Commensurate and incommensurate states of a spin density wave in a quasi-two-dimensional system with an anisotropic energy spectrum in an external magnetic field of arbitrary direction relative to magnetization

A theory of thermodynamic properties of a spin density wave (SDW) in a quasi-two-dimensional system (with a preset impurity concentration x) is constructed. We choose an anisotropic dispersion relation for the electron energy and assume that external magnetic field H has an arbitrary direction relative to magnetic moment M _Q . The system of equations defining order parameters M _Q ^z , M _Q ^σ , M _z , and M ^σ is constructed and transformed with allowance for the Umklapp processes. Special cases when H ‖ M _Q and H ⊥ M _Q (H _Z H ^σ = 0) are considered in detail as well as cases of weak fields H of arbitrary direction. The condition for the transition of the system to the commensurate and incommensurate states of the SDW is analyzed. The concentration dependence of magnetic transition temperature T _M is calculated, and the components of the order parameter for the incommensurate phase are determined. The phase diagram (T,~x) is constructed. The effect of the magnetic field on magnetic transition temperature T _M is analyzed for H _Z H ^σ = 0, and longitudinal magnetic susceptibility χ‖ is calculated; this quantity demonstrates the temperature dependence corresponding to a system with a gap for x < x _c and to a gapless state for x > x _c . In the immediate vicinity of the critical impurity concentration (x ～ x _c ), the temperature dependence of the magnetic susceptibility acquires a local maximum. The effect of anisotropy of the electron energy spectrum on the investigated physical quantities is also analyzed.     

Thiolated cyclodextrin self-assembled monolayer-like characterized with secondary ion mass spectrometry

In the work the focus is on the preparation of self-assembled monolayer-like films consisting of thiolated cyclodextrin on gold substrate and a characterization by using secondary ion mass spectrometry. The short (1 min) and long (1 h) time preparations of self-assembled monolayer-like films, resulting in submonolayer and monolayer regimes, are investigated, respectively. The observed species of thiolated cyclodextrin (M as molecular ion) self-assembled monolayer-like films are assigned to three groups: Au_xH_yS_z clusters, fragments with origin in cyclodextrin molecule associated with Au, and molecular ions. The group of Au_xH_yS_z (x = 2-17, y = 0-2, z = 1-5) clusters have higher intensities than other species in the positive and even more in negative mass spectra. Interestingly, the dependence between the number of Au and S atoms shows that with the increasing size of Au_xH_yS_z clusters up to 11 Au atoms, the number of associated S atoms is also increasing and then decreasing. Molecular species as (M−S+H)Na⁺, (M+H)Na⁺, AuMNa⁺, (M₂−S)Na⁺, and M₂Na⁺ are determined, and also in cationized forms with K⁺. The intensities of thiolated cyclodextrin fragments at the long time preparation are approximately 10 times higher than the intensities of the same fragments observed at the short time. The largest observed ions in thiolated cyclodextrin self-assembled monolayer-like films are AuM₂ and Au₂M. The thiolated cyclodextrin molecular ions are compared with hexadecanethiol molecular ions in the form of Au_xM_w where the values of x and w are smaller for thiolated cyclodextrin than for hexadecanethiol. This result is supported with larger, more compact, and more stabile thiolated cyclodextrin molecule.     

On the Lie-Trotter theorems inL p -spaces

In this paper we consider operatorsH ₀ andV possessing the following properties:

1. H ₀ is a positive self-adjoint operator acting inL ²(M, γ) with γ a probability measure, so that exp(?tH ₀) is a contraction onL ¹(M, γ) for eacht>0.
2. V is a semibounded multiplicative operator acting inL ²(M, γ) {fx379-1}

Under these assumptions theorems of Lie-Trotter type are derived for the operatorsH, H ₀, V, whereH is a self-adjoint extension of the algebraic sumH ₀+V, and is built by the form method. Under the additional assumption thatV(·)∈L ²(M, γ) we prove an essential self-adjointness ofH ₀+V. The results obtained are applicable to non-relativistic quantum mechanics.     

