The n = 0 replica limit of U(n) and U(n)/SO(n) models

Recently the replica limit n = 0 of the U(n) and U(n)/SO(n) models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and U(n)/SO(n). This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and U(n)/SO(n) and draw consequences for these functions in this limit.     

Matrix elements for the representations of SO(n) and SO0(n, 1)

Matrix elements of the unitary irreducible representations of the group SO(n) of class higher then 1 (with respect to SO(n−1)) in Gel'fand-Zetlin basis are obtained in explicit form. They are represented as polynomials in cosθ and sinθ of the order equal to the first coordinate of the highest weight. Making use of them the representation matrix elements for the group SO₀(n, 1) in SO(n) basis are calculated.     

The n = 0 replica limit of U(n) and models

Recently the replica limit n = 0 of the U(n) and models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and . This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and and draw consequences for these functions in this limit.     

Integrable string models with constant torsion in terms of chiral invariants of SU(n), SO(n), SP(n groups

We used the invariant local chiral currents of principal chiral models for SU(n), SO(n), SP(n) groups to construct new integrable string equations of hydrodynamic type on the Riemann space of the chiral primitive invariant currents and on the chiral nonprimitive Casimir operators as Hamiltonians.     

Scaling contributions to the free energy in the 1/n expansion of O(n) nonlinear sigma models in d-dimensions

Within the 1/N expansion of O(N) nonlinear σ models for d≤4 it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them to O(1/N). For critical dimensions d=2+2/n the Abe-Hikami anomaly is recovered, while for d=2 the removal of the spin-wave term is justified.     

Lower bounds for eigenvalues of the Dirac operator on n-spheres with SO(n)-symmetry

In this paper we derive estimates for the eigenvalues of the Dirac operator and their multiplicity on manifolds diffeomorphic to Sⁿ with an isometric SO(n)-action. Especially we prove a new lower bound for the first eigenvalue and show an example, where this new bound coincides in the limit with the known upper bounds.     

Raman study of HgBa2Can−1CunO2n+2+δ (n=1,2,3,4 and 5) superconductors

Polarized micro-Raman scattering measurements have been performed on the five members of the HgBa₂Ca_n−1Cu_nO_2n+2+δ (n=1,2,3,4 and 5) high-T_c superconductor family using different laser frequencies. Local laser annealing measurements were carried out to investigate the variation of the Raman spectra with the excess oxygen content, δ. A systematic evolution of the spectra, which display mainly peaks near 590, 570, 540 and 470 cm⁻¹, with increasing number of CuO₂ layers has been observed; its origin has been shown to lie in the variation of the interstitial oxygen content. In addition to confirming that the 590 cm⁻¹ mode represents vibration of apical oxygens in the absence of neighboring excess oxygen, the 570 cm⁻¹ mode, which may be composed of some finer structures, has been assigned to the vibration of the apical oxygen modified by the presence of the neighboring excess oxygens. The 540 and 470 cm⁻¹ modes may represent the direct vibration of excess oxygens. The implication of possible different distribution sites of excess oxygens is discussed. All other observed lower-frequency modes are also assigned.     

Electron impact ionization of Ar n , (H2O) n , Ar n (H2O) m clusters

Signals from ions forming in a supersonic molecular beam consisting of an argon-water vapor mixture are measured as functions of the exciting electron energy in the range to 120 eV. The thresholds of electron impact excitation of (H₂O) _{n − 1}H⁺ and Ar _n (H₂O _m ⁺ clusters are determined for the first time. It is found that the proton-hydroxyl group binding energy decreases considerably both in the case of water molecule clustering and when mixed Ar _n (H₂O) _m clusters arise.     

Integrable systems on so(n)-valued Lie algebras on higher genus curves

We consider special quasi-graded so(n)-valued Lie algebras on higher genus curves. Using them we find new Lie theoretical interpretation of the integrability of generalized Manakov tops and generalized Clebsch systems and explicitly construct their isomorphism on trajectories.     

Investigation of the excitation of metastable states of 197Pt and 197Hg in (γ, n) and (d, 2n) reactions

The isomeric ratios of the ^197m,g Pt and ^197m,g Hg yields in the respective (γ, n) reactions are measured for the first time in the energy range 8–17 MeV. The isomeric ratios σ _m/σ_g for ^197m,g Hg in the (d, 2n) reaction are measured in the energy range 8–50 MeV. The experimental data are compared with the results of theoretical calculations. The effect of the structure of low-lying states and of the yrast line on the behavior of σ _m/σ_g is revealed. __________ Translated from Yadernaya Fizika, Vol. 67, No. 5, 2004, pp. 899–905. Original Russian Text Copyright ? 2004 by Zheltonozhsky, Mazur, Bigan.     

Novel structure and electronic property of Sin (21n30) clusters

Using first-principles simulated annealing generalized gradient approximation density functional calculations based on norm-conserving pseudopotentials, we have investigated the geometric and electronic structures of low-energy silicon clusters (Si_n, n=21–30). We have obtained new low-energy structures not reported previously. Our calculations suggest that the lowest energy structures are spherical ones including core atoms whose number increases with the cluster size. The trend of the binding energy as well as that of the energy difference between the highest occupied and the lowest unoccupied molecular orbitals is studied as a function of the cluster size and the number of core atoms.     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters

Full-size image (2K)

, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with

Full-size image (1K)

as well as in an orthorhombic cell with lattice parameters

Full-size image (1K)

.     

