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.     

Multigap superconductivity in doped p-type cuprates

Andreev and tunneling spectroscopy studies of Bi₂Sr₂Ca _{n ? 1}Cu _n O_{2n + 4 + δ}, HgBa₂Ca _{n ? 1}Cu _n O_{2n + 2 + δ} and Tl₂Ba₂Ca _{n ? 1}Cu_{2n + 4 + δ} have shown that superconductivity in single-layer (n = 1) and two-layer (n = 2) phases has a single-gap character. Qualitatively different results were obtained for three-layer phases. In doped p-type Hg-1223, Bi-2223, and Tl-2223 samples two (or three) superconducting gaps were observed. The existence of multigap superconductivity in superconducting cuprates with n ≥ 3 is explained by a difference in doping levels of outer (OP) and internal (IP) CuO₂ planes.     

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.     

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.     

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.     

Representations and inequalities for Ising model Ursell functions

We describe and investigate representations for the Ursell functionu _n of a family ofn random variables {σ _i}. The representations involve independent but identically distributed copies of the family. We apply one of these representations in the case that the random variables are spins of a finite ferromagnetic Ising model with quadratic Hamiltonian to show that (?1) ^n/2+1 u _n(σ ₁, ...,σ _n) ≧ 0 forn=2, 4, and 6 by proving the stronger statement \(( - 1 )^{\frac{n}{2} + 1} \frac{{\partial ^m }}{{\partial J_{i1j1} \cdots \partial J_{imjm} }}Z^{\frac{n}{2}} u_n \left| {_{J = 0} } \right. \geqq {}^\backprime 0\) forn=2, 4, and 6, theJ _ij being coupling constants in the Hamiltonian andZ the partition function. For generaln we combine this result with various reductions to show that sufficiently simple derivatives of (?1) ^n/2+1 Z ^n/2u_n, evaluated at zero coupling, are nonnegative. In particular, we conclude that (?1) ^n/2+1 u _n ≧ 0 if all couplings are nonzero and the inverse temperature β is sufficiently small or sufficiently large, though this result is not uniform in the ordern or the system size. In an appendix we give a simple proof of recent inequalities which boundn-spin expectations by sums of products of simpler expectations.     

Fluorescence resolue dans le temps des niveax de singulet et d du zinc

The time resolved spectroscopy technique is applied to investigate the (4s, nd) ¹D₂ series of Zn I using a selective stepwise excitation via the resonant 4¹P₁ state. Radiative lifetimes of n¹S₀ (n = 6?8) and n¹D₂ (n = 4,5) levels are measured. Upper limits for transition probabilities 4¹P₁?n¹S₀ (n = 9?12) and 4¹P₁?n¹ (n = 6?10 ) are obtained. Strong configuration interaction effects are observed in the ¹D₂ series and compared with those in Mg I and Cd I.     

Quantum hall effect of two-dimensional interacting boson systems

While non-interacting two-dimensional (2-D) boson systems cannot have the quantum Hall effect (QHE), we show that 2-D interacting boson systems can have the QHE if there is a downward cusp in the ground state energy. A necessary condition to have the QHE at filling factor v = p/q with σ_H = (p/q)e²/h is that p and q must satisfy e^ipqπ= 1, so the possible candidates are v = 2n₁/(2n₂ + 1) and (2n₁ + 1)/2n₂ where n₁ and n₂ are integers.     

Solvable RSOS models based on the dilute BWM algebra

In this paper we present representations of the recently introduced dilute Birman-Wenzl-Murakami algebra. These representations, labelled by the level-l B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ affine Lie algebras, are baxterized to yield solutions to the Yang-Baxter equation. The thus obtained critical solvable models are RSOS counterparts of the, respectively, D_n+1⁽²⁾, A_2n⁽²⁾ and B_n⁽¹⁾R-matrices of Bazhanov and Jimbo. For the D_n+1⁽²⁾ and B_n⁽¹⁾ algebras the RSOS models are new. An elliptic extension which solves the Yang-Baxter equation is given for all three series of dilute RSOS models.     

Role of metastable atoms and molecules of helium in excitation transfer to hydrogen atoms

The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤10¹¹ cm^?3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 ³ S ₁) k ₁(n) and molecules of helium He₂(a 2sσ ³Σ _u ⁺ ) k ₂(n) to atomic hydrogen H*(n) are measured to be k ₁(n=3)/k ₂(n=3)=0.04±0.02 and k ₁(n=4)/k ₂(n=4)=0.01±0.02. The ratios of excitation rate constants k ₂(n) corresponding to different states H(n) are measured to be k ₁(n=4)/k ₂(n=3)=0.023±0.01; k ₁(n=5)/k ₂(n=3)≤0.013; and k ₁(n=6)/k ₂(n=3)≤0.007.     

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.     

Effective Values of Variable Components of the Refractive Index upon Nonlinear Recording of Phase Holograms

The diffraction of a plane wave incident on a thick hologram at the first and second Bragg angles in the process of nonlinear recording is analyzed using the coupled-wave equations. It is shown that, in this case, the two-wave approximation with the use of effective modulation amplitudes of the refractive index, n _1ef and n _2ef, can be applied. Analytical dependences of n _1ef and n _2ef on the modulation amplitudes of the refractive index n ₁ and n ₂ at the fundamental and doubled spatial frequencies are obtained and the criteria of their applicability are determined. The dependences found are used to calculate the parameters of gratings recorded in a photopolymeric material.     

