Singular Resonance in Fluctuation-Induced Electromagnetic Phenomena at the Rotation of a Nanoparticle near the Surface of a Condensed Medium

It has been shown that the rotation of a spherical nanoparticle with the radius R near the surface of a semi-infinite homogeneous medium can result in singular resonance in fluctuation-induced electromagnetic phenomena (Casimir force, Casimir friction, and radiative heat generation). Fluctuation electromagnetic effects increase strongly near this resonance even in the presence of dissipation in the system. The resonance occurs at distances of the particle from the surface d < d₀R(3/4ε″₁(ω₁)ε″₂ (ω₂))^1/3 (where ε″_i(ω_i) is the imaginary part of the dielectric function of the particle or the medium at the frequency of a surface phonon or plasmon polariton ω_i), when the rotation frequency coincides with poles in the photon generation rate at Ω ≈ ω₁ + ω₂. These poles are due to the multiple scattering of electromagnetic waves between the particle and surface under conditions of the anomalous Doppler effect. These poles exist even in the presence of dissipation. At d < d₀, depending on the particle rotation frequency, the Casimir force can change sign; i.e., the attraction of the particle to the surface changes to repulsion. The results can be important for the development of experimental methods for the detection of quantum friction.     

Finite-size scaling from the self-consistent theory of localization

Accepting the validity of Vollhardt and Wölfle’s self-consistent theory of localization, we derive the finite-size scaling procedure used for studying the critical behavior in the d-dimensional case and based on the consideration of auxiliary quasi-1D systems. The obtained scaling functions for d = 2 and d = 3 are in good agreement with numerical results: it signifies the absence of substantial contradictions with the Vollhardt and Wölfle theory on the level of raw data. The results ν = 1.3–1.6, usually obtained at d = 3 for the critical exponentν of the correlation length, are explained by the fact that dependence L + L ₀ with L ₀ > 0 (L is the transversal size of the system) is interpreted as L ^1/ν with ν > 1. The modified scaling relations are derived for dimensions d ≥ 4; this demonstrates the incorrectness of the conventional treatment of data for d = 4 and d = 5, but establishes the constructive procedure for such a treatment. The consequences for other finite-size scaling variants are discussed.     

Stabilizer of a function in the gage group

It is proved that, for the dimension d of the stabilizer of an analytic function z(x, y) in the gage pseudogroup G = {z(x, y) → c(z(a(x), b(y))}, there are precisely four possibilities: (1) d = ∞ and the complexity of z is zero, (2) d = 3 and the complexity of z is equal to one, (3) d = 1 and z is equivalent the function r(x + y) ? x of complexity two, (4) d = 0 in all remaining cases.     

A New Family of Solvable Pearson-Dirichlet Random Walks

An n-step Pearson-Gamma random walk in ? ^d starts at the origin and consists of n independent steps with gamma distributed lengths and uniform orientations. The gamma distribution of each step length has a shape parameter q>0. Constrained random walks of n steps in ? ^d are obtained from the latter walks by imposing that the sum of the step lengths is equal to a fixed value. Simple closed-form expressions were obtained in particular for the distribution of the endpoint of such constrained walks for any d≥d ₀ and any n≥2 when q is either \(q = \frac{d}{2} - 1 \) (d ₀=3) or q=d?1 (d ₀=2) (Le Caër in J. Stat. Phys. 140:728–751, 2010). When the total walk length is chosen, without loss of generality, to be equal to 1, then the constrained step lengths have a Dirichlet distribution whose parameters are all equal to q and the associated walk is thus named a Pearson-Dirichlet random walk. The density of the endpoint position of a n-step planar walk of this type (n≥2), with q=d=2, was shown recently to be a weighted mixture of 1+floor(n/2) endpoint densities of planar Pearson-Dirichlet walks with q=1 (Beghin and Orsingher in Stochastics 82:201–229, 2010). The previous result is generalized to any walk space dimension and any number of steps n≥2 when the parameter of the Pearson-Dirichlet random walk is q=d>1. We rely on the connection between an unconstrained random walk and a constrained one, which have both the same n and the same q=d, to obtain a closed-form expression of the endpoint density. The latter is a weighted mixture of 1+floor(n/2) densities with simple forms, equivalently expressed as a product of a power and a Gauss hypergeometric function. The weights are products of factors which depends both on d and n and Bessel numbers independent of d.     

