Cosmology from <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>,<Emphasis Type="Italic">T</Emphasis>) Theory in a Variant Speed of Light Scenario

In this work I present a generalization of f(R, T) gravity, by allowing the speed of light to vary. Cosmological solutions are presented for matter and radiation-dominated universes, the former allowing the universe expansion to accelerate while the latter contemplating a possible alternative to inflationary scenario. Remarkably, standard gravity is always retrieved for a special case of f(R, T).     

Restricting Positive Energy Representations of Diff<Superscript>+</Superscript>(<Emphasis Type="Italic">S</Emphasis><Superscript>1</Superscript>) to the Stabilizer of <Emphasis Type="Italic">n</Emphasis> Points

Let G _n ? Diff⁺(S ¹) be the stabilizer of n given points of S ¹. How much information do we lose if we restrict a positive energy representation \(U^c_h\) associated to an admissible pair (c, h) of the central charge and lowest energy, to the subgroup G _n ? The question, and a part of the answer originate in chiral conformal QFT. The value of c can be easily “recovered” from such a restriction; the hard question concerns the value of h. If c ≤ 1, then there is no loss of information, and accordingly, all of these restrictions are irreducible. In this work it is shown that \(U^c_{h}|_{G_n}\) is always irreducible for n =  1 and, if h =  0, it is irreducible at least up to n ≤  3. Moreover, an example is given for c >  2 and certain values of \(h \neq \tilde{h}\) such that \(U^c_{h}|_{G_1}\simeq U^c_{\tilde{h}}|_{G_1}\) . It is also concluded that for these values \(U^c_{h}|_{G_n}\) cannot be irreducible for n ≥  2. For further values of c, h and n, the question is left open. Nevertheless, the example already shows that, on the circle, there are conformal QFT models in which local and global intertwiners are not equivalent.     

The influence of magnetic and structural heterogeneity on thermopower,magnetothermopower, electrical resistivity,and magnetoresistivity of Nd<Subscript>0.5</Subscript>Sr<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> manganite

The thermopower, S, magnetothermopower, ΔS/S, resistivity, ρ, and magnetoresistivity, Δρ/ρ, depending on the temperature T and magnetic field H, have been studied in an Nd_0.5Sr_0.5MnO₃ single crystal consisting of three types of clusters: an antiferromagnetic CE-type with charge-orbital ordering (below the Neel temperature T_NCE ~ 145 K) and an A-type with T_NA ~ 220 K; a ferromagnetic at 234 ≤ T ≤ 252 K, and a ferromagnetic metal phase below the Curie temperature T_C = 248 K. The thermopower was found to be negative, indicating the dominance of the electronic type of conductivity. In the S(T) curves, a sharp minimum is observed in the temperature range of 100 K ≤ T ≤ 133 K, close to T_NCE, where the absolute S value attains 53 μV/K. With a further increase in temperature, the absolute S value decreases rapidly; at 200 K it is equal to 7 μV/K. It then slightly increases, reaching its maximum value of 15 μV/K at a temperature of 254 K, which is close to T_C. The absolute thermopower decreased under the influence of the magnetic field; i.e., a negative magnetothermopower occurs. In {ΔS/S}(T) curves, a sharp minimum is observed at T = 130 K close to T_NCE, where the magnetothermopower reaches a huge value of ~45% at H = 13.23 kOe. A broad minimum in the {ΔS/S}(T) curves is observed near the Curie temperature and its value is also high, viz., ~15% in the maximum measuring magnetic field of 13.23 kOe. The extremely high magnetothermopower values mean that the charge-orbital ordered nanoclusters or ferron type make the main contribution to the thermopower of the entire sample. The behavior of the ρ(T) and {Δρ/ρ}(T) curves is similar to that of the S(T) and {ΔS/S}(T) dependencies, which is in agreement with this conclusion.     

