Mean Field Magnetic Phase Diagrams for the Two Dimensional <Emphasis Type="Italic">t</Emphasis> — <Emphasis Type="Italic">t</Emphasis>′ — <Emphasis Type="Italic">U</Emphasis> Hubbard Model

We study the ground state phase diagram of the two dimensional t — t′ — U Hubbard model concentrating on the competition between antiferro-, ferro-, and paramagnetism. It is known that unrestricted Hartree–Fock- and quantum Monte Carlo calculations for this model predict inhomogeneous states in large regions of the parameter space. Standard mean field theory, i.e., Hartree–Fock theory restricted to homogeneous states, fails to produce such inhomogeneous phases. We show that a generalization of the mean field method to the grand canonical ensemble circumvents this problem and predicts inhomogeneous states, represented by mixtures of homogeneous states, in large regions of the parameter space. We present phase diagrams which differ considerably from previous mean field results but are consistent with, and extend, results obtained with more sophisticated methods. PACS: 71.10.Fd, 05.70.Fh, 75.50.Ee     

δ/γ transformation in non-equilibrium solidified peritectic Fe-Ni alloy

Through phase transformation kinetic analysis and experimental observation, the δ/γ transformation occurring in the non-equilibrium peritectic Fe-4.33at.%Ni alloys was systematically investigated. According to JMA solid-state transformation kinetic theory, the Time-Temperature-Transformation (TTT) curves of the δ/γ transformation in peritectic Fe-Ni alloy were calculated. On this basis, the physical correlation between the δ/γ transformation and the initial undercooling of melt (△T) was elucidated. The results indicate that the change of △T can alter not only the overall δ/γ transformation pathways but also the transformation fraction with respect to each transformation mechanism.     

Super <Emphasis Type="Italic">D</Emphasis>-Differentiation for <Emphasis Type="Italic">R</Emphasis><Superscript> ∞ </Superscript>-Supermanifolds

The concept of ‘D-Differentiation’, which, in the context of smooth manifolds, generalises Lie and covariant differentiation, is extended to R ^∞-supermanifolds under the name of ‘Super D-Differentiation’. This is done by defining new (non-linear) mappings, called ‘μ-mappings’ and by relating their non-linearity to the Leibniz rule that a derivation must satisfy when it acts on a tensor product. The resulting axiomatics, which is basis-independent and coordinate-free, is then expressed in a general basis (not necessarily holonomic). Super Lie and Super covariant differentiation are, amongst others, special cases of Super D-Differentiation. In particular, the transformation rules for the connection coefficients and the commutation coefficients of non-holonomic bases are obtained. These special cases are found to be in agreement with the DeWitt Super covariant and Super Lie derivatives.      

Once more about gauge invariance in <Emphasis Type="Italic">ϕ</Emphasis> → <Emphasis Type="Italic">γπ</Emphasis><Superscript>0</Superscript><Emphasis Type="Italic">π</Emphasis><Superscript>0</Superscript>

It is argued that the realization of gauge invariance condition as a consequent of cancellation between the ϕ → γf ₀ → γπ ⁰ π ⁰ resonance contribution and the ϕ → γπ ⁰ π ⁰ background one, suggested by A.V. Anisovich et al., Yad. Fiz. 68, 1614 (2005), is misleading. The text was submitted by the author in English.     

GaSe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript><Emphasis Type="Italic">S</Emphasis><Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> solid solutions

The most probable parameters of the pure, doped, and mixed GaSe_1−xS_x (x ≤ 0.4) crystals (solid solutions) are presented together with the results of investigations of their crystal structure and defects, optical and mechanical properties, and damage thresholds. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 35–40, June, 2007.     

The determination of <Emphasis Type="Italic">α</Emphasis><Subscript><Emphasis Type="Italic">S</Emphasis></Subscript> from <Emphasis Type="Italic">τ</Emphasis> decays revisited

We revisit the determination of α _S (m _τ ²) using a fit to inclusive τ hadronic spectral moments in light of (1) the recent calculation of the fourth-order perturbative coefficient K ₄ in the expansion of the Adler function, (2) new precision measurements from BABAR of e⁺e⁻ annihilation cross sections, which decrease the uncertainty in the separation of vector and axial-vector spectral functions, and (3) improved results from BABAR and Belle on τ branching fractions involving kaons. We estimate that the fourth-order perturbative prediction reduces the theoretical uncertainty, introduced by the truncation of the series, by 20% with respect to earlier determinations. We discuss to some detail the perturbative prediction of two different methods: fixed-order perturbation theory (FOPT) and contour-improved perturbative theory (CIPT). The corresponding theoretical uncertainties are studied at the τ and Z mass scales. The CIPT method is found to be more stable with respect to the missing higher order contributions and to renormalization scale variations. It is also shown that FOPT suffers from convergence problems along the complex integration contour. Nonperturbative contributions extracted from the most inclusive fit are small, in agreement with earlier determinations. Systematic effects from quark-hadron duality violation are estimated with simple models and found to be within the quoted systematic errors. The fit based on CIPT gives α _S (m _τ ²)=0.344±0.005±0.007, where the first error is experimental and the second theoretical. After evolution to M _Z we obtain α _S (M _Z ²)=0.1212±0.0005±0.0008±0.0005, where the errors are respectively experimental, theoretical and due to the evolution. The result is in agreement with the corresponding N³LO value derived from essentially the Z width in the global electroweak fit. The α _S (M _Z ²) determination from τ decays is the most precise one to date.     

