Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.

     

Localization in the ground state of a disordered array of quantum rotators

We consider the zero-temperature behavior of a disordered array of quantum rotators given by the finite-volume Hamiltonian: $$H_\Lambda = - \mathop \Sigma \limits_{x \in \Lambda } \frac{{h(x)}}{2}\frac{{\partial ^2 }}{{\partial \varphi (x)^2 }} - J\mathop \Sigma \limits_{\left\langle {x,y} \right\rangle \in \Lambda } \cos (\varphi (x) - \varphi (y))$$ , wherex,y∈Z ^d , 〈,〉 denotes nearest neighbors inZ ^d ;J>0 andh={h(x)>0,x∈Z ^d } are independent identically distributed random variables with common distributiondμ(h), satisfying ∫h ^?δ dμ(h)<∞ for some δ>0. We prove that for anym>0 it is possible to chooseJ(m) sufficiently small such that, if 0<J<J(m), for almost every choice ofh and everyx∈Z ^d the ground state correlation function satisfies $$\left\langle {\cos (\varphi (x) - \varphi (y))} \right\rangle \leqq C_{x,h,J} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _x,h,J <∞.     

Bis-Benzimidazolyl Diamide Based Fluorescent Probe for Copper(II): Synthesis, Structural and Fluorescence Studies

A new fluorescent probe based on a bis-benzimidazole diamide N ²,N ^2′-bis[(1-ethyl-benzimidazol-2-yl)methyl]biphenyl-2,2′-dicarboxamide ligand L ₁ with a biphenyl spacer group and a Copper(II) trinuclear metallacycle has been synthesized and characterized by X-ray single crystallography, elemental and spectral (FT-IR, ¹H & ¹³C NMR, UV-Visible) analysis. The fluorescence spectra of L ₁ in MeOH show an emission band centered at 300 nm. This band arises due to benzimidazolyl moiety in the ligating system. The diamide L ₁ in the presence of Cu²⁺ show the simultaneous ‘quenching’ of (300 nm) and ‘enhancement’ of (375 nm) emission band. Similar fluorescence behavior was found in water–methanol mixture (9:1). The new emission band at 375 nm is attributed to intra ligand π–π* transition of the biphenyl moiety. L ₁ exhibited high selectivity and sensitivity towards Cu²⁺ in both the medium over other common metal ions like Ni²⁺, Co²⁺, Mn²⁺, Mg²⁺, Zn²⁺, Pb²⁺ and Hg²⁺. The binding constant with Cu²⁺ was calculated by the Benesi-Hildebrand equation. Selective “off-on-off” behavior of L ₁ in methanol has also been studied. The fluorescent intensity of 375 nm bands in L ₁ enhances (turns-on) upon addition of Cu²⁺ and quenches (turn-off) upon addition of Na₂-EDTA.     

Influence of the kinematical constraints on the transverse momentum correlation features

The influence of the kinematical constraints on the transverse momentum correlation features in multiparticle processes is studied by means of thedN/(d r ₁ d r ₂) distribution,r ₁ andr ₂ being the transverse momenta of the particles entering in each pair. Using a limited transverse momentum phase space we obtain for high energy reactions a simple analytical expression fordN/(d r ₁ d r ₂). This expression, similar to a phenomenological parametrization proposed for analyzing¯pp annihilation data, served to define a correlation parameter, the non vanishing value of which is due to the energy-momentum conservation constraints.     

Decay of helicity in homogeneous turbulence

The self-similar relaxation of helicity in homogeneous turbulence has been considered taking into account integral invariants ∫ ₀ ^∞ r ^m 〈u(x)ω(x + r)〉 dr = I _m ^h (where ω = curlu and r = |r|). It has been shown that integral invariants with m = 3 for both helicity and energy are possible in addition to helical analogs of Loitsyanskii (m = 4) and Birkhoff-Saffman (m = 2) invariants associated with the conservation laws of momentum and angular momentum, respectively. Helicity always relaxes more rapidly than the energy. Its decay exponent is in the interval from ?3/2 to ?5/2 versus the interval from ?6/5 to ?10/7 for the energy.     