Nonergodic state of relaxation ferroelectric Cd<Subscript>2</Subscript>Nb<Subscript>2</Subscript>O<Subscript>7</Subscript> in a constant electric field

The temperature dependence of the residual polarization of the nonergodic relaxation state (NERS) obtained from the measurements of pyroelectric current during zero-field heating (ZFH) in the temperature interval from 10 to 295 K is investigated for the Cd₂Nb₂O₇ relaxation system in two cases: (1) after sample cooling in a constant electric field E (FC) from T = 295 K to a preset temperature, which is much lower than the “freezing” temperature of the relaxation state (T _f ≈ 182 K), field removal, and subsequent cooling in zero field (ZFC) to T = 10 K and (2) after ZFC from T = 295 K to the same temperature below T _f , application of the same field, and FC to T = 10 K. The behavior of the P _r ^FC (T) and P _r ^ZFC (T) dependences is analyzed. In the field E < 2 kV/cm, the P _r ^ZFC curves as functions of 1/T have a broad low-intensity peak in the region T ≈ T _f , which vanishes in stronger fields, when the P _r ^FC (1/T) curves intersect at T ≈ T _f and have no anomalies. The difference in the behavior of P _r ^ZFC (T) and P _r ^FC (T) indicates the difference in the nature of NERS formed during ZFC and FC of the system upon a transition through T _f . In the ZFC mode, NERS exhibits glasslike behavior; in the FC regime, features of the ferroelectric behavior even in the weak field. Analogous variations of P _r ^ZFC (T) and P _r ^FC (T) in a classical ferroelectric KDP are also given for comparison.     

Low-temperature anomalies in the specific heat and thermal conductivity of MgB<Subscript>2</Subscript>

The temperature dependences of the specific heat C(T) and thermal conductivity K(T) of MgB₂ were measured at low temperatures and in the neighborhood of T _c . In addition to the well-known superconducting transition at T _c ≈40 K, this compound was found to exhibit anomalous behavior of both the specific heat and thermal conductivity at lower temperatures, T≈10–12 K. Note that the anomalous behavior of C(T) and K(T) is observed in the same temperature region where MgB₂ was found to undergo negative thermal expansion. All the observed low-temperature anomalies are assigned to the existence in MgB₂ of a second group of carriers and its transition to the superconducting state at T_c2≈10?12 K.     

Extended <Emphasis Type="Italic">E</Emphasis>(5) and <Emphasis Type="Italic">X</Emphasis>(5) symmetries: Series of models providing parameter-independent predictions

The E(5) symmetry describes nuclei related to the U(5)-SO(6) phase transition, while the X(5) symmetry is related to the U(5)-SU(3) phase transition. First, a chain of potentials interpolating between the U(5) symmetry of the five-dimensional harmonic oscillator and the E(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ = E(4)/E(2) ratios of 2.093, 2.135, and 2.157 (compared to the ratio of 2.000 of the U(5) case and the ratio of 2.199 of the E(5) case) are derived numerically and compared to existing experimental data, suggesting several new experiments. TheX(5) symmetry describes nuclei characterized byR₄=2.904.Using the same separation of variables of the original Bohr Hamiltonian as in X(5), an exactly soluble model with R₄=2.646 is constructed and its parameter-independent predictions are compared to existing spectra and B(E2) values. In addition, a chain of potentials interpolating between this new model and the X(5) symmetry is considered. Parameter-independent predictions for the spectra and B(E2) values of nuclei with R₄ ratios of 2.769, 2.824, and 2.852 are derived numerically and compared to existing experimental data, suggesting several new experiments.     

Electron gas induced in SrTiO<Subscript>3</Subscript>

This mini-review is dedicated to the 85th birthday of Prof. L.V. Keldysh, from whom we have learned so much. In this paper, we study the potential and electron density depth profiles in surface accumulation layers in crystals with a large and nonlinear dielectric response such as SrTiO₃ (STO) in the cases of planar, spherical, and cylindrical geometries. The electron gas can be created by applying an induction D₀ to the STO surface. We describe the lattice dielectric response of STO using the Landau–Ginzburg free energy expansion and employ the Thomas–Fermi (TF) approximation for the electron gas. For the planar geometry, we arrive at the electron density profile n(x) ∝ (x + d)^–12/7, where d ∝ D₀^–12/7. We extend our results to overlapping electron gases in GTO/STO/GTO heterojunctions and electron gases created by spill-out from NSTO (heavily n-type doped STO) layers into STO. Generalization of our approach to a spherical donor cluster creating a big TF atom with electrons in STO brings us to the problem of supercharged nuclei. It is known that for an atom with a nuclear charge Ze where Z > 170, electrons collapse onto the nucleus, resulting in a net charge Zn < Z. Here, instead of relativistic physics, the collapse is caused by the nonlinear dielectric response. Electrons collapse into the charged spherical donor cluster with radius R when its total charge number Z exceeds the critical value Z_c ≈ R/a, where a is the lattice constant. The net charge eZ_n grows with Z until Z exceeds Z* ≈ (R/a)^9/7. After this point, the charge number of the compact core Z_n remains ≈ Z*, with the rest Z* electrons forming a sparse TF atom with it. We extend our studies of collapse to the case of long cylindrical clusters as well.     

