Magnetic transformations in the Sr0.78Y0.22Co1 ? xFexO3 ? γ system with a perovskite structure

The Sr_0.78Y_0.22Co_{1 − x} Fe _x O_{3 − γ} cobaltite system is studied by neutron and X-ray diffraction and by measuring the magnetization and elastic properties. The crystal structure of the composition with x = 0 is described in terms of the monoclinic space group A2/m with the unit cell 2 a _p × 4a _p × 2 a _p , and the crystal structure of the composition with x = 0.12 is orthorhombic (space group Imma). The crystal structure of these compounds is characterized by alternating CoO₆ and CoO_4.5 layers. The magnetic structure is a G-type antiferromagnetic structure. The magnetic moments in the CoO₆ layers are significantly higher than those in the CoO_4.5 layers. In the compound with x = 0, magnetic measurements reveal a small ferromagnetic component (0.2 μ_B/Co) below T _N ≈ 350 K. Near T _N, a phase transformation occurs and lowers the crystallographic symmetry. Doping with iron ions suppresses the ferromagnetic component and sharply increases the average magnetic moments in both layers. The spontaneous magnetization is assumed to result from noncollinear magnetic moments, which can be caused by the competition of exchange interactions of different signs and magnetic anisotropy. The compounds with x = 0.5 and 1.0 are cubic (space group Pm3m) and are characterized by a G-type collinear antiferromagnetic structure. Original Russian Text ? I.O. Troyanchuk, D.V. Karpinsky, V.M. Dobryanskiĭ, A.N. Chobot, G.M. Chobot, A.P. Sazonov, 2009, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 135, No. 3, pp. 490–497.     

The Probability of Entanglement

We show that states on tensor products of matrix algebras whose ranks are relatively small are almost surely entangled, but that states of maximum rank are not. More precisely, let and be full matrix algebras with m ≥  n, fix an arbitrary state ω of N, and let E(ω) be the set of all states of that extend ω. The space E(ω) contains states of rank r for every r = 1, 2, . . . , m · rank ω, and it has a filtration into compact subspaces

On the ground state energy of a two-dimensional electron fluid

A new theory of the ground state energy of a two-dimensional electron fluid is presented. It is shown that the ring diagram contribution changes its analytical behavior atr _s =2^1/2, wherer _s is the usual density parameter defined by r_S = 1/a ₀( n)^1/2,a ₀ being the Bohr radius andn is the electron density. For smallr _s , a high density series is obtained in agreement with the previous calculation. For larger _s , a hitherto unknown low density series is obtained. In the low density region, the first order exchange energy is completely cancelled out by a term from the ring contribution so that the ground state energy decreases in proportion tor _s ^–2/3 , followed byr _s ^/–4/3 and higher order terms. The energy is found to be minimum atr _s=1.4757, the minimum value being –0.481915 Rydbergs.     

Large Deviations for the Fermion Point Process Associated with the Exponential Kernel

For the fermion point process on the whole complex plane associated with the exponential kernel , we show the central limit theorem for the random variable ξ(D _r , the number of points inside the ball D _r of radius r, as r → ∞ and we establish the large deviation principle for the random variables {r ⁻²ξ (D _r ), r > 0}.     

A variational problem for a system of magnetic monopoles joined by Abrikosov vortices

An action functional, related to the Higgs model to field theory, depending on a complex scalar field and aU(1) connection is defined. The complex scalar field is a section of a line bundle associated to a principalU(1)-bundle with base space ³\{x ₁,...,x _n }. The pointsx ₁,...,x _n are the positions ofn magnetic monopoles of magnetic chargesm ₁,...,m _n, with . The existence of minimizers of the action functional is proven using direct methods of the calculus of variation. Regularity and decay properties of the minimizers are obtained. By constructing explicit comparison field configurations, we establish accurate upper and lower bounds for the action of the minimizers in a variety of special situations, e.g.n=2 andm ₁=–m ₂.     

Distribution of Particles Which Produces a “Smart” Material

If A _q(β, α, k) is the scattering amplitude, corresponding to a potential , where D⊂ℝ³ is a bounded domain, and is the incident plane wave, then we call the radiation pattern the function , where the unit vector α, the incident direction, is fixed, β is the unit vector in the direction of the scattered wave, and k>0, the wavenumber, is fixed. It is shown that any function , where S ² is the unit sphere in ℝ³, can be approximated with any desired accuracy by a radiation pattern: , where ∊ >0 is an arbitrary small fixed number. The potential q, corresponding to A(β), depends on f and ∊, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles D _m⊂ D, 1≤ m≤ M, distributed in an a priori given bounded domain D⊂ℝ³. The geometrical shape of a small particle D _m is arbitrary, the boundary S _m of D _m is Lipschitz uniformly with respect to m. The wave number k and the direction α of the incident upon D plane wave are fixed. It is shown that a suitable distribution of the above particles in D can produce the scattering amplitude , at a fixed k>0, arbitrarily close in the norm of L ²(S ²× S ²) to an arbitrary given scattering amplitude f(α ', α), corresponding to a real-valued potential q∊ L ²(D), i.e., corresponding to an arbitrary refraction coefficient in D. MSC: 35J05, 35J10, 70F10, 74J25, 81U40, 81V05, 35R30. PACS: 03.04.Kf.     