Hyperfine structure investigations of some odd levels of Co I by level crossing and optical methods

Using the level crossing technique the ratios and absolute values of the hyperfine structure (hfs) constants of the levelsz ⁴F_9/2 andz ⁴F_7/2 of the configuration 3d ⁷4s4p of Co I were measured:z ⁴ F _9/2: ¦A¦=(811±12)MHz; ¦B¦=(48±93) MHz;B/A=?0.06±0.11 A>0; B<0z ⁴ F _7/2: ¦A¦ = (659 ±11)MHz; ¦B¦=(33±84)MHz;B/A=?0.05±0.13 A>0; B<0. In addition the hfs constants of three other excited levels of Co I could be determined by optical methods:z ⁴ F _9/2:A=525±26 MHz;B=200 MHzy ⁴ F _9/2:A=300±30 MHz;B=?500 MHzy ⁴ G _11/2:A=315±20 MHz;B=400 MHz. The experimental results are compared with known experimental and also with theoretical values which where calculated using the parametric potential method.     

On the temperature behavior of second sound and Poiseuille flow

The linearized Peierls equation for the phonon densityN (k λ,r t) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants byk-dependent relaxation rates. For the normal process relaxation time the behaviorτ _N (k λ)∝|k|^?p for smallk is assumed. Taking into account thisk-dependence ofτ _N explicitly and avoiding an expansion with respect toΩτ _N (kλ) before performing the necessary integration overk yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments.     

Laser-Rf double-resonance studies of the hyperfine structure of metastable atomic states of55Mn

The hyperfine structure (hfs) of the metastable atomic states 3d⁶4s⁶ D _{1/2, 3/2, 5/2, 7/2, 9/2} of⁵⁵Mn was measured using theABMR- LIRF method (atomicbeammagneticresonance, detected bylaserinducedresonancefluorescence). The hfs constantsA andB, corrected for second order hfs perturbations, could be derived from these measurements. The theoretical interpretation of these correctedA- andB-factors was performed in the intermediate coupling scheme taking into account the configurations 3d ⁵4s ², 3d ⁶4s and 3d ⁷. Examining the influence of the composition of the eigenvectors on the hfs parameters \(\left\langle {r^{ - 3} } \right\rangle ^{k_s k_l } \) it was found, that for the configuration 3d ⁶4s the two-body magnetic interaction should be considered in the calculation of the eigenvectors. Investigating second order electrostatic configuration interactions and relativistic effects and using calculated relativistic correction factors we obtained for the nuclear quadrupole moment of the nucleus⁵⁵Mn a value ofQ=0.33(1) barn, which is not perturbed by a shielding or antishielding Sternheimer factor. The following hfs constants have been obtained: $$\begin{gathered} A\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 882.056\left( {12} \right)MHz \hfill \\ A\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 469.391\left( 7 \right)MHzB\left( {{3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 65.091\left( {50} \right)MHz \hfill \\ A\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 436.715\left( 3 \right)MHzB\left( {{5 \mathord{\left/ {\vphantom {5 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = - 46.769\left( {30} \right)MHz \hfill \\ A\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 458.930\left( 3 \right)MHzB\left( {{7 \mathord{\left/ {\vphantom {7 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 21.701\left( {40} \right)MHz \hfill \\ A\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 510.308\left( 8 \right)MHzB\left( {{9 \mathord{\left/ {\vphantom {9 2}} \right. \kern-\nulldelimiterspace} 2}} \right) = 132.200\left( {120} \right)MHz \hfill \\ \end{gathered} $$      