The elliptical dimension of space-time atmospheric stratification of passive admixtures using lidar data

State-of-the-art airborne lidar data of passive scalars have shown that the spatial stratification of the atmosphere is scaling: the vertical extent (Δz) of structures is typically ≈Δx^H_z where Δx is the horizontal extent and H_z is a stratification exponent. Assuming horizontal isotropy, the volumes of the structures therefore vary as ΔxΔxΔx^H_z=Δx^D_s where the “elliptical dimension” D_s characterizes the rate at which the volumes of typical non-intermittent structures vary with scale. Work on vertical cross-sections has shown that 2+H_z=2.55±0.02 (close to the theoretical prediction 23/9).In this paper we extend these (x, z) analyses to (z, t). In the absence of overall advection, the lifetime Δt of a structure of size Δx varies as Δx^H_t with H_t=2/3 so that the overall space-time dimension is D_st=29/9=3.22…. However, horizontal and vertical advection lead to new exponents: we argue that the temporal stratification exponent H_t≈1 or ≈0.7 depending on the relative importance of horizontal versus vertical advection velocities. We empirically test these space-time predictions using vertical-time (z, t) cross-sections using passive scalar surrogates (aerosol backscatter ratios from lidar) at ∼3 m resolution in the vertical, 0.5-30 s in time and spanning 3-4 orders of magnitude in scale as well as new analyses of vertical (x, z) cross-sections (spanning over 3 orders of magnitude in both x, z directions). In order to test the theory for density fluctuations at arbitrary displacements in (Δz, Δt) and (Δx, Δz) spaces, we developed and applied a new Anisotropic Scaling Analysis Technique (ASAT) based on nonlinear coordinate transformations. Applying this and other analyses to data spanning more than 3 orders of magnitude of space-time scales we determined the anisotropic scaling of space-time finding the empirical value D_st=3.13±0.16. The analyses also show that both cirrus clouds and aerosols had very similar space-time scaling properties. We point out that this model is compatible with (nonlinear) “turbulence” waves, hence potentially explaining the observed atmospheric structures.     

A Highly Selective and Sensitive Fluorescent Chemosensor for Aluminum Ions Based on Schiff Base

An efficient “off–on” type fluorescent chemosensor, (E)-N′-(4-(diethylamino)-2-hydroxybenzylidene)-2-hydroxybenzohydrazide (H ₂ L), based on Schiff base for the determination of Al³⁺ has been designed, synthesized, and evaluated. Upon treated with Al³⁺, the fluorescence of H ₂ L was enhanced 45-fold due to the chelation-enhanced fluorescence (CHEF) effect based on the formation of a 1:1 complex between the chemosensor and Al³⁺. Other metal ions, such as Na⁺, K⁺, Mg²⁺, Ca²⁺, Cu²⁺, Ga³⁺, Zn²⁺, Cr³⁺, Cd²⁺, Ag⁺, Fe³⁺, In³⁺, Mn²⁺, Pb²⁺, Co²⁺, and Ni²⁺ had little effect on the fluorescence. The results demonstrate that the chemosensor H ₂ L has stronger affinity with Al³⁺ than other metal ions. The detection limit of H ₂ L for sensing Al³⁺ is 3.60 × 10^?6 M in EtOH–H₂O (3:7, v/v) solution. And the recognizing behavior has been investigated both experimentally and computationally.     

Calculation of high-order rotational centrifugal-distortion matrix elements for a Hund's case (a) basis set

The derivation of explicit expressions for the Hund's case (a) matrix elements of R^2k is discussed, where R is the mechanical rotational angular momentum operator of the molecule. A recursion relation is developed that permits matrix elements of R^2k to be expressed in terms of those of R^2(k?1), thus affording a straightforward means of calculating the case (a) matrix elements of rotational centrifugal-distortion constants D_v, H_v, L_v, M_v, etc., to an arbitrarily high order. The explicit matrix elements of L_v are listed.     