Harmonic analysis of coefficients of free energy decomposition in the polarization of a Rb<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> crystal

Landau–Devonshire decomposition coefficients W_C in a series with respect to P_C are determined via harmonic analysis of experimental free energy coordinates W_C of a Rb₂ZnCl₄ crystal, depending on its polarization P_C. The number of terms needed in W_C decomposition is determined for quantitative evaluation of the measured data.     

Structural and magnetic phase transformations in the BiFeO<Subscript>3</Subscript>-CaFe<Subscript>0.5</Subscript>Nb<Subscript>0.5</Subscript>O<Subscript>3</Subscript> system

The crystal structure and magnetic properties of the Bi_{1 ? x} Ca _x Fe_{1 ? x/2}Nb _x/2O₃ system were studied. It is shown that, at x ≤ 0.15, the unit-cell symmetry of solid solutions is rhombohedral (space group R3c). Solid solutions with x ≥ 0.3 have an orthorhombic unit cell (space group Pbnm). The rhombohedral compositions are antiferromagnetic, while the orthorhombic compositions exhibit a small spontaneous magnetization due to Dzyaloshinski?-Moriya interaction. In CaFe_0.5Nb_0.5O₃, the Fe³⁺ and Nb⁵⁺ ions are partially ordered and the unit cell is monoclinic (space group P2₁/n). In the concentration range 0.15 < x < 0.30, a two-phase state (R3c + Pbnm) is revealed.     

<Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity solutions for evolving wormholes

The scalar–tensor f(R) theory of gravity is considered in the framework of a simple inhomogeneous space-time model. In this research we use the reconstruction technique to look for possible evolving wormhole solutions within viable f(R) gravity formalism. These f(R) models are then constrained so that they are consistent with existing experimental data. Energy conditions related to the matter threading the wormhole are analyzed graphically and are in general found to obey the null energy conditions (NEC) in regions around the throat, while in the limit \(f(R)=R,\) NEC can be violated at large in regions around the throat.     

Conditions for T<Superscript>2</Superscript> resistivity from electron-electron scattering

Many complex oxides (including titanates, nickelates and cuprates) show a regime in which resistivity follows a power law in temperature (ρ ∝ T ²). By analogy to a similar phenomenon observed in some metals at low temperature, this has often been attributed to electron-electron (Baber) scattering. We show that Baber scattering results in a T ² power law only under several crucial assumptions which may not hold for complex oxides. We illustrate this with sodium metal (ρ _el?el ∝ T ²) and strontium titanate (ρ _el?el \(\hbox{$\not\propto$}\) T ²). We conclude that an observation of ρ ∝T ² is not always sufficient evidence for electron-electron scattering.     

Line shape of <Superscript>57</Superscript>Co sources exhibiting self absorption

The effect of selfabsorption in Mössbauer sources is studied in detail. Spectra were measured using an old ⁵⁷ C o/R h source of 74M B q activity with an original activity of ca. 3.7G B q and a 0.15G B q ⁵⁷ C o/α ? F e source magnetized by an in-plane magnetic field of 0.2 T. The ⁵⁷ C o/α ? F e source of a thickness of 25 μ was used both from the active and the inactive side giving cause to very different selfabsorption effects. The absorber was a single crystal of ferrous ammonium sulphate hexahydrate (FAS). Its absorption properties were taken over from a detailed study (Bull et al., Hyperfine Interact. 94(1–3), 1; Spiering et al. 2). FAS (space group P21/c) crystallizes as flat plates containing the (\(\overline {2}\)01) plane. The γ-direction was orthogonal to the crystal plate. The ⁵⁷ C o atoms of the ⁵⁷ C o/R h source were assumed to be homogeneously distributed over a 6μ thick Rh foil and to follow a one dimensional diffusion profile in the 25 μ Fe-foil. The diffusion length was fitted to 10 μ. The theory follows the Blume-Kistner equations for forward scattering (Blume and Kistner, Phys. Rev. 171, 417, 3) by integrating over the source sampled up to 128 layers.     

