EPR of trivalent iron ions in a LiCaAlF6 crystal

The orientational dependences of the EPR spectra of Fe³⁺-doped LiCaAlF₆ single crystals (space group P31c, Z=2), grown at the Laboratory of Magnetic Radio Spectroscopy at Kazan’ State University, have been investigated in detail. The spectrum is described by a trigonal spin Hamiltonian with the following parameters: B ₂₀=40.072×10⁻⁴ cm⁻¹, B ₄₀=−5.799×10⁻⁴ cm⁻¹, B ₄₃=−4.281×10⁻⁴ cm⁻¹, A _s=24.33±1, A _p=6.13±1, g _∥=g _⊥=2.00217±0.0003. A theoretical calculation of the hyperfine structure parameters shows that they are described quite well when allowance is made for the overlapping of the wave functions of the paramagnetic center and the ligands (F⁻). Fiz. Tverd. Tela (St. Petersburg) 39, 488–490 (March 1997)     

Asymptotic behavior of orbits of C 0-semigroups and solutions of linear and semilinear abstract differential equations

In this paper, we study the asymptotic behavior of solutions of semilinear abstract differential equations (*) u′(t) = Au(t) + t ⁿ f(t, u(t)), where A is the generator of a C ₀-semigroup (or group) T(·), f(·, x) ∈ A for each x ∈ X, A is the class of almost periodic, almost automorphic or Levitan almost periodic Banach space valued functions ϕ: ℝ → X and n ∈ {0, 1, 2, ...}. We investigate the linear case when T(·)x is almost periodic for each x ∈ X; and the semilinear case when T(·) is an asymptotically stable C ₀-semigroup, n = 0 and f(·, x) satisfies a Lipschitz condition. Also, in the linear case, we investigate (*) when ϕ belongs to a Stepanov class S ^p-A defined similarly to the case of S ^p-almost periodic functions. Under certain conditions, we show that the solutions of (*) belong to A _u:= A ∩ BUC(ℝ, X) if n = 0 and to t ⁿ A _u ⊕ w _n C ₀ (ℝ, X) if n ∈ ℕ, where w _n(t) = (1 + |t|)ⁿ. The results are new for the case n ∈ ℕ and extend many recent ones in the case n = 0. Dedicated to the memory of B. M. Levitan     

The Unusual Magnetic Resonance Properties of Trigonal Prismatic Tc and Re Complexes

The electron paramagnetic resonance (EPR) spectra of the trigonal prismatic complexes Tc(abt)₃, Tc(bdt)₃, Re(abt)₃ and Re(bdt)₃ (abt, O-aminobenzenethiol; bdt, benzene-1,2-dithiol) in dilute frozen solution are interpreted in terms of an axially symmetric spin Hamiltonian, with g values close to two, principal hyperfine couplings of |A ^Tc| ~ 5–12 × 10⁻⁴ cm⁻¹, nuclear quadrupole couplings of |P ^Tc| ~ 0.3–0.35 × 10⁻⁴ cm⁻¹ and the unusual values 5 × 10⁻⁴ cm⁻¹ ~ |A _zz ^Re| < |P ^Re| ~ |A _xx ^Re| ~ |A _yy ^Re| ~ 25 × 10⁻⁴ cm⁻¹. Similar magnitudes of the parameters have been obtained by simulation of the previously published spectra of Re(pda)₃, Re(tdt)₃ and Re(pdt)₃ (pda, O-phenylenediamine; tdt, toluene-3,4-dithiol; pdt, cis-1,2-diphenylethene-1,2-dithiol) by other authors. The unexpectedly large value of P relative to A is a common feature of all the Re tris-dithiolato and related trigonal prismatic complexes studied by EPR and is attributed to the high degree of delocalization of the unpaired electron onto the ligands and the distortion of the electron charge cloud. These factors are less evident in the complexes Tc(abt)₃ and Tc(bdt)₃. Intermolecular dipolar interactions, narrowed by weak exchange, are responsible for some of the spectral features observed in the solid state and concentrated (≫1 mM) frozen solutions, although there is no evidence for specific solute–solute interactions.     