Magnetooptical evidence of exchange interactions in zero-gap Hg1−xFexTe mixed crystals

Interband magnetoabsorption is carried out on zero gap Hg_1-xFe_xTe alloys of x ～ 0.015.Γ₆ → Γ₈ magnetooptical spectra for σ⁺, σ^-, γ 6 H polarization are quantitatively interpreted within the “quasi Ge” model modified by the inclusion of exchange contributions. The field dependence of the magnetization provides evidence of antiferromagnetic interactions between localized spins.     

Infrared-to-visible upconversion luminescence of Er doped barium-natrium-yttrium-fluoride phosphor

Infrared-to-visible upconversion luminescence has been investigated in Er³⁺-doped barium-natrium-yttrium-fluoride phosphor (Ba_xNa_yY_zF_2x+y+3z+3m:Er_m) with different cation concentrations. Intense upconversion emissions around 530, 550, and 660 nm corresponding to the ²H_11/2, ⁴S_3/2, and ⁴F_9/2 transitions, respectively to the ⁴I_15/2 ground state were observed when excited by CW laser radiation at 1550 nm. We adopted the low-temperature combustion synthesis (LCS) method to decrease the phosphor particle size to 40-70 nm in order to couple to the photosensitive surface of CCD. The effect of the amount of carbamide on the particle size and the upconversion luminescence intensity was analyzed. The upconversion luminescence mechanism was studied by the log-log plot of intensity-power.     

Heats of solution/substitution in TlNO3 and CsNO3 crystals and in RbNO3 and CsNO3 crystals from heats of transition: the complete phase diagrams of TlNO3-CsNO3 and RbNO3-CsNO3 systems

From measurements of the decrease in the heat (enthalpy) of transition in the solid phase using differential scanning calorimetry, the apparent molar heats of solution, slope ΔH_t/x, the partial molar heats of solution at infinite dilution, χ, and the heats of solution, ΔH_s^°, of Tl⁺ in CsNO₃ crystal and Cs⁺ in TlNO₃ crystal and Rb⁺ in CsNO₃ crystal and Cs⁺ in RbNO₃ crystal along with their recovered lattice energies, ΔH_L^°, are reported. ΔH_s^° of Tl⁺ and Rb⁺ in CsNO₃ crystal are each found to be negligible or zero representing an ideal solid solution, i.e. ΔH_mix=0. The complete phase diagrams of the TlNO₃-CsNO₃ and RbNO₃-CsNO₃ systems with details of the sub-solidus regions are included. The properties of Tl_(1−x)Cs_xNO₃ and Rb_(1−x)Cs_xNO₃ compositions are discussed in terms of a ‘mixed crystal’ or ‘crystalline solid solution’ in relation to parallel compositions of Tl_(1−x)Rb_xNO₃.     

On the mass operator in a diagonally disordered binary alloy

It is shown that the multiple-occupancy corrections imply identities between skeleton diagrams generating a perturbation calculus for the mass operator M. Self-consistent equations for M_ii, M_i, i+1 are obtained. The corrections to the obtained M begin with terms of order z^-6 where z is the coordination number.     

Weak-coupling expansion of the low-lying energy values in the SU(2) gauge theory on a torus

Relying on analytic results obtained previously, we complete the one-loop computation of the low-lying energy values of the SU(2) gauge theory in an L × L × L periodic box. The expansions are then rewritten in terms of the universal parameter z = M(0⁺) · L (M(0⁺): energy gap in the J^p = 0⁺ sector). We find that the crossover from small-volume to large-volume behaviour is likely to take place at z ? 2. Furthermore, near the crossover, the lowest energy levels (above the ground state) in the 0⁺ sector and the 2⁺ sector are practically degenerate. In each of these sectors there is one more state at about 1.5 · M(0⁺). In the 0^? sector, on the other hand, the lowest energy value is greater than 3 · M(0⁺).     