Superconducting states of the cylinder with a single vortex in magnetic field according to the Ginzburg-Landau theory

Self-consistent solutions of the nonlinear Ginzburg-Landau (GL) equations are investigated numerically for a superconducting (SC) cylinder, placed in an axial magnetic field, with a single vortex on the axis (m=1). Two modes, which show the original state of the cylinder, SC or normal (s ₀ andn ₀), are studied. The field increase (FI) and the field decrease (FD) regimes are studied. The critical fields destroying the SC state withm=1 are found in both regimes. It is shown that in a cylinder of radiusR and GL-parameter ϰ, there exist a number of solutions depending only on the radial co-ordinater corresponding to different states such as M,e, d, p,i, n, ,n ^*, and the state diagram on the plane of the variables (ϰ,R) is described. The critical fields corresponding to intrastate transitions and the onset of hysteresis are obtained. The critical fieldH ₀(R) dividing the paramagnetic and diamagnetic states of the cylinder withm=1 is determined. The limiting fields of supercooling or superheating of the normal state at which the restoration of the SC state occurs are established. It is shown, that (in both casesm=1,0) there exist two critical parameters, and , which divide bulk SC into three groups (with and ), in accordance with the behavior in a magnetic field. The parameters and mark the boundary for the existence of a supercooled normal -state in FD-regime and a superheated SC M-state in FI-regime respectively. It is shown, that the value , which was claimed in a number of papers as related to type-I superconductors, is illusory. We regret to inform that Professor Gely Zharkov passed away on 9th July 2004.     

Magnetic relaxation in a three-dimensional ferromagnet with weak quenched random-exchange disorder

Isothermal remanent magnetization decay,M _r(t), and ‘in-field’ growth of zero-field-cooled magnetization,M _ZFC(t), with time have been measured over four decades in time at temperatures ranging from 0.25T _c to 1.25T _c (whereT _c is the Curie temperature, determined previously for the same sample from static critical phenomena measurements) for a nearly ordered intermetallic compound Ni₃Al, which is an experimental realization of a three-dimensional (d = 3) ferromagnet with weak quenched random-exchange disorder. None of the functional forms ofM _r(t) predicted by the existing phenomenological models of relaxation dynamics in spin systems with quenched randomness, but only the expressions and closely reproduce such data in the present case. The most striking features of magnetic relaxation in the system in question are as follows: Aging effects are absent in bothM _r t andM _ZFC(t) at all temperatures in the temperature range covered in the present experiments. A cross-over in equilibrium dynamics from the one, characteristic of a pured = 3 ferromagnet with complete atomic ordering and prevalent at temperatures away from T_c, to that, typical of ad = 3 random-exchange ferromagnet, occurs asT → T_c. The relaxation times τ₁(T)(τ₁ ^′(T)) and τ₂(T)(τ₂ ^′(T)) exhibit logarithmic divergence at critical temperatures and ; and both increase with the external magnetic field strength,H, such that at any given field value, . The exponent characterizing the logarithmic divergence in τ ₁ ^′ (T) and τ ₂ ^′ T possesses a field-independent value of ≃16 for both relaxation times. Of all the available theoretical models, the droplet fluctuation model alone provides a qualitative explanation for some aspects of the present magnetic relaxation data     

Local exponential estimates for h-pseudodifferential operators and tunneling for Schrödinger, Dirac, and square root Klein-Gordon operators