EPR study of the Jahn-Teller effect of Cu2+ ions in ZnGa2O4

The Jahn-Teller effect in the ZnGa₂O₄ spinel single crystal has been investigated using electron paramagnetic resonance of Cu²⁺ ions in the temperature range 110–560 K. It has been shown that copper ions occupy octahedral sites 16d in the ZnGa₂O₄ crystal with cubic symmetry O _h ⁷ (Fd-3m). At T < 560 K, the octahedra undergo tetragonal distortions (predominantly tension) and rotation around the fourfold axes by the angle θ ≈ 2.6°. The parameters of the spin Hamiltonian, which characterize the prolate (g _‖ = 2.355, g _⊥ = 2.077, A _‖ = 116 Oe, A _tp = 12 Oe) and oblate (g _‖ = 2.018, g _⊥ = 2.246, A _‖ = 75 Oe, A _⊥ = 44 Oe) octahedra, have been determined. At temperatures above 560 K, the static Jahn-Teller effect transforms into the dynamic effect and the spectrum of the magnetic resonance becomes isotropic with g = 2.116 (the experimental frequency corresponds to the X band).     

Classes on Compactifications of the Moduli Space of Curves Through Solutions to the Quantum Master Equation

In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A _∞-algebra. The initial data for our construction are what we call a ‘quantum A _∞-algebra’, which arises as a type of deformation of a cyclic A _∞-algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum A _∞-algebras which extend a family of cyclic A _∞-algebras, introduced by Kontsevich, which are known to produce all the kappa classes using his construction.      

ESR of V4+ in α-RbTiOPO4 single crystals

We have recorded and investigated the ESR spectrum of vanadium-doped α-RbTiOPO₄ single crystals in the temperature interval 77–300 K. Two types of structurally distinct centers, V1 and V2, with a 4:1 ratio of the peak intensities were observed. The angular dependences of the resonance magnetic fields are described by a spin Hamiltonian corresponding to axial symmetry with the parameters g _∥1=1.9305, g _⊥1=1.9565, A _∥1=−168.2×10⁻⁴cm⁻¹, and A _⊥1=−54.3×10⁻⁴cm⁻¹ for V1 centers and g _∥2=1.9340, g _⊥2=1.9523, A _∥2=−169.0×10⁻⁴cm⁻¹, and A _⊥2=−55.2×10⁻⁴cm⁻¹ for V2 centers. A model of a paramagnetic center is proposed: The vanadium ions replace titanium ions in two structurally distinct positions Ti1 and Ti2 (V1 and V2 centers, respectively). The possibility that a VO²⁺ ion forms when α-RbTiOPO₄ crystals and crystals of the KTP group (KTiOPO₄, NaTiOPO₄, α-and β-LiTiOPO₄), studied earlier, are doped with vanadium is discussed. Fiz. Tverd. Tela (St. Petersburg) 40, 534–536 (March 1998)     

ESR study of exchange coupled pairs in copper diethyldithiocarbamate

ESR investigations on exchange coupled pairs of Cu ions in single crystals of Cu(dtc)₂, isomorphously diluted with the corresponding diamagnetic zinc salt, are reported. The spin Hamiltonian parameters for the coupled species (S=1) are:g _‖=2.1025,g ₊=2.031,A=75.1×10⁻⁴ cm⁻¹,B=14.8×10⁻⁴,D=276.0×10⁻⁴ cm⁻¹ andE=46.7×10⁻⁴ cm⁻¹. While theg andA tensors show tetragonal symmetry, the zeor-field splitting tensor is rhombic and has principal axes different from those of theg andA tensors. Intensity measurements made down to 4.2 K indicate that the exchange is ferromagnetic with |FFF| ∼ 10 cm⁻¹. Direct dipole-dipole interaction appears to be the major contribution to the zero-field splitting. A calculation on the distributed point dipole model shows that dipolar interaction is considerably modified by the high covalency of the Cu-S bond and accounts for the rhombic nature of the tensor. The possible exchange mechanisms in Cu(dtc)₂—direct exchange and superexchange through the bridging sulphurs—are discussed.     