Synthesis and characterization of HgBa2Can−1CunO2n+2+δ (n = 1, 2, and 3)

We have successfully prepared the first three members of the mercury-based superconducting compounds Hg--- Ba₂Ca_n−1Cu_nO_2n+2+δ, namely Hg---1201, Hg---1212 and Hg---1223 with high purity and very good quality. T he influence of the synthesis parameters is studied in detail. Using the sealed quartz tube method, very simple procedures are found to ensure a 100% reproducibility of nearly 100% pure Hg---1201 and 85–90% Hg---1212 and Hg---1223. Oxygen annealing of the sample Hg---1201 at 300°C for 18 h results in an enhancement of its critical temperature up to 97 K. The symmetry of the first and second members is tetragonal with lattice parameters a = 3.8831 (1) Å, C = 9.5357 (2) Å, and A = 3.8624 (1) Å, C = 12.7045 (2) Å, respectively. X-ray diffraction lines of Hg---1223 can be indexed in a tetragonal cell with a = 3.8564 (1) Å and C = 15.8564 (9) Å as well as in an orthorhombic cell with lattice parameters a = 5.4537 (1) Å, B = 5.4247 (1) Å, and C = 15.8505 (7) Å.     

The A2 (n, 3px) Rydberg state of formaldehyde

Pairs of bands were observed in the absorption spectrum of H₂CO, HDCO, and D₂CO in the 1470-1430 Å region which were characterized by well-defined rotational band contours. A band contour synthesis of the observed band envelopes demonstrated that the bands are described by type C selection rules. From the observed intervals and their shifts on deuterium isotope substitution these bands were assigned to quantum additions of ν₅ and ν₆. The symmetry of the upper state was deduced to be ¹A₂ from the vibrational assignment of the bands and their polarizations, while the results from MO theory lead to the orbital assignment n → 3p_x. The electronic transition then is .     

Simple numerical method of computing the probabilities of angular momentum Jν occurring among possible vectors J Resulting from n angular momentum jμ summation (μ=1?n)

Arelatively simple numerical method of summing angular momentum vectors with maintaining space quantization rules of each summed angular momentum has been presented. The method enables the calculation of the values of probability (p j _μ) of finding a definite angular momentum J _μ among all vectors J being the results of quantum summation of n angular momentum vectors j _μ(μ=1-n. It may be used, e.g., in the calculations of angular momentum of many-particle states. The significance of the paper is connected with the possibility of taking into account, in a simple way, the angular momentum conservation principle for a system which consists of an arbitrary number of excitons. From Yadernaya Fizika, Vol. 67, No. 11, 2004, pp. 2123–2128. Original English Text Copyright ? 2004 by Kaczmarczyk. This article was submitted by the author in English.     

The quantum groups GLq(n) and Weyl-Heisenberg operators

It is shown that for deformation parameters q = 1, the bilinear product relations which define the quantum groups GL_q(n) can be recast as Weyl-Heisenberg relations, provided some invertibility conditions are met. Finite- and infinite-dimensional representations of GL_q(n) are then easily constructed, as shown in a few examples.     

Local environment of fluorine atoms in Sr2Can ? 1CunO2n + δF2 ± y (n = 2, 3) high-temperature superconductors grown under high pressure

The local environment of fluorine atoms in Sr₂Ca _{n − 1}Cu _n O_{2n + δ}F_{2 ± y} (n = 2, 3) high-temperature superconductors (T _c = 99 and 111 K) is studied using soft x-ray emission and absorption spectroscopy. The fluorine spectra of the samples studied are found to be similar to those of SrF2, which supports the conjecture that fluorine atoms substitute for apex oxygen atoms and form double SrF layers. __________ Translated from Fizika Tverdogo Tela, Vol. 47, No. 7, 2005, pp. 1170–1174. Original Russian Text Copyright ? 2005 by Kurmaev, Moewes, Wilks, Nechkina, Zatsepin, Kawashima, Takayama-Muromachi.     

Hierarchical and probabilistic quantum information splitting of an arbitrary two-qubit state via two cluster states

Based on non-maximally entangled four-particle cluster states, we propose a new hierarchical information splitting protocol to probabilistically realize the quantum state sharing of an arbitrary unknown two-qubit state. In this scheme, the sender transmits the two-qubit secret state to three agents who are divided into two grades with two Bell-state measurements,and broadcasts the measurement results via a classical channel. One agent is in the upper grade and two agents are in the lower grade. The agent in the upper grade only needs to cooperate with one of the other two agents to recover the secret state but both of the agents in the lower grade need help from all of the agents. Every agent who wants to recover the secret state needs to introduce two ancillary qubits and performs a positive operator-valued measurement(POVM) instead of the usual projective measurement. Moreover, due to the symmetry of the cluster state, we extend this protocol to multiparty agents.     

Measurement of the fine structure of the n = 4 state of hydrogen

A time-resolved spectroscopy technique has been used to measure the fine structure of the n = 4 state of hydrogen. The excited hydrogen atoms were formed by the use of an electron beam to dissociate molecular hydrogen. The resonance transitions were observed by keeping the radio frequency field fixed and sweeping the magnetic field. Measurements on deuterium were used to study the effects of pressure and motional electric fields. The ²S_1/2 → ²P_1/2 Lamb shift transition , the ²P_3/2 → ²S_1/2 fine structure interval ΔE − L, and the ambient electric field in the measurement volume were determined by using measurements on three separate transitions made at fixed magnetic field. The measurements gave and     

Localized solutions of (N+1)-dimensional evolution equations

We give a method of constructing nonlinear Schrödinger equations which are similar to the Davey-Stewartson equation, but in N+1 dimensions, and posses, by construction, solutions describing interacting soliton-like objects.