Cosmological implications of different baryon acoustic oscillation data

In this work, we explore the cosmological implications of different baryon acoustic oscillation(BAO) data, including the BAO data extracted by using the spherically averaged one-dimensional galaxy clustering(GC) statistics(hereafter BAO1) and the BAO data obtained by using the anisotropic two-dimensional GC statistics(hereafter BAO2). To make a comparison, we also take into account the case without BAO data(hereafter NO BAO). Firstly, making use of these BAO data, as well as the SNLS3 type Ia supernovae sample and the Planck distance priors data, we give the cosmological constraints of the ΛCDM, the w CDM, and the Chevallier-Polarski-Linder(CPL) model. Then, we discuss the impacts of different BAO data on cosmological consquences, including its effects on parameter space, equation of state(Eo S), figure of merit(Fo M), deceleration-acceleration transition redshift,Hubble parameter H(z), deceleration parameter q(z), statefinder hierarchy S_3(1)(z), S_4(1)(z) and cosmic age t(z). We find that:(1)NO BAO data always give a smallest fractional matter density ?_(m0), a largest fractional curvature density ?k0and a largest Hubble constant h; in contrast, BAO1 data always give a largest ?_(m0), a smallest ?_(k0) and a smallest h.(2) For the w CDM and the CPL model, NO BAO data always give a largest Eo S w; in contrast, BAO2 data always give a smallest w.(3) Compared with the case of BAO1, BAO2 data always give a slightly larger Fo M, and thus can give a cosmological constraint with a slightly better accuracy.(4) The impacts of different BAO data on the cosmic evolution and the comic age are very small, and cannot be distinguished by using various dark energy diagnoses and the cosmic age data.     

Properties of strained TaS<Subscript>3</Subscript> samples in the state of charge density wave and in the normal state

The uniaxial strain of quasi-one-dimensional conductor whiskers of orthorhombic TaS₃ at a strain higher than ε _c ~ 0.8% leads to a sharp increase in the coherence of the properties of a charge density wave (CDW), which manifests itself in its motion in fields higher than threshold field E _t . During uniaxial elongation, TaS₃ is shown to exhibit the following unusual properties even in weak fields: Peierls transition temperature T _P depends nonmonotonically on ε, one-dimensional fluctuations weaken near T _P , and the coherence length of a charge density increases at T < T _P . Investigations in fields higher than E _t show that the ultracoherent properties of CDW exist in a wide temperature range and are retained when temperature increases up to T _P . These properties of CDW make it possible to observe a sharp increase in E _t near T _P and an almost jumplike increase in E _t at T < 90 K. The increase in E _t at T _P is explained by a decrease in the coherence volume of CDW because of a fluctuational suppression of the Peierls gap.     

Galvanomagnetic properties of Heusler alloys Co<Subscript>2</Subscript>Fe<Emphasis Type="Italic">Z</Emphasis> (Z = Al,Si, Ga,Ge, In,Sn, Sb)

The magnetization, Hall effect, and resistivity of Heusler alloys Co₂FeZ (where Z = Al, Si, Ga, Ge, In, Sn, and Sb are s- and p-elements) have been studied at T = 4.2 K in magnetic fields H ≤ 100 kOe. In strong fields (H > 20 kOe), magnetization can be described by the Stoner model. The normal R ₀ and anomalous R _S Hall effect coefficients have been determined. The coefficient RS is positive for almost all the studied alloys and represents a “linearly quadratic” resistivity function incorporating linear and quadratic terms. The constant R ₀ is negative for most alloys, and its absolute value is two or three orders of magnitude smaller than for R _S . The magnetoresistivity of the studied alloys does not exceed several percent and may be both positive and negative for different specimens.     

Phase diagrams of bosonic AB<Subscript>n</Subscript> chains

The AB_{N ?1} chain is a system that consists of repeating a unit cell withN siteswhere between the A and B sites there is an energy difference ofλ. Weconsidered bosons in these special lattices and took into account the kinetic energy, thelocal two-body interaction, and the inhomogenous local energy in the Hamiltonian. We foundthe charge density wave (CDW) and superfluid and Mott insulator phases, and constructedthe phase diagram for N =2 and 3 atthe thermodynamic limit. The system exhibited insulator phases for densitiesρ =α/N, with α being an integer. Weobtained that superfluid regions separate the insulator phases for densities larger thanone. For any N value, we found that for integer densitiesρ, thesystem exhibits ρ +1 insulator phases, a Mott insulator phase, and ρ CDW phases. Fornon-integer densities larger than one, several CDW phases appear.     