Two-photon production of vector resonance in <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> collisions

A parameterization of the amplitude of the two-photon production of 1⁺⁺ and 1^?+ vector resonances V in the e ⁺ e ^? → e ⁺ e ^? V reaction has been obtained. The differential (in momentum transfer) scattering cross section dσ/dQ ² has been found for this reaction in the equivalent-photon approximation. The result obtained is model-independent.     

Experimental Study and Analysis of Absorption Spectra of Ni<Superscript>2+</Superscript> Ions in Nickel Orthoborate Ni<Subscript>3</Subscript>(BO<Subscript>3</Subscript>)<Subscript>2</Subscript>

The results of studies of the absorption spectra of nickel orthoborate Ni₃(BO₃)₂ in the range of electronic d–d-transitions are reported. The obtained data are analyzed in the framework of the crystal field theory. The Ni²⁺ ions are located in two crystallographically nonequivalent positions 2a and 4f with point symmetry groups C_2h and C₂, respectively, surrounded by six oxygen ions forming deformed octahedra. The absorption spectra exhibit three intense bands corresponding to spin-resolved transitions from the ground state of nickel ion ³A_2g (³F) to the sublevels of the ³T_2g (³F), ³T_1g (³F) and ³T_1g (³P) triplets split by the spinorbit interaction and the rhombic component of the crystal field. At temperatures below 100 K, the spectra exhibit a thin structure, in which phonon-free lines can be distinguished. Comparison of the calculated frequencies of the zero-phonon transitions with the experimental data allows estimating parameters of the crystal field acting on the nickel ions in the 2a- and 4f-positions, as well as the parameters of electrostatic interaction between the 3d electrons and spin-orbit interaction constants.     

Hyperfeinstruktur-Untersuchungen im Rhenium-I-Spektrum

By optical means (i.e. hollow cathode, Fabry-Perot-interferometer and spectrograph) the hyperfine structure of 15 transitions in the Re-I spectrum was investigated. This permits to state the hfs coupling constantsA, B for 15 levels belonging to the configurations (5d ⁵) 6s ², (5d ⁵) 6s 6p, (5d ⁵) 6s 7s, (5d ⁶) 6s, (5d ⁶) 6p and (5d ⁴) 6s ² 6p. It was found that the (5d ⁵) 6s ^{2 6} S _5/2 ground state, too, shows a small hfs. Of its magnetic splitting both size and sign could be determined (A _0,185,187=?2,2±0,4 mK); for a possible quadrupole splitting upper limits were obtained. Estimates of the quadrupole moments resulted inQ _185,187?2,9b. — In the case of two levels (x ⁶ P _7/2 andy ⁶ F _11/2) the hfs analysis raises doubts as to their classification.     

New magic nuclei and conditions of their formation

The systematic studies of the arrangement features of single-particle nucleon subshells in even-even ^90,92,94,96Zr isotopes and behavior of some known “magicity parameters” in isotopes and isotones neighboring the ⁹⁶Zr nucleus have led to the interpretation of ⁹⁶Zr as a new doubly magic nucleus. Analysis of the structure of nucleon shells in the ⁹⁶Zr nucleus revealed a feature, which consisted in that near the Fermi energy it had filled proton (π1f _5/2) and neutron (v2d _5/2) subshells with an identical and large total momentum j = 5/2, which was called the j-j coupling. Above the π1f _5/2 shell, there is another filled shell (π2p _1/2) with two j = 1/2 protons. Applied to other filled shells, this empirical rule allowed revealing several new nontraditional magic nuclei: ⁹⁶Sr (Z = 38, N = 58), π1f _5/2, v2d _5/2, and v3s _1/2 subshells; ⁵⁴Ca (Z = 20, N = 34), π2p _3/2, v1d _3/2, and v2p _1/2 subshells; a pair of ³⁰Si (Z = 14, N = 16) and ³⁰S (Z = 16, N = 14) nuclei, π1d _5/2, v1d _5/2, and (π/v)2s _1/2 subshells; and a pair of ¹⁴C (Z = 6, N = 8) and ¹⁴O (Z = 8, N = 6) nuclei, 1p _3/2, v1p _3/2, and v2p _1/2 subshells. The existence of the magic nuclei ^52,54Ca is widely discussed in the literature, the possibility of the existence of the other nuclei found is confirmed by the systematics of the behavior of the “magicity” parameters. The fact that shells with some nucleon numbers different from the classical magic numbers are closed may be due to the manifestation of a new type of interaction between nuclear protons and neutrons occupying certain subshells.     