A <Emphasis Type="Italic">CR</Emphasis>-manifold in general position as an {<Emphasis Type="Italic">e</Emphasis>}-structure

In the paper, it is proved that a “generic” CR-structure is reduced to an {e}-structure. Using the invariant frames obtained as a result of this reduction (an analog of the Darboux frame of classical differential geometry), we give a simple proof of an analog of the Vitushkin theorem on the extension of a germ for a rather broad class of real submanifolds of complex spaces. Partially financially supported by the RFBR grants nos. 05-01-0981 and NSh-2040.2003.1.     

The <Emphasis Type="Italic">Φ</Emphasis>→K<Superscript>0</Superscript>¯<Emphasis Type="Italic">γ</Emphasis> decay

The scalar contributions to the radiative decay φ→K ⁰ˉ⁰ γ are studied within the framework of the Linear Sigma Model (LσM). Theoretical predictions for the associated subprocesses φ→f ₀ γ and φ→a ₀ γ as well as the ratio φ→f ₀ γ/a ₀ γ are also given.     

Enhancement of the defect field of one-dimensional photonic crystals containing <Emphasis Type="Italic">ε</Emphasis>-and <Emphasis Type="Italic">μ</Emphasis>-negative layers

Employing the transfer matrix method, we study the electromagnetic field of one-dimensional photonic crystals with a defect inserted by pairs of μ-negative (MNG) and ε-negative (ENG) material layers. The fields within the pairs of layers and the matrix defect are independent of each other, and the whole field is their superposition. The whole defect field can be significantly enhanced by pairs of ε-negative and μ-negative layers. In contrast to the conventional defect modes, the intensity and volume of the defect field with pairs of ε-negative and μ-negative layers can be precisely adjusted.     

Little Higgs model effects in <Emphasis Type="Italic">γγ</Emphasis> → <Emphasis Type="Italic">γγ</Emphasis>

Though the predictions of the standard model (SM) are in excellent agreement with experiments, there are still several theoretical problems associated with the Higgs sector of the SM, where it is widely believed that some new physics will take over at the TeV scale. One beyond the SM theory which resolves these problems is the Little Higgs (LH) model. In this work we have investigated the effects of the LH model on γγ → γγ scattering [1].      

<Emphasis Type="Italic">Q</Emphasis> kink of the nonlinear <Emphasis Type="Italic">O</Emphasis>(3) <Emphasis Type="Italic">σ</Emphasis> model involving an explicitly broken symmetry

The (1 + 1)-dimensional nonlinear O(3) σ model involving an explicitly broken symmetry is considered. Sphalerons are known to exist in this model. These sphalerons are of a topological origin and are embedded kinks of the sine-Gordon model. In the case of a compact spatial manifold S ¹, sine-Gordon multikinks exist in the model. It is shown that the model admits a nonstatic generalization of the sine-Gordon kink/multikink, Q kink/multikink. Explicit expressions are obtained for the dependence of the Q kink energy and charge on the phase frequency of rotation. The Q kink is studied for stability, and expressions are obtained for the eigenfunctions and eigenfrequencies of the operator of quadratic fluctuations. It is shown that the Q kink is unstable over the entire admissible frequency range ω ∈ [−1, 1]. The one-loop quantum correction to the static-kink mass is calculated, and the Q-kink zero mode is quantized. It is shown that, in a general static case, the field equations of the model are integrable in quadratures.     

<Emphasis Type="Italic">Λ</Emphasis>N scattering length from the reaction <Emphasis Type="Italic">γ</Emphasis>d→K<Superscript>+</Superscript><Emphasis Type="Italic">Λ</Emphasis>n

The prospects of utilizing the strangeness production reaction γd→K ⁺ Λn for the determination of the Λn low-energy scattering parameters are investigated. The spin observables that need to be measured in order to isolate the Λn singlet (¹ S ₀) and triplet (³ S ₁) states are identified. Possible kinematical regions where the extraction of the Λn scattering lengths might be feasible are discussed.     