Critical magnetic field of the vortex-free state in NbC thin films and prospects for its observation in MgB<Subscript>2</Subscript>

The critical magnetic fields H _c‖ and H _c2 are measured for thin films of the isotropic superconductor NbC. It is revealed that the critical fields exhibit strong anisotropy due to the vortex-free state of the film in a magnetic field aligned parallel to its surface. The H _c‖/H _c2 ratio at 2 K exceeds 6 and increases with increasing temperature. The dependence H _c‖(T) agrees quantitatively with the concepts of microscopic theory on the vortex-free state of a thin film of a clean superconductor in the temperature range below T _c . As the electron mean free path decreases under irradiation of the film with a low dose of He⁺ ions, the critical field H _c‖ remains unchanged near T _c but increases significantly at lower temperatures. The well-known theoretical models are used to estimate the electronic parameters and thicknesses of MgB₂ films for which the specific features associated with the vortex-free state of the two-gap superconductor can manifest themselves in the temperature dependence of the critical magnetic field H _c‖(T).     

X-ray study of [N(CH<Subscript>3</Subscript>)<Subscript>4</Subscript>]<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> at low temperatures

The unit cell parameters a, b, and c of [N(CH₃)₄]₂ZnCl₄ have been measured by x-ray diffraction in the temperature range 80–293 K. Temperature dependences of the thermal expansion coefficients α_a, α_b, and α_c along the principal crystallographic axes and of the unit cell thermal expansion coefficient α_V were determined. It is shown that the a=f(T), b=f(T), and c=f(T) curves exhibit anomalies in the form of jumps at phase transition temperatures T₁=161 K and T₂=181 K and that the phase transition occurring at T₃=276 K manifests itself in the a=f(T) and b=f(T) curves as a break. A slight anisotropy in the coefficient of thermal expansion of the crystal was revealed. The phase transitions occurring at T₁=161 K and T₂=181 K in [N(CH₃)₄]₂ZnCl₄ were established to be first-order.     

Dissimilarity between metallic-like transport in the dielectric spin density wave and field-induced spin density wave states in (TMTSF)<Subscript>2</Subscript>PF<Subscript>6</Subscript>

We report similarities and differences of the transport features in the spin density wave (SDW) and in the field-induced SDW (FISDW) phases of the quasi-one-dimensional compound (TMTSF)₂PF₆. As temperature decreases below ≈2 K, the resistance in both phases exhibits a maximum and a subsequent strong drop. However, the characteristic temperature of the R(T) maximum and its scaling behavior in different magnetic fields B are evidence that the nonmonotonic R(T) dependences have different origin in SDW and FISDW regions of the phase diagram. We also found that the borderline T₀(B, P) which divides the FISDW region of the P-B-T phase diagram into the hysteresis and nonhysteresis domains terminates in the N=1 subphase; the borderline thus has no extension to the SDW N=0 phase.     

Friedmann Cosmology with Matter Creation in Modified <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>, <Emphasis Type="Italic">T</Emphasis>) Gravity

The theoretical and observational consequences of thermodynamics of open systems which allow matter creation, are investigated in modified f(R, T) (R is the Ricci scalar and T is the trace of energy-momentum tensor) theory of gravity within the framework of a flat Friedmann-Robertson-Walker line element. The simplest model f(R, T)=R+2f(T) with “gamma-law” equation of state p = (γ?1)ρ is assumed to obtain the exact solution. A power-law expansion model is proposed by considering the natural phenomenological particle creation rate ψ = 3β n H, where β is a pure number of the order of unity, n the particle number density and H is the Hubble parameter. A Big Rip singularity is observed for γ<0 describing phantom cosmology. The accelerated expansion of the Universe is driven by the particle creation. The density parameter shows the negative curvature of the Universe due to particle creation. The entropy increases with the evolution of the Universe. Some kinematics tests such as lookback time, luminosity distance, proper distance, angular diameter versus redshift are discussed in detail to observe the role of particle creation in early and late time evolution of the Universe.