Generalized q-Hermite Polynomials

We consider two operators A and A ⁺ in a Hilbert space of functions on the exponential lattice , where 0<q<1. The operators are formal adjoints of each other and depend on a real parameter . We show how these operators lead to an essentially unique symmetric ground state ψ₀ and that A and A ⁺ are ladder operators for the sequence . The sequence (ψ _n /ψ₀) is shown to be a family of orthogonal polynomials, which we identify as symmetrized q-Laguerre polynomials. We obtain in this way a new proof of the orthogonality for these polynomials. When γ=0 the polynomials are the discrete q-Hermite polynomials of type II, studied in several papers on q-quantum mechanics. Received: 6 December 1999 / Accepted: 21 May 2001     

Interference in Phase Space of Squeezed States for the Time-Dependent Hamiltonian System

We showed that the idea of Schleich and Wheeler (1987, Nature 326, 574) for the semiclassical approach of the interference in phase space of harmonic oscillator squeezed states can be extended to that of general time-dependent Hamiltonian system. The quantum phase properties of squeezed states for the general time-dependent Hamiltonian system are investigated by using the quantum distribution function. The weighted overlaps A _n and phases θ _n for the system are evaluated in the semiclassical limit.     

C*-Algebras associated with one dimensional almost periodic tilings

For each irrational number, 0<α<1, we consider the space of one dimensional almost periodic tilings obtained by the projection method using a line of slope α. On this space we put the relation generated by translation and the identification of the “singular pairs”. We represent this as a topological spaceX _α with an equivalence relationR _α. OnR _α there is a natural locally Hausdorff topology from which we obtain a topological groupoid with a Haar system. We then construct the C^*-algebra of this groupoid and show that it is the irrational rotation C^*-algebra,A _α. Research supported by the Natural Sciences and Engineering Research Council of Canada and the Fields Institute for Research in Mathematical Sciences.     

Thermal stability and electrical conductivity of multiferroics BiFeO<Subscript>3</Subscript>/REEs

Ceramic samples of bismuth ferrite and solid solutions of Bi_{1 − x} A _x FeO₃ type (where A = Lu, Yb, Tm, Er, Ho, Dy, Tb, Gb, Eu, Sm, Nd, Pr, La; 0.05 ≤ x ≤ 0.20; Δx = 0.05) were prepared. Spectra of the real part of electrical conductivity were studied within the range 10⁻⁴–10⁻⁶ Hz. The dependence of the samples’ thermal stability and electrical conductivity on the size of the substituting ions was established.     

Bound states and critical behavior of the Yukawa potential

We investigate the bound states of the Yukawa potential V (r)=−λexp(−αr)/r, using different algorithms: solving the Schr?dinger equation numerically and our Monte Carlo Hamiltonian approach. There is a critical α = α_C, above which no bound state exists. We study the relation between α_C and λ for various angular momentum quantum number l, and find in atomic units, α_C(l) = λ[A ₁ exp(−l/B ₁) + A ₂ exp(−l/B ₂)], with A ₁ = 1.020(18), B ₁ = 0.443(14), A ₂ = 0.170(17), and B ₂ = 2.490(180).     

Magnetic circular dichroism in the absorption of theF A centre in KCl doped with Li and Na

Summary The spin-orbit structure ofF _A centres in KCl:Li and KCl:Na have been studied by means of the magnetic circular dichroism. Due to theirC _4V symmetry theF _A centres have two different spin-orbit parameters, Δ^‖ and Δ^⊥, which only in the KCl:Li case follow the relation: Δ^‖ < Δ_F < Δ^⊥ as expected from the theory. For a close comparison we have also reported our measurement of the spin-orbit coupling ofF centre in KCl. The spin-orbit parameters of theF andF _A centres have been determined using the method of moment.     

