ³.     

Density functional theory study of AunMn(n=1-8) clusters

Equilibrium geometries, relative stabilities, and magnetic properties of small Au_nMn (n=1-8) clusters have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms in the ground state Au_nMn isomers tend to occupy the most highly coordinated position and the lowest energy structure of Au_nMn clusters with even n is similar to that of pure Au_n+1 clusters, except for n=2. The substitution of Au atom in Au_n+1 cluster by a Mn atom improves the stability of the host clusters. Maximum peaks are observed for Au_nMn clusters at n=2, 4 on the size dependence of second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. The HOMO-LUMO energy gaps of the ground state Au_nMn clusters show a pronounced odd-even oscillation with the number of Au atoms, and the energy gap of Au₂Mn cluster is the biggest among all the clusters. The magnetism calculations indicate that the total magnetic moment of Au_nMn cluster, which has a very large magnetic moment in comparison to the pure Au_n+1 cluster, is mainly localized on Mn atom.     

Temperature dependence of radiative strength functions and isomeric cross sections

The effect of a parametrization of the temperature dependence of radiative strength functions for electric dipole transitions on the cross sections for isomer excitation in (n, γ), (n, 2n), (n, p), (n, α), (γ, \g′), (γ, n), (γ, p), and (γ, 2n) reactions is investigated. It is shown that the agreement of the results of calculations with the observed isomeric cross sections can be considerably improved by using the proposed method.     

Breaking of the SO(n) symmetry with vector and adjoint higgses

The spontaneous symmetry breaking of SO(n) is investigated by studying the most general quartic SO(n)-invariant Higgs potential with two multiplets of scalars belonging to a vector and to an adjoint representation. In the most general cases largest residual symmetry is found to be SU(l), SU(l-1), SO(l), SO(l-1) or SO(n-2) wherel is the rank of SO(n). In particular, the breaking of SO(n) into SU(n ₁)×SU(n ₂) is found to occur only in special cases.     

On the specific features and transformation of the band structure of mercury-based HTSC compounds

A systematic analysis of the temperature dependences of the thermopower S(T) for different phases of the HgBa₂Ca _n?1Cu _n O_2n+2+δ family (n=1, 2, 3) at different doping levels is performed in the framework of a narrow-band phenomenological model. Quantitative estimates of the main parameters of the band responsible for conduction in the normal phase of HgBa₂Ca _n?1Cu _n O_2n+2+δ are given for optimally doped samples. The character of the variation in these parameters with an increasing number n of the copper-oxygen layers is discussed. A trend toward broadening of the conduction band with increasing n is revealed, which can be due to the increase of the density-of-states (DOS) peak near the Fermi level with an increasing number of the CuO₂ layers responsible for the formation of the conduction band. It is found that an increase in the number n leads to an increase in the fraction of localized carriers in the band owing to a more defective structure observed in the more complex phases of HgBa₂Ca _n?1Cu _n O_2n+2+δ. The variations in the band-structure parameters in going from under-to overdoped compositions in the HgBa₂Ca _n?1Cu _n O_2n+2+δ family are also discussed.     

Solitary wave interactions in lattice systems with pure higher-order nonlinearity

In this paper, we investigate in detail the interactions of solitary waves in lattice systems with interaction potential V(q)=qⁿ/n, where n is 4,6,8…, through their all possible collision types, and establish a quantitative connection between the scattering property of solitary waves and the chaotic dynamics of the systems. Kink and antikink are excited in such lattice systems and the variation of their scattering effect with n is concerned. After a kink-antikink collision, the dominant interaction in the systems, if n is small, is that solitary waves pass through each other and the scattering effect increases with n; if n is large, solitary waves reflect back sometimes due to the influence of phase and this leads to a decrease of the scattering effect with n. The largest Lyapunov exponents of systems at fixed energy density first increase and then decrease with n, which is consistent with a variation of the scattering effect. The application of the special scattering behaviors between kink and antikink in information propagation is also discussed.     

Helium emission spectra—I. intermediate pressure studies

The apparent cross sections of the n¹P(n = 3,4,5,6) and n^1,3D(n = 4,5,6,7) levels have been measured as a function of pressure between 5 and 200 mTorr at 1·5KeV electron impact excitation energy. The 4¹S apparent cross section was measured under the same conditions to observe secondary electron effects. A detailed analysis is made on the mechanisms of excitation transfer out of the n¹P levels in terms of radiative and collision processes. Collisional n¹P?nF transfer cross sections are calculated for the n = 4 and n = 5 levels and the results are in agreement with the principle of detailed balance. An analysis of the 6¹P apparent cross section indicates that collision processes other than n¹P?nF become important at n = 6 level in determining collisional transfer out of n¹P. Evaluation of n^1,3D apparent cross sections show that direct collisional gain and loss become more important as n increases.     