Preparative and Mössbauer studies of Bi2Sr2Ca n-1Cu n O y compounds withn=2 or 3

The influence of sintering temperatures and nominal starting compositions on the phase contents of polycrystalline Bi₂Sr₂Ca _n-1Cu _n O_4+2n samples are reported. After every sintering the samples were characterized with X-ray diffraction and magnetic AC susceptibility measurements. For Mössbauer studies, in each case also a corresponding specimen containing⁵⁷Fe was synthetized. The identification of various superconducting Bi₂Sr₂Ca _n-1Cu _n O_4+2n phases on the basis of Mössbauer spectra consisting usually of three quadrupole doublets is discussed.     

Structure change of basins by crisis in a two-dimensional map

The structure of basin boundaries for a two-dimensional map (X_n+1 = 2X_n (mod 1), Y_n+1 = -αY_n+Y³_n −βcos2πX_n) is studied using analytical methods. It is shown that basin boundaries do not play the role of a barrier when the crisis occurs as two parameters are changed. The escaping mechanism over basin boundaries is also discussed.     

Virasoro type Lie algebras and deformations

The first and second cohomologies of Cartan Type Lie algebras with coefficients in irreducible tensor modules are calculated. The spaceH ¹(L, U) is interpreted as a space of deformations of (L, U)-modules.H ²(L, L)≠0 ifL=S ₂,S ₂ ⁺ orL=H _n ,H _n ⁺ . Lie algebra of divergenceless vector fieldsS ₂ ⁺ has only one nontrivial local deformation. The two-sided simple hamiltonian algebraH _n has 2n ²+n new local deformations in addition to Moyal cocycle. The Lie algebrasL=W _n (n>3),S _n?1(n>2),H _n (n>1),K _n+1(n>1) have 3, 1, 1, 3 nonisomorphic tensor modules with irreducible bases and nonzero 1-cohomologies; respectively, the corresponding numbers for 2-cohomologies are 9, 6, 7 and 9.     

Algebraic construction of higher-rank dilute A models

Starting from representations of the Birman-Wenzl-Murakami algebra underlying the critical B_n⁽¹⁾, C_n⁽¹⁾ and D_n⁽¹⁾ RSOS models of Jimbo, Miwa and Okado, we derive four series of solvable, critical RSOS models associated with the twisted affine Lie algebra A_n⁽²⁾. Two of these are the critical limit of the A_2n−1⁽²⁾ and A_2n⁽²⁾ models obtained previously by Kuniba. The other two series, again one of the A_2n−1⁽²⁾ and one of the A_2n⁽²⁾ type, are new, and the latter generalizes the dilute A models to arbitrary rank n. For the two new series we present an elliptic extension which satisfies the Yang-Baxter equation, and show that for certain values of the parameters the higher-rank dilute A models break the ℤ₂ symmetry of the underlying adjacency graphG, whereGis the level-l C_n⁽¹⁾ weight lattice.     

Chloride perovskite layer compounds of [NH3-(CH2)n-NH3]MnCl4 formula

[NH₃-(CH₂)_n-NH₃]MnCl₄ compounds with n = 2, …, 5 are chloride perovskite layer structures. The room temperature phase of members with odd numbers of carbon atoms is orthorhombic, whereas even numbers lead to monoclinic structures. Structural phase transitions were found in all compounds with n > 2. The magnetic behaviour is similar to the (C_nH_2n+1NH₃)₂MnCl₄-family.     

Emission secondaire de petits agregats NipCn par des carbures de nickel

The intensities of emission of Ni_pC_n⁺(p = 1–3) and NiC_n^? secondary ions given by two alloys: Ni₃C and NiC 5% at. C, show off a saw-toothed behaviour according to the parity of the number n of carbon atoms. Maxima occur when n is odd for NiC_n⁺ ions and when n is even in the other cases (p = 2, 3; negative ions). Besides, the influence of the carbon concentration in the alloy can be observed.The alternations of NiC_n⁺ and Ni₂C_n⁺ ions can be interpreted from Pitzer and Clementi model (the clusters are supposed to be linear). Thus it can be found greater stabilities for NiC_2k+1 and Ni₂C_2k chains than for NiC_2k and Ni₂C_2k+1 chains respectively, which very well agrees with the “correspondence rule” between the emissions of different species of ions and their electronic properties.     

Density-functional theory study of structures,stabilities, and electronic properties of the Cu2-doped silicon clusters: Comparison with pure silicon clusters

Equilibrium geometric structures, stabilities, and electronic properties of Si_nCu₂ (n=1–8) clusters and pure silicon Si_n (n=3–10) clusters are investigated systematically by exchange-correlation density functional (B3LYP). The optimized geometries show that the most stable isomers have 3D structure for n=2, 4–8, and Cu-substituted Si_n+2 clusters is dominating growth pattern for the Si_nCu₂ clusters. The calculated averaged binding energies, fragmentation energies, second-order difference of energies, and the HOMO–LUMO gaps show that Si₂Cu₂ and Si₅Cu₂ clusters have enhanced relative stabilities and chemical stability than their neighboring clusters. Electronic properties of Si_nCu₂ (n=1–8) clusters are studied by calculating the natural population analysis and electrostatic potential, where the results show that the two copper atoms always possess positive charge and positive potential surround them. In addition, the VIP, VEA and the chemical hardness (η) are also analyzed and compared.     

Standard and non-standard metarefraction with confocal lenslet arrays

A recent paper demonstrated that two lenslet arrays with focal lengths f₁ and f₂, separated by f₁+f₂, change the direction of transmitted light rays approximately like the interface between isotropic media with refractive indices n₁ and n₂, where n₁/n₂=-f₁/f₂ [J. Courtial, New J. Phys. 10 (2008) 083033]. This is true if light passes through corresponding lenslets, that is lenslets that share an optical axis. Light can also pass through different combinations of non-corresponding lenslets. Such light can be either absorbed or allowed to form “ghost images”; either way, it leads to a limitation of the field of view of confocal lenslet arrays. This paper describes, qualitatively and quantitatively, a number of such field-of-view limitations.