Some estimates for magnetic fluctuations in a turbulent medium

A new integral relationship between the fluctuations b(r, t) of a magnetic field and its mean B ₀(r, t) is derived for the steady-state magnetic field in a turbulent medium. This formula provides the estimate 〈b?curlb〉=?B ₀?curlB ₀. Simultaneously, the coefficient of amplification of the mean magnetic field α effect) is obtained: α=(η+β)B ₀? curlB ₀/B ₀ ² . The formula for α allows for a decrease in this coefficient owing to the back action of the magnetic field on the turbulent velocity field. It is shown that the Zel’dovich’s estimate 〈 b ²〉?β/η B ₀ ² for two-dimensional turbulence holds for magnetic fields at the instant the fluctuations 〈a ²〉 of the vector potential, rather than 〈b ²〉, reach a maximum. Here, η and β are the ohmic (molecular) and turbulent diffusion coefficients, respectively. This estimate is refined with allowance made for the fact that the condition for diffusion approximation itself relates the β, b, and B ₀ quantities to each other.     

Aging effect in CaLaBa{Cu1???xFex}3O7???�� with 0 �� x �� 0.07 studied by M?ssbauer spectroscopy

In this work, we study the long-term aging effect caused by Fe atoms in the superconductor CaLaBa{Cu_1???xFe_x}₃O_7????? with 0 ?? x ?? 0.07. XRD confirms that this system has a YBCO-like structure. The critical temperature (T_c) is strongly affected by aging and depends on the amount of Fe in the structure. Room temperature Mössbauer spectroscopy reveals the presence of the typical species A, B?CB ??, C and new species E ?? and F. Interestingly; A, which corresponds to the Fe^3?+? atom located in the Cu(1) of the chains with spin S _z = 3/2, shows a drastic reduction which means migration to the species B, B ?? and C. Species B and B ?? correspond to the Fe^3?+? in the Cu(2) site forming planar quasi-octahedral and planar square pyramidal, while the C specie is a square pyramidal with O(5) respectively (spin S_z = 3/2 in all these cases). Aging causes loss of superconductivity in the samples with 5 and 7% of iron content.     

Theoretical studies of ground and excited states in a series of Zn(II) complexes,derived from thiourea and thiosemicarbazide

Theoretical studies for a series of mono- and binuclear zinc (II) complexes Zn(CH₃COO)₂(H₂L)₂ [H₂L = N-2-propenyl-N ^′-2-pyridinylthiourea] (A), Zn₂(CH₃COO)₂(H₃L-a)₂ [H₃L-a = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-phenylcarbothioamide] (B), and Zn(H₃L-b)₂ [H₃L-b = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-(2-propenyl)carbothioamide] (C) have been performed on their structures and excited-state absorption spectra. The singlet ground-state geometries are fully optimised at three DFT levels, i.e., B3LYP, B3PW91, and M06. Different geometries, i.e., strongly distorted tetrahedral coordination environment in complex A, distorted square-pyramidal environment in complex B, and irregular octahedral mode in complex C are identified. Consequently, the spectroscopic properties are calculated by means of time-dependent density functional theory (TDDFT) with the Polarisable Continuum Model (PCM) based on the optimised gas-phase geometries. Three absorption peaks are identified for every complex, which are in good agreement with the experimental ones. For complex A, all three absorption peaks centered at 280.33 nm, 268.09 nm, and 250.87 nm, respectively, are ascribed to the (p,π) → π* transition with a mixed intraligand charge-transfer (ILCT)/ligand-ligand charge-transfer (LLCT) character. The composition of frontier orbitals involved in major absorption bands for the three complexes shows similarities, which results in the almost homologous transition attributions and characteristics. A remarkable bathochromic shift in the lowest-lying absorption band is observed for complexes B and C as compared with complex A, which is attributed to the decreased H (HOMO)-L (LUMO) energy gap (ΔE |HOMO-LUMO|) by the formation of conjugate metallocycles in complexes B and C.     