We consider the class of matrix h-pseudodifferential operators Op _h (a) with symbols a = (a _ij ) _i,j=1 ^N , where the coefficients a _ij ∈ C ^∞(? _x ⁿ × ? _ξ ⁿ ? C(0, 1] satisfy the estimates |? _x ^β g6 _ξ ^α α _ij (x, ξ, h)| ? C _αβ 〈ξ〉 ^m and 〈ξ〉 = (1 + |ξ|²)^1/2 for every multi-indices α, β. We also assume that a _ij (x, ξ) is analytically continued with respect to ξ to a tube domain ? ⁿ + i $ \mathcal{B} We consider the class of matrix h-pseudodifferential operators Op _h (a) with symbols a = (a _ij ) _i,j=1^N, where the coefficients a _ij ∈ C ^∞(ℝ _x ⁿ × ℝ _ξ ⁿ ⊗ C(0, 1] satisfy the estimates |ϖ _x ^β g6 _ξ ^α α _ij (x, ξ, h)| ⩽ C _αβ 〈ξ〉 ^m and 〈ξ〉 = (1 + |ξ|²)^1/2 for every multi-indices α, β. We also assume that a _ij (x, ξ) is analytically continued with respect to ξ to a tube domain ℝ ⁿ + i , where is a bounded domain in ℝ ⁿ containing the origin. The main results of the paper are the local estimates for solutions of h-pseudodifferential equations. Let H _h ^s (ℝ ⁿ , ℂ ^N ) be the space of distributions with values in ℂ ^N which is equipped with the norm , let Ω ⊂ ℝ ⁿ be a bounded open set, let v ∈ C ^∞(ℝ ⁿ ), let ▿v(x) ∈ for any x ∈ Ω, and let . Let u _h (∈ H _h ^s (ℝ ⁿ ,‒ ^N )) be a solution of the equation Op _h (α)u = 0. In this case, for every ϕ ∈ C ₀^∞ (Ω) such that ϕ(x) = 1 on Supp v and for a sufficiently small h ₀ > 0, there exists a constant C > 0 such that the following estimate holds for every h ∈ (0, h ₀]:

((1))

We apply estimate (1) to local tunnel exponential estimates for the behavior as h → 0 of the eigenfunctions of matrix Schr?dinger, Dirac, and square-root Klein-Gordon operators. To the memory of Professor V. A. Borovikov     

Spectral Measures of Small Index Principal Graphs

The principal graph X of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If Δ is the adjacency matrix of X we consider the equation Δ = U + U ⁻¹. When X has square norm ≤ 4 the spectral measure of U can be averaged by using the map u→ u ⁻¹, and we get a probability measure on the unit circle which does not depend on U. We find explicit formulae for this measure for the principal graphs of subfactors with index ≤ 4, the (extended) Coxeter-Dynkin graphs of type A, D and E. The moment generating function of is closely related to Jones’ Θ-series.D.B. was supported by NSF under Grant No. DMS-0301173.     

On Local Borg–Marchenko Uniqueness Results

We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl–Titchmarsh m-functions, m _j (z), of two Schr?dinger operators , j≡ 1,2 in L ²((0,R)), 0<R≤∞, are exponentially close, that is, , 0<a<R, then q ₁≡q ₂ a.e. on [0,a]. The result applies to any boundary conditions at x≡ 0 and x≡R and should be considered a local version of the celebrated Borg–Marchenko uniqueness result (which is quickly recovered as a corollary to our proof). Moreover, we extend the local uniqueness result to matrix-valued Schr?dinger operators. Received: 22 October 1999 / Accepted: 2 November 1999     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

The Relativistic non-abelian Chern-Simons Equations

We study ther xr system of nonlinear elliptic equations ,a=1,2,...,r,x∈R ², where λ τ 0 is a constant parameter,K = (K_ab) is the Cartan matrix of a semi-simple Lie algebra, and β_p is the Dirac measure concentrated atp R ². This system of equations arises in the relativistic non-Abelian Chern-Simons theory and may be viewed as a nonintegrable deformation of the integrable Toda system. We establish the existence of a class of solutions known as topological multivortices. The crucial step in our method is the use of the decomposition theorem of Cholesky for positive definite matrices so that a variational principle can be formulated. Research supported in part by the National Science Foundation under grant DMS-9596041     

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body Gaussoids that respectively depend on six (r ₁₂, r ₁₃, r ₁₄, r ₂₃, r ₂₄, r ₃₄) and ten (r ₁₂, r ₁₃, r ₁₄, r ₁₅, r ₂₃, r ₂₄, r ₂₅, r ₃₄, r ₃₅ and r ₄₅) relative coordinates. The approach allows operating with the more than one electron spin functions. In particular, the trial wave functions for the ¹ S states in four-electron atomic systems include the two independent spin functions χ₁ = αβαβ + βαβα − βααβ − αββα and χ₂ = 2ααββ + 2ββαα − βααβ − αββα − βαβα − αβαβ. We also discuss the construction of variational wave functions for the excited 2³ S states in four- electron atomic systems.     