A new Morse-oscillator based Hamiltonian for H3+: Calculation of line strengths

In two recent publications [V. Špirko, P. Jensen, P. R. Bunker, and A. Čejchan, J. Mol. Spectrosc. 112, 183–202 (1985); P. Jensen, V. Špirko, and P. R. Bunker, J. Mol. Spectrosc. 115, 269–293 (1986)], we have described the development of Morse oscillator adapted rotation-vibration Hamiltonians for equilateral triangular X₃ and Y₂X molecules, and we have used these Hamiltonians to calculate the rotation-vibration energies for H₃⁺ and its X₃⁺ and Y₂X⁺ isotopes from ab initio potential energy functions. The present paper presents a method for calculating rotation-vibration line strengths of H₃⁺ and its isotopes using an ab initio dipole moment function [G. D. Carney and R. N. Porter, J. Chem. Phys. 60, 4251–4264 (1974)] together with the energies and wave-functions obtained by diagonalization of the Morse oscillator adapted Hamiltonians. We use this method for calculating the vibrational transition moments involving the lowest vibrational states of H₃⁺, D₃⁺, H₂D⁺, and D₂H⁺. Further, we calculate the line strengths of the low-J transitions in the rotational spectra of H₃⁺ in the vibrational ground state and in the ν₁ and ν₂ states. We hope that the calculations presented will facilitate the search for further rotation-vibration transitions of H₃⁺ and its isotopes.     

Spectral resonances which become eigenvalues

The stationary Schrödinger equation is ? _x ² φ + λV(x)φ=zφ for φ∈?²(R ⁺,dx). If the potential is bounded below, singular only atx=0, negative on some compact interval and behaves likeV(x)～1/x ^μ asx→∞ with 2≧μ>0, then the system admits shape resonances which continuously become eigenvalues as λ increases. Here λ>0 and for μ=2 a sufficiently large λ is required. Exponential bounds are obtained on Im(z) as λ approaches a threshold. The group velocity near threshold is also estimated.     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).     

A New On-fluorescent Probe for Manganese (II) Ion

A new fluorescent probe for Mn²⁺ ion, (6E)-N-((E)-1,2-diphenyl-2-(pyridin-2-ylimino)ethylidene)pyridin-2-amine (L), has been synthesized from benzil and 2-amino pyridine and characterized. In 1:1 (v/v) CH₃CN:H₂O (pH 4.0, universal buffer) L exhibits fluorescent intensity with emission peak at λ_max 360 nm on excitation with photons of 310 nm. Fluorescent intensity of L increases distinguishingly on interaction with Mn²⁺ ion compared to metal ions—Na⁺, K⁺, Ca²⁺, Mg²⁺, Ba²⁺, Fe²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺, Cd²⁺, Hg²⁺, Pb²⁺ and Ag⁺ individually or all together. The enhancement in fluorescent intensity is due to snapping of photoinduced electron transfer (PET) prevailed in free L. Fluorescence and UV/visible spectral data analysis shows that binding stoichiometry between Mn²⁺ and L is 1:1 with log β?≈?3.0. Both L and its Mn²⁺ complex were optimised using density functional theory (DFT) and vibrational frequency calculations confirm that both are at local minima on the potential energy surfaces.     

Synthesis of anionic clay minerals (mixed metal hydroxides,hydrotalcite)

A number of approaches to the synthesis of a class of anionic clay minerals (M_a²⁺M_b³⁺ (OH)_2a+2b(X⁻)_2b ·xH₂O; M²⁺ = Mg, Ni, Co, Zn, Cu, etc.; M³⁺ = Al, Cr, Fe, Sc; M²⁺/M³⁺ ∼ 1−5; X⁻ = water and base stable anion; x = 0−6) have been sumarized. The most general method involves the mixing of a concentrated, aqueous solution of M²⁺ and and M³⁺ with aqueous hydroxide-carbonate to yield an amorphous gel followed by crystallization at 60–325°. For a number of these materials, the synthetic latitudes with respect to the nature of M²⁺, M³⁺, the M²⁺/M³⁺ ratio, the solution pH and the crystallization temperature has been detailed. The crystallization temperature and time influences the particle size, morphology, surface area and the appearance of foreign phases. The incorporation of various interstitial anions by exchange or synthesis is discussed.     