Trovacenyl-based organometallic triradicals: Spin frustration, competing interactions and redox splitting

Two new triradicals based on trovacene [η⁷-tropylium)vanadium(η⁵-cyclopentadienyl)], 1,3,5-tri([5]trovacenyl) benzene4 and 1,3,5-tri([5]trovacenyl)-6-methoxybenzene5 were prepared and their magnetic properties were studied by continuous-wave X-band electron paramagnetic resonance (EPR) spectroscopy and by temperature-dependent magnetic susceptometry. The EPR spectra of4 and5 in liquid toluene solution demonstrate that the three unpaired electrons localized on the vanadium atoms interact with each other in both complexes. The data from magnetic susceptometry revealed that the electron spins in both triradicals are antiferromagnetically coupled despite themeta-phenylene bridge. The exchange coupling constants are equal in the C₃-symmetrical triradical4 (J=J′=?0.68 cm^?1), which leads to a twofold degenerate spin ground state (spin frustration). The symmetry lowering by methoxy substitution of the benzene spacer in5 results in the effect of c ompeting interactions (J=?1.83 cm^?1 andJ′=?2.38 cm^?1). In addition to magnetocommunication, the effect of ring substitution on electrocommunication is also discernable. It manifests itself indisparate redox splittings δE _1/2 (0/?, ?/2?) and δE _1/2 (?/2?, 2?/3?) for5, while these parameters are equal for the C₃-symmetrical trinuclear complex4.     

Gyromagnetic ratios of 4+ and 6+ states in156Gd and158Gd

The followingg-factors have been derived from time integral measurements of γ-γ angular correlations in the static magnetic hyperfine field of magnetized gadolinium metal probes:¹⁵⁶Gd:g(4 ₁ ⁺ )=+0.310(19)g(6 ₁ ⁺ )=+0.25(21)g(4 ₃ ⁺ , 1511 keV)=+0.809(27)¹⁵⁸Gd:g(4 ₁ ⁺ )=+0.409(15). The 5.35d ¹⁵⁶Tb sources were produced by the reaction¹⁵⁶Gd(d, 2n)¹⁵⁶Tb in our cyclotron. A carrier-free 150y ¹⁵⁸Tb source was obtained from ISOLDE/CERN. In comparison with the precisely knowng-factors of the 2 ₁ ⁺ states,g(2 ₁ ^su+ ,¹⁵⁶Gd) =+0.386(4) andg(2 ₁ ⁺ ,¹⁵⁸Gd)=0.381(4), we observe a large reduction for the¹⁵⁶Gd 4 ₁ ⁺ state whereasg increases slightly for¹⁵⁸Gd. The half-life of the 4 ₁ ⁺ state of¹⁵⁸Gd was remeasured as¹⁵⁸Gd:T _1/2(4 ₁ ⁺ )=148(2) ps. A measurement of the rotation in the 4 ₃ ⁺ state of¹⁵⁶Gd in external magnetic fields of various strengths up toB _ext=9.5 T did not confirm the anomalous dependence of the magnetic hyperfine field in gadolinium metal on the external field, which has been reported by Persson et al. [29].     

The influence of disorder on magnetocaloric effect and the order of transition in ferromagnetic manganite (La1−x Nd x )2/3(Ca1−y Sr y )1/3MnO3

Magnetocaloric effect and order of transition in (La_1?x Nd _x )_2/3(Ca_1?y Sr _y )_1/3MnO₃, prepared by conventional solid-state reaction, have been investigated. Using Banerjee criterion, we demonstrate first-order transition for (J1) and (J2 ) as well as second-order transition for (J3 ), (J4 ), and (J5 ) samples. The ΔS _M ^max is ranging between 9.18 Jkg^?1 K^?1 and 4.87 when Nd and Sr content changes leading to relative cooling power (RCP) varying between 330 and 229.35 J/kg. Both ΔS _M ^max and the RCP are found sensitive to the disorder σ ². The universal behavior obtained from ΔS variation curves confirmed the first-order transition for (J1) and (J2 ) samples and second-order transition for (J3), (J4), and (J5 ) samples obtained by Banerjee criterion. All samples with second-order phase transition exhibit inhomogeneous character estimated from local exponent n.     