On Yang–Mills Instantons over Multi-Centered Gravitational Instantons

 In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang–Mills instantons on Gibbons–Hawking multi-centered gravitational instantons, which come in two parallel families: the multi-Eguchi–Hanson, or A _k ALE gravitational instantons and the multi-Taub–NUT spaces, or A _k ALF gravitational instantons. We calculate their energy and find the reducible ones. Following Kronheimer we also exploit the U(1) invariance of our solutions and study the corresponding explicit singular SU(2) magnetic monopole solutions of the Bogomolny equations on flat ℝ³. Received: 16 September 2002 / Accepted: 22 October 2002 Published online: 21 February 2003 Communicated by A. Connes     

Determination of the degree of crystallinity of poly(vinyl alcohol) by FTIR spectroscopy

Quantitative correlations between the intensity of the crystalline band at 1144 cm⁻¹ (A ₁₁₄₄) normalized to the intensity of the C–O stretching band at 1094 cm⁻¹ (A ₁₀₉₄) in IR spectra of PVA films and the degree of crystallinity (α) of these films measured by an x-ray diffraction method were investigated. It was found that α and A ₁₁₄₄/A ₁₀₉₄ were related by the linear dependence α (%) = a + b(A ₁₁₄₄/A ₁₀₉₄) with correlation coefficient 0.999 for α values in the range 18–60%.     

The analysis of π− mesons produced in nucleus-nucleus collisions at a momentum of 4.5 GeV/c nucleon in light front variables

The light front analysis of π⁻ mesons in He(Li,C), C-Ne, C-Cu and O-Pb collisions is carried out. The phase space of secondary pions is divided into two parts in one of which the thermal equilibrium assumption seems to be in a good agreement with the data. Corresponding temperatures T are extracted and their dependence on (A _P·A _T)^1/2 is studied. The results are compared with the predictions of the Quark-Gluon String Model (QGSM). The QGSM satisfactorily reproduces the experimental data for light and intermediate-mass nuclei. Received: 29 September 1999     

The Perturbation of the Quantum¶Calogero–Moser–Sutherland System¶and Related Results

The Hamiltonian of the trigonometric Calogero–Sutherland model coincides with a certain limit of the Hamiltonian of the elliptic Calogero–Moser model. In other words the elliptic Hamiltonian is a perturbed operator of the trigonometric one. In this article we show the essential self-adjointness of the Hamiltonian of the elliptic Calogero–Moser model and the regularity (convergence) of the perturbation for the arbitrary root system. We also show the holomorphy of the joint eigenfunctions of the commuting Hamiltonians w.r.t the variables (x ₁, …,x _N ) for the A _{N -1}-case. As a result, the algebraic calculation of the perturbation is justified. Received: 30 May 2001 / Accepted: 27 November 2001     

Formality Theorem for Hochschild Cochains via Transfer

We construct a 2-colored operad Ger _∞ which, on the one hand, extends the operad Ger _∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy algebras. We show that Tamarkin’s Ger _∞-structure on the Hochschild cochain complex C ^•(A, A) of an A _∞-algebra A extends naturally to a Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure on the pair (C ^•(A, A), A). We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer of this Ger⁺_￥{{\bf Ger}^+_{\infty}}-structure to the cohomology of the pair (C ^•(A, A), A). We show that Ger⁺_￥{{\bf Ger}^+_{\infty}} is a sub DG operad of the first sheet E ¹(SC) of the homology spectral sequence for the Fulton–MacPherson version SC of Voronov’s Swiss Cheese operad. Finally, we prove that the DG operads Ger⁺_￥{{\bf Ger}^+_{\infty}} and E ¹(SC) are non-formal.     

A Variational Principle in the Dual Pair of Reproducing Kernel Hilbert Spaces and an Application

Given a positive definite, bounded linear operator A on the Hilbert space ₀≔l ²(E), we consider a reproducing kernel Hilbert space ₊ with a reproducing kernel A(x,y). Here E is any countable set and A(x,y), x,y∊ E, is the representation of A w.r.t. the usual basis of ₀. Imposing further conditions on the operator A, we also consider another reproducing kernel Hilbert space ₋ with a kernel function B(x,y), which is the representation of the inverse of A in a sense, so that ₋⊃ ₀⊃ ₊ becomes a rigged Hilbert space. We investigate the ratios of determinants of some partial matrices of A and B. We also get a variational principle on the limit ratios of these values. We apply this relation to show the Gibbsianness of the determinantal point process (or fermion point process) defined by the operator A(I+A)⁻¹ on the set E. 2000 Mathematics Subject Classification: Primary: 46E22 Secondary: 60K35