The bootstrap condition for many reggeized gluons and the photon structure function at lowx andN c→∞

The bootstrap condition is generalized ton reggeized gluons. As a result it is demonstrated that the intercept generated byn reggeized gluons cannot be lower than the one forn=2. Arguments are presented that in the limitN _c→∞ the bootstrap condition reduces then gluon chain with interacting neighbours to a single BFKL pomeron. In this limit the contribution fromn gluons leading at high energies corresponds ton/2 non-interacting BFKL pomerons (then/2 pomeron cut). The sum overn leads to a unitaryγ*γ amplitude of the eikonal form.     

Analysis of the diffraction by the gratings generated in the materials with a nonlinear response

Diffraction by a thick transmission phase grating being illuminated by a plane wave at the first, second and third Bragg angles is analyzed using the rigorous coupled-wave theory for the materials having a nonlinear response to the holographic illumination. It is shown that in the case of nonlinear holographic recording the two-wave approximation can be applied with the use of the effective value of the amplitudes of the refractive index modulation (n_1ef, n_2ef, and n_3ef). The applicability conditions of such approximation are defined. The analytical dependencies of n_1ef, n_2ef, and n_3ef on the amplitudes of the first, second and third harmonics of spatial frequency of the refraction index modulation amplitude n₁, n₂ and n₃ are derived and the criteria of their applicability are established here. The resulting expressions for the diffraction efficiencies are given for readout at three Bragg angles. The results of analytical and numerical methods are compared. The obtained formulas are used for the calculation of n₁, n₂ and n₃ of the holographic gratings generated in the photopolymer material.     

Production of 6He and 9Be by radiative capture and four-body recombination

In this work we estimate the production rates for the three-body radiative capture processes α + n + n → ⁶He + γ and α + α + n → ⁹Be + γ, as well as the four-body recombination reactions α + α + n + n → ⁶He + α, ^α + n + n + n → ⁶He + n, α + α + n + n → ⁹Be + n and α + α + α + n → ^BeBe + α. These processes compete as a source of ⁶He and ⁹Be. The hyperspherical adiabatic expansion method is used. With this method no assumption is made about the capture mechanism. Both sequential and direct capture are included. The production rates for the radiative and the four-body recombination processes are found to be comparable for a mass density of about 10⁷g/cm³ ( ～ 10³⁰ neutrons/cm³) and temperatures of a few GK.     

Spin structure of the “forward” charge-exchange reaction n + p → p + n and deuteron charge-exchange breakup d + p → (pp) + n

The spin structure of the nucleon charge-exchange process n + p → p + n is investigated. Analysis shows that the spin-dependent part of the differential cross section of the process n + p → p + n at zero angle, which is proportional to the differential cross section of the deuteron charge-exchange breakup d + p → (pp) + n in the “forward” direction, plays the predominant role in the wide range of neutron momenta.     

Multicritical behavior of the two-field Ginzburg-Landau model coupled to a gauge field

In this paper, we study the multicritical behavior of the Ginzburg-Landau model in a O(n₁)⊕O(n₂)-symmetric version containing (n₁/2+n₂/2)-complex order parameters coupled to a gauge field. We develop the RG analysis at a one-loop approximation in the context of the ?-expansion approach. The beta functions are obtained, and in the case of equal couplings between the two scalar fields and the gauge field and n₁=n₂=n/2, the infrared stability of the fixed points is discussed. It is found that the charged infrared-stable fixed point exists for n>393.2. Calculations of the relevant critical exponents are also carried out.     

On the vacuum rearrangement in massless chromodynamics

It is shown that in the weak coupling limit the Bethe-Salpeter equation of massless chromodynamics admits a colourless tachyon solution when the number of quark multiplets n ? n_c, where for the colour group SU(N) the critical value n_c ≈ 0.14 N³/(N² ? 1). When n ? n_c, the vacuum rearrangement results in the gluons acquiring a mass; n > n_c all particles remain massless.     

The bootstrap condition for many reggeized gluons and the photon structure function at lowx andN c����

The bootstrap condition is generalized ton reggeized gluons. As a result it is demonstrated that the intercept generated byn reggeized gluons cannot be lower than the one forn=2. Arguments are presented that in the limitN _c???? the bootstrap condition reduces then gluon chain with interacting neighbours to a single BFKL pomeron. In this limit the contribution fromn gluons leading at high energies corresponds ton/2 non-interacting BFKL pomerons (then/2 pomeron cut). The sum overn leads to a unitary??*?? amplitude of the eikonal form.