Gottfried Sum Rule in QCD Nonsinglet Analysis of DIS Fixed-Target Data

Deep-inelastic-scattering data from fixed-target experiments on the structure function F₂ were analyzed in the valence-quark approximation at the next-to-next-to-leading-order accuracy level in the strong-coupling constant. In this analysis, parton distributions were parametrized by employing information from the Gottfried sum rule. The strong-coupling constant was found to be α _s (M²_Z) = 0.1180 ± 0.0020 (total expt. error), which is in perfect agreement with the world-averaged value from an updated Particle Data Group (PDG) report, α^PDG _s (M²_Z) = 0.1181 ± 0.0011. Also, the value of 〈x〉_u?d = 0.187 ± 0.021 found for the second moment of the difference in the u- and d-quark distributions complies very well with the most recent lattice result 〈x〉^LATTICE_u?d = 0.208 ± 0.024.     

Energy levels of ions of silver and rhodium isoelectronic sequences with <Emphasis Type="Italic">Z</Emphasis> < 86

The method of extrapolation of the parameter of a model potential for states of one electron (4f, 5s, 5p, 5d, 5f) above the core 1s ²2s ²2p ⁶3s ²3p ⁶3d ¹⁰4s ²4p ⁶4d ¹⁰ and one vacancy (4d ⁹) in the same core is applied to calculate the energy levels in the silver and rhodium isoelectronic sequences with the maximum nuclear charge Z = 86. The energy levels of Ag-and Rh-like ions were used for the calculation of the energies of resonance transitions to the ground state ¹ S ₀ in Pd-like ions. Good agreement between the theoretical and calculated energies of the resonance transitions in Pd-like ions indicates the reliability of the results obtained.     

Conductance distribution near the Anderson transition

Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L ^d–1 × L _z , characterizing by parameters L/ξ and L _z /L (ξ is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d = 2 + ? obtained in the framework of the σ-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g = 1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apart of this singularity, the critical distribution for d = 3 is well described by the present theory. One-parameter scaling for the whole distribution takes place under condition, that two independent parameters characterizing this distribution are functions of the ratio L/ξ.     

Elastic Deuteron Scattering on the <Superscript>12</Superscript>C Nucleus within a Three-Body Model

The formalism developed earlier for elastic pd scattering on the basis of Glauber theory with allowance for a total spin dependence is modified by replacing pN amplitudes by amplitudes for N¹²C scattering and is applied to elastic deuteron scattering on the ¹²C nucleus. The amplitudes for elastic N¹²C scattering are obtained within the optical model. Respective numerical calculations performed at the kinetic deuteron-beam energy of 270 MeV lead to results that agree well with data on the differential cross section for d¹²C scattering into the forward hemisphere, but the calculated spin observable A _y ^d agrees with experimental data only qualitatively.     

Effect of spin crossovers on the Mott-Hubbard transition at high pressures

The effect of spin crossovers in d _n terms on the effective Hubbard parameter (U _eff) determining the gap between the lower and upper Hubbard bands is analyzed using a many-electron approach to describe the electron structure of Mott insulators. A new mechanism of the insulator-metal transition is established for d ⁵ ions, which is related to a decrease in U _eff caused by spin crossover. For other ions, the U _eff value is either independent of pressure (d ², d ⁴, d ⁷) or it exhibits nonmonotonic growth (d ³, d ⁶, d ⁸).     

EPR study of impurity iron ion clusters in BaF<Subscript>2</Subscript> crystals

Tetragonal paramagnetic centers with spin S = 7/2 were detected in x-ray-irradiated BaF₂: Fe (c_Fe ≈ 0.002 at. %) crystals using the EPR method. Electronic transitions between the |±1/2〉 states of a Kramers doublet were observed in the X and Q ranges. In the EPR spectra of the tetragonal centers, a ligand hyperfine structure (LHFS) was observed corresponding to the interaction of the electron magnetic moment of the tetragonal center with eight equivalent ligands. The large spin moment, significant anisotropy of the magnetic properties, and the characteristic LHFS indicate that the tetragonal center is a Fe^1.5+?Fe^1.5+ dimer in which the two iron ions are bound via superexchange interaction. It is assumed that, before crystal irradiation, this dimer was in the Fe³⁺(3d⁵)?Fe⁺(3d⁷) state.     

