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.     

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.     

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.     

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.     

Long-range spin correlations in a honeycomb spin model with a magnetic field

We consider the spin-1/2 model on the honeycomb lattice [A. Kitaev, Ann. Phys. 321, 2 (2006)] in the presence of a weak magnetic field h _α ? J. Such a perturbation treated in the lowest nonvanishing order over h _α leads [K.S. Tikhonov, M.V. Feigel’man, and A.Yu. Kitaev, Phys. Rev. Lett. 106, 067203 (2011)] to a powerlaw decay of irreducible spin correlations 《s ^z (t, r)s ^z (0, 0)》 ∝ h _z ² f(t, r), where f(t, r) ∝ [max(t, Jr)]^–4. We have studied the effects of the next order of perturbation in h _z and found an additional term of the order h _z ⁴ in the correlation function 《s ^z (t, r)s ^z (0, 0)》 which scales as h _z ⁴ cosγ/r ³ at Jt? r, where γ is the polar angle in the 2D plane. We demonstrate that such a contribution can be understood as a result of a perturbation of the effective Majorana Hamiltonian by the weak imaginary vector potential A _x ∝ i h _z ² .     

Many-atom interactions in the theory of higher order elastic moduli: A general theory

The total potential energy of a crystal U({r _ik }) as a function of the vectors r _ik connecting centers of equilibrium positions of the ith and kth atoms is assumed to be represented as a sum of irreducible interaction energies in clusters containing pairs, triples, and quadruples of atoms located in sites of the crystal lattice A2: U({r _ik }) ≡ Σ _N=1 ⁴ E _N ({r _ik }). The curly brackets denote the “entire set.” A complete set of invariants {I _j ({r _ik })} _N , which determine the energy of each individual cluster as a function of the vectors connecting centers of equilibrium positions of atoms in the cluster E _N ({r _ik }) ≡ E _N ({I _j ({r _ik })} _N ), is obtained from symmetry considerations. The vectors r _ik are represented in the form of an expansion in the basis of the Bravais lattice. This makes it possible to represent the invariants {I _j ({r _ik })} _N in the form of polynomials of integers multiplied by τ ₂ ^m . Here, τ₂ is one-half of the edge of the unit cell in the A2 structure and m is a constant determined by the model of interaction energy in pairs, triples, and quadruples of atoms. The model interaction potential between atoms in the form of a sum of the Lennard-Jones interaction potential and similarly constructed interaction potentials of triples and quadruples of atoms is considered as an example. Within this model, analytical expressions for second-order and third-order elastic moduli of crystals with the A2 structure are obtained.     

Magnetic-impurity states of electron in two-dimensional semiconductor structures

Electron states on an attractive center of small-radius r _c ? l (l = $\sqrt {\frac{{c\hbar }}{{eH}}} $ is the magnetic length) located in a two-dimensional structure are investigated in a uniform magnetic field H applied perpendicularly to the structure surface. The spectrum of magnetic-impurity (MI) particle states with an arbitrary moment projection on the direction H for Landau bands 0 ≤ N < l ²/r _c ² is derived in the approximation that mixing of Landau levels is weak. The dependence of the electron energy states on magnetic field, the layer thickness, and the impurity position are studied. It is shown that dimension lowering leads to a qualitatively different spectrum of MI states compared to the three-dimensional case [1]. A comparison of the obtained binding energy of the D ^? center with experimental data is performed.     

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.     

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.     

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.     

Resonant dislocation motion in NaCl crystals in the EPR scheme in the Earth’s magnetic field with pulsed pumping

Resonant dislocation motions in NaCl(Ca) crystals under the simultaneous action of the Earth’s magnetic field B _Earth (～66 μT) and a pulsed pump field $\tilde B$ of sufficient amplitude $\tilde B_m $ and certain duration τ have been detected and studied. The measured dislocation path peaks l(τ) have a maximum at τ = τ _r ≈ 0.53 μs. The resonance criterion has been found to be the ordinary EPR condition in which the g-