Luminescence and crystal-field fitting of two optical isomeric complexes of europium

FT-IR and Raman vibrational spectra and electronic emission spectra have been recorded for enantiomers of europium complexes with DBM: dibenzoylmethanate 1,2, and TTFA: 2-thenoyltrifluoroacetonate 3,4, employing the chiral ligands L_SS(+)- and L_RR(-)-4,5-pinene bipyridine. Contrary to the previously published X-ray data, where geometrical differences were stated to occur for particular enantiomers, the vibrational (and the emission) spectra of the individual optical isomers of a complex are not distinguishable. Using excitation into the Eu³⁺⁵D₂ multiplet term, the emission intensity is weak from ⁵D₁, whereas a complex structure is observed for the ⁵D₀→⁷F_J transitions. Features in the vibronic sidebands exhibit similar derived vibrational energies to those observed in the Raman spectra. Fittings of 25 4f⁶ crystal-field energy levels of 2 and 4 have been attempted with some approximations concerning the local Eu³⁺ environments. The ⁵D₀ emission lifetimes are monoexponential and are 0.5 (1,2) and 0.9 ms (3,4) at room temperature.     

Magnetostriction and thermal expansion of HoAl3(BO3)4

The magnetostriction and thermal expansion of rare-earth aluminoborate HoAl₃(BO₃)₄ have been studied theoretically. The calculated field and temperature dependences of the multipole moments of the Ho³⁺ ion in HoAl₃(BO₃)₄ made it possible to describe the known experimental data and to predict possible anomalies of thermal expansion. It has been shown that, for the direction of the field B ‖ c, the nonmonotonic character of magnetostriction along the axis a is determined by the multipole moments, the main of which is β _J 〈O ₄ ⁰ 〉. For B ‖ a and B ‖ b, the maximum moments are β _J 〈O ₄ ² 〉and α _J 〈O ₂ ² 〉; their variation with the field and temperature explain well the form of magnetostriction. It has been established that the greater value of magnetostriction Δa/a for B ‖ b than for B ‖ a and the greater value of magnetostriction for the field in the basal plane than for B ‖ c are caused by greater variations in the field of actual multipole moments.     

Evaluating the validity of parametrized relativistic wave equations

We wish to determine the correct partial differential equation(s) for describing a relativistic particle. A physical foundation is presented for using a parametrized wave equation with the general form $$i\frac{{\partial \psi }}{{\partial s}} = K\psi$$ where s is the invariant evolution parameter. Several forms have been proposed for the generator K of evolution parameter translations. Of the proposed generators, only the generator K ₂ which is proportional to the inner product P _μ P ^μ of fourmomentum operators can be derived from first principles, notably a probabilistic basis. Although experimental tests must be made to establish the validity of K ₂,we conclude that K ₂ is the leading theoretical candidate for the form of a generator of evolution parameter translations.     

Structurally Simple Ferrocene Derivatives for Selective Cadmium Sensing

Three new ferrocene based Schiff bases 4-{[(E)-ferrocenylmethylidene] amino}benzenethiol (1b), 3-{[(E)-ferrocenylmethylidene]amino} benzenethiol (1c), 2-{[(E)-ferrocenylmethylidene]amino} benzenethiol (1d) have been synthesized to study their sensor property to various metal ions. It has been observed that 1b is highly fluorescent and its fluorescence changes in presence of metal ions. It was further observed that compound 1b is highly selective towards Cd²⁺ ion in solution.     

Synthesis and Spectroscopic Properties of Novel Fluorescent Compounds Containing Bis-pyrazole Ring

A series of pyrazoline derivatives containing pyrazole group were synthesized and characterized by means of ¹H NMR, FT-IR, MS and elemental analysis, and their UV–vis absorption behavior and fluorescent properties were also measured. Moreover, the influence of metal ions on spectral properties of synthetic products was examined with compound A ₅ as an example. It has been found that all synthetic pyrazoline derivatives show two remarkable absorption peaks at about 260 and 360 nm and the maximum emission peak at 445–467 nm. Especially, the joined of Co²⁺ can quench the fluorescence of compound A ₅ obviously.