Confinement Through a Two Dimensional Flux of the Thick Center Vortices

A two dimensional picture of the thick center vortex model is introduced. The spatial extent of the Wilson loop is oriented along the line with equation y = b x and the vortex movement is considered on the x ? y plane. A two-variable function with one free parameter a is considered as the vortex profile where a is proportional to the inverse of the vortex thickness. The potentials obtained from the two dimensional picture obey the N-ality dependence at large distances and Casimir scaling at intermediate distances. Furthermore, the concavity of the potentials corresponding to higher representations is slightly decreased in the two dimensional picture.     

AdS branes from partial breaking of superconformal symmetries

It is shown how the static-gauge world-volume superfield actions of diverse superbranes on the AdS_d+1 superbackgrounds can be systematically derived from nonlinear realizations of the appropriate AdS supersymmetries. The latter are treated as superconformal symmetries of flat Minkowski superspaces of the bosonic dimension d. Examples include the N = 1 AdS₄ supermembrane, which is associated with the 1/2 partial breaking of the OSp(1|4) supersymmetry down to the N = 1, d = 3 Poincaré supersymmetry, and the T-duality related L3-brane on AdS₅ and scalar 3-brane on AdS₅ × S¹, which are associated with two different patterns of 1/2 breaking of the SU(2, 2|1) supersymmetry. Another (closely related) topic is the AdS/CFT equivalence transformation. It maps the world-volume actions of the codimension-one AdS_d+1 (super)branes onto the actions of the appropriate Minkowski (super)conformal field theories in the dimension d.     

Kramers–Kronig Relations in Representation of Modulation Polarimetry by an Example of the Transmission Spectra of GaAs Crystal

The increments of the real and imaginary components of the complex refractive index ΔN = Δn–iΔk of a lightly doped GaAs crystal with a donor concentration of ~10¹⁶ cm^–3 have been measured using modulation polarimetry. It is shown that, within this representation, the birefringence and dichroism spectra (Δn(ω) and Δk(ω), respectively) obtained in the transparency window of a sample subjected to probe strain are derivatives of the corresponding functions: Δn(ω) ≈ dn/dω and Δk(ω) ≈ dk/dω. The experimental characteristics and primary dependences n(ω) and k(ω) derived from them by graphical integration are in agreement with the results of other researchers and measurements carried out by independent methods. The results obtained are compared (taking into account the integral (Kramers–Kronig) relations) with the resonance parameters: amplitude and phase in the Drude–Lorenz model. Agreement between the experimental characteristics and theoretical model predictions can be obtained by choosing an appropriate value of resonance damping parameter.     

Charge state of a transition metal impurity in II–VI semiconductors

The results of calculating the electronic structure of semiconductor compounds A^IIB^VI: 3d(A = Zn; B = S, Se, Te; 3d = Sc-Cu) at a low content of 3d impurities are discussed. The excess charge of an impurity ion with respect to the charge of the zinc ion is determined for the whole series of 3d impurities. It is found that the excess charge gradually varies from +0.6|e| for the scandium impurity to ?0.2|e| for the copper impurity. Photoionization of an impurity ion is simulated by adding a hole or an electron to the impurity center. The added charge is redistributed between the impurity ion and its nearest neighbors, thus decreasing or increasing the total excess charge of the impurity center by a magnitude of ～ 0.2|e|.     

Band interaction in <Superscript>162</Superscript>Dy, <Superscript>168</Superscript>Er,and <Superscript>172</Superscript>Yb

Coriolis interaction between levels of two rotational bands in ¹⁷²Yb with K ^π = 2⁺ and 3⁺ and in ¹⁶⁸Er between levels with K ^π = 0^?, 1^?, and 2^? is studied. The values of the interaction parameters are obtained. The mutual influence of two bands in ¹⁶²Dy with ΔK = 2, K _i ^π = 0 ₂ ⁺ and 2 ₁ ⁺ due to Coriolis interaction is demonstrated.     

Schiff moment of the mercury nucleus and the proton dipole moment

The Schiff moment of the ¹⁹⁹Hg nucleus is calculated using finite range P-and T-violating weak nucleon-nucleon interaction. Both the contributions of the P-and T-odd interaction and of internal nucleon electric dipole moments to the Schiff moment of ¹⁹⁹Hg are calculated. The contribution of the proton electric dipole moment is obtained via core-polarization effects treated in the framework of RPA with effective residual interactions. We derive a new upper bound |d _p |<5.4×10^?24e cm for the proton electric dipole moment.