Near-threshold production of a0(980) mesons in πN and NN collisions and a0-f0 mixing

We consider near-threshold a ₀(980)-meson production in πN and NN collisions. An effective Lagrangian approach with one-pion exchange is applied to analyze different contributions to the cross section for different isospin channels. The Reggeon exchange mechanism is also evaluated for comparison. The results from πN reactions are used to calculate the contribution of the a ₀ meson to the cross sections and invariant mass distributions of the reactions and pp → ppK ⁺ K ⁻. It is found that the experimental observation of a ₀ ⁺ mesons in the reaction is much more promising than the observation of a ₀ ⁰ mesons in the reaction pp → ppK ⁺ K ⁻. Effects of isospin violation in the reactions pN → da ₀, pd → ³He(³H)a ₀, and dd → ⁴Hea ₀, which are induced by a ₀(980)-f ₀(980) mixing, are also analyzed. From Yadernaya Fizika, Vol. 66, No. 1, 2003, pp. 155–174. Original English Text Copyright ? 2003 by Kondratyuk, Bratkovskaya, Grishina, Büscher, Cassing, Str?her. This article was submitted by the authors in English.     

Deexcitation of K π = 0 2+ , 0 3+ , and 21/+ levels by M 1 transitions in nonspherical even-even nuclei

The signs of the experimental values of the multipole-mixture parameters δ are compared with the signs of ℛ = Σa _i μ _i for (2⁺0₂−2⁺0₁) and (2⁺0₃−2⁺0₁) transitions and with the signs of = Σa _i [(μ _i + μ _kν ) or (μ _kπ − 1/2)] for (2⁺2₁−2⁺0₁) transitions in nonspherical even-even nuclei, where a _i is the contribution of the ith pair of quasiparticles to the wave function for 2⁺0₂, 2⁺0₃, and 2⁺2₁ single-phonon states according to the quasiparticle-phonon model and μ is the magnetic moment for the corresponding Nilsson state. Original Russian Text ? A.M. Demidov, L.I. Govor, V.A. Kurkin, I.V. Mikhailov, 2009, published in Yadernaya Fizika, 2009, Vol. 72, No. 2, pp. 228–235.     

Nuclear magnetic moment of 57Cu ground state

The nuclear magnetic moment of the ground state of ⁵⁷Cu(I^π = 3/2^-, T_1/2 = 196.3 ms) has been measured to be |μ(⁵⁷Cu)| = (2.00 ±0.05) μ_N using the β-NMR technique. Together with the known magnetic moment of the mirror partner ⁵⁷Ni, the spin expectation value was extracted as = -0.78 ± 0.13. Discrepancy between present results and shell model calculations in the full fp shell implies significant shell breaking at ⁵⁶Ni with the neutron number N = 28.     

CP-violation in B → π+π- and the unitarity triangle

We analyze the extraction of weak phases from CP-violation in B → π⁺π^- decays. We propose to determine the unitarity triangle by combining the information on mixing-induced CP-violation in B → π⁺π^-, S, with the precision observable sin2β obtained from the CP-asymmetry in B → ψK_S. It is then possible to write down exact analytical expressions for and as simple functions of the observables S and sin2β and of the penguin parameters r and ϕ. As an application clean lower bounds on and can be derived as functions of S and sin2β, essentially without hadronic uncertainty. Computing r and ϕ within QCD factorization yields precise determinations of and since the dependence on r and ϕ is rather weak. It is emphasized that the sensitivity to the phase ϕ enters only at second order and is extremely small for moderate values of this phase, predicted in the heavy-quark limit. Transparent analytical formulas are further given and discussed for the parameter C of direct CP-violation in B → π⁺π^-. Predictions and uncertainties for r and ϕ in QCD factorization are examined in detail. It is pointed out that a simultaneous expansion in 1/m_b and 1/N leads to interesting simplifications. At first order infrared divergences are absent, while the most important effects are retained. Independent experimental tests of the factorization framework are briefly discussed. Received: 16 April 2005, Revised: 6 August 2005, Published online: 21 November 2005 PACS: 11.30.Er, 12.15.Hh, 13.25.Hw     

Small representations of quantum affine algebras

We characterize the finite-dimensional representations of the quantum affine algebra U _q ( _n+1) (whereq ^× is not a root of unity) which are irreducible as representations of U _q (sl _n+1). We call such representations small. In 1986, Jimbo defined a family of homomorphismsev _a from U _q (sl _n+1) to (an enlargement of) U _q (sl_,n+1), depending on a parametera ^·. A second family,ev ^a can be obtained by a small modification of Jimbo's formulas. We show that every small representation of U _q ( _n+1) is obtained by pulling back an irreducible representation of U _q (sl _n+1) byev _a orev ^a for somea ^·.