An asymmetric imidazole derivative as potential fluorescent chemosensor for Fe in aqueous solution

A novel conjugated molecule, L, based on 2,4,5-triphenylimidazole and 6-phenyl-2,2′-bipyridine (HC^∧N^∧N) was synthesized in two steps. The molecule can recognize Fe³⁺ in aqueous solution (THF/H₂O, 1/1, v/v) by the appearance of new emission bands at 416 and 442 nm, which can be attributed to the emission of the newly formed L-Fe³⁺ complex. The binding constant of the complex was calculated to be (6.6±0.39)×10³ M⁻¹, and its formation was also confirmed by the appearance of isosbestic points at 312 and 381 nm in the UV-visible spectral titration experiment. While other transition and rare-earth metal ions, such as Mn²⁺, Fe²⁺, Co²⁺, Ni²⁺, Zn²⁺, Cd²⁺, Hg²⁺, Pb²⁺, Eu³⁺ and Nd³⁺, can only cause some decrease of L's fluorescence, alkali and alkaline earth metal ions, such as Li⁺, Na⁺, K⁺, Mg²⁺ and Ca²⁺, almost have no effect on L's fluorescence. The fluorescence of L can be recovered by the addition of EDTA to the L-Fe³⁺ system just due to EDTA's stronger chelating ability than that of L.     

A rigorous replica trick approach to Anderson localization in one dimension

LetH=?Δ+V onl ²(?), whereV(x),x∈?, are i.i.d.r.v.'s, and letG _L (x,y;E+iη)= 〈x|(H _L?(E+iη))^?1|y〉, whereH _L denotes the operatorH restricted to {?L, ?L+1,...,L} with Dirichlet boundary conditions. We use a supersymmetric replica trick to prove that $$E(|G_L (0,x; E + i\eta )|^2 ) \leqq K\eta ^{ - 2} \exp \{ - m|\log \eta |^{ - \sigma } |x|\} $$ for somem>0, σ>0,K<∞, uniformly inL andE. This estimate, together with the usual necessary estimate on the density of states, implies zero conductivity and gives exponential localization by the Fröhlich, Martinelli, Scoppola, and Spencer method.     

Differential-geometric structures associated with Lagrangians corresponding to scalar physical fields

The paper is devoted to the investigation, using the method of Cartan–Laptev, of the differential-geometric structure associated with a Lagrangian L, depending on a function z of the variables t, x ¹,...,x ⁿ and its partial derivatives. Lagrangians of this kind are considered in theoretical physics (in field theory). Here t is interpreted as time, and x ¹,...,x ⁿ as spatial variables. The state of the field is characterized by a function z(t, x ¹,..., x ⁿ ) (a field function) satisfying the Euler equation, which corresponds to the variational problem for the action integral. In the present paper, the variables z(t, x ¹,..., x ⁿ are regarded as adapted local coordinates of a bundle of general type M with n-dimensional fibers and 1-dimensional base (here the variable t is simultaneously a local coordinate on the base). If we agree to call t time, and a typical fiber an n-dimensional space, then M can be called the spatiotemporal bundle manifold. We consider the variables t, x ¹,...,x ⁿ , z (i.e., the variables t, x ¹,...,x ⁿ with the added variable z) as adapted local coordinates in the bundle H over the fibered base M. The Lagrangian L, which is a coefficient in the differential form of the variational action integral in the integrand, is a relative invariant given on the manifold J ¹ _H (the manifold of 1-jets of the bundle H). In the present paper, we construct a tensor with components Λ⁰⁰, Λ⁰ⁱ , Λ ^ij (Λ ^ij = Λ ^ji ) which is generated by the fundamental object of the structure associated with the Lagrangian. This tensor is an invariant (with respect to admissible transformations the variables t, x ¹,...,x ⁿ , z) analog of the energy-momentum tensor of the classical theory of physical fields. We construct an invariant I, a vector G ⁱ , and a bivalent tensor G ^jk generated by the Lagrangian. We also construct a relative invariant of E (in the paper, we call it the Euler relative invariant) such that the equation E = 0 is an invariant form of the Euler equation for the variational action integral. For this reason, a nonvariational interpretation of the Euler equation becomes possible. Moreover, we construct a connection in the principal bundle with base J ² H (the variety of 2-jets of the bundle H) and with the structure group GL(n) generated by the structure associated with the Lagrangian.