The K<Emphasis Type="Italic">π</Emphasis> and <Emphasis Type="Italic">ππ</Emphasis> S-wave amplitude from D-meson decays

The issue of Kπ and ππ S-wave amplitude is addressed using decays of D-mesons. Model-independent measurements of the phases of the π ⁺ π ⁺ and K ^- π ⁺ S-wave amplitude from D ⁺→π ^- π ⁺ π ⁺ and D ⁺→K ^- π ⁺ π ⁺ decays are discussed. The result indicates a deviation from the phase of the K ^- π ⁺ S-wave amplitude obtained by scattering experiments. This could be interpreted as an indication of the presence of 3-body final-state interaction, or in other words, that the phases from production and scattering process cannot be directly compared.     

Electric Instability in <Emphasis Type="Italic">n</Emphasis>-CdTe:In Layers with <Emphasis Type="Italic">S</Emphasis>-Shaped Voltage-Current Characteristics

A switching of the S-type in the 20–200 μm thick polycrystalline n-CdTe:In layers with resistance of 10³–10⁶ Ω·cm is studied. The electric instability in the layers is found to be due to the electron-thermal breakdown mechanism. The dependence of the switching threshold parameters on the intensity of exposure can be used for fabrication of infrared-radiation controlled electric switches on the basis of n-CdTe:In layers. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 28–30, June, 2005.     

<Emphasis Type="Italic">X</Emphasis>(3): An exactly separable <Emphasis Type="Italic">γ</Emphasis>-rigid version of the <Emphasis Type="Italic">X</Emphasis>(5) critical point symmetry

A γ-rigid version (with γ = 0) of the X(5) critical point symmetry is constructed. The model, to be called X(3) since it is proved to contain three degrees of freedom, utilizes an infinite well potential, is based on exact separation of variables, and leads to parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates which are in good agreement with existing experimental data for ¹⁷²Os and ¹⁸⁶Pt. An unexpected similarity of the β ₁ bands of the X(5) nuclei ¹⁵⁰Nd, ¹⁵²Sm, ¹⁵⁴Gd, and ¹⁵⁶Dy to the X(3) predictions is observed. The text was submitted by the authors in English.     

Disappearing cosmological constant in <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

For higher-derivative f(R) gravity, where R is the Ricci scalar, a class of models is proposed, which produce viable cosmology different from the ACDM at recent times and satisfy cosmological, Solar System, and laboratory tests. These models have both flat and de Sitter spacetimes as particular solutions in the absence of matter. Thus, a cosmological constant is zero in a flat spacetime, but appears effectively in a curved one for sufficiently large R. A “smoking gun” for these models would be a small discrepancy in the values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed out, which is connected with the possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe. The text was submitted by the author in English.     

<Emphasis Type="Italic">Y</Emphasis> and <Emphasis Type="Italic">Z</Emphasis> luminescence of polycrystalline cadmium telluride

The properties of polycrystalline CdTe with a grain size of 5–30 μm have been investigated using the microphotoluminescence methods of spectral analysis and topography. This material has been prepared by direct synthesis in a vapor flow of components at a low temperature. The dominance of the Y and Z bands in the spectra reflects a nonequilibrium character of the crystallization processes. The superlinear dependences of the luminescence intensity on the level of the band-to-band excitation indicate the exciton nature of the corresponding transitions. The activation energies for temperature quenching of luminescence in the temperature range T = 100–150 K are found to be 120 meV for the Y luminescence and 180 meV for the Z luminescence, which correspond to the dissociation of excitons bound to defects with the transition of charge carriers to the conduction and valence bands. The monochromatic topography data indicate that Y and Z defects have different material bases.     

Conformal Continuations in Gravitation Theory with Lagrangian <Emphasis Type="Italic">F</Emphasis>(<Emphasis Type="Italic">R</Emphasis>)

Static spherically-symmetric vacuum solutions of gravitation theory equations with Lagrangian f(R) are examined, where R is a scalar curvature and f is an arbitrary function. Equations of f(R)-theories are reduced to the Einstein scenario — general relativity theory (GRT) equations with a source in the form of a scalar field with potential — with the use of the well-known conformal transformation. The necessary and sufficient conditions of existence of solutions admitting conformal continuations are formulated. This means that the central singularity of the Einstein scenario is mapped into a regular sphere S_trans of the Jordan scenario (that is, into the manifold corresponding to the initial formulation of the theory), and a solution of the field equations can be smoothly continued through it. The value of curvature R on the sphere S_trans corresponds to an extremum of the function f(R). Concrete examples are considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 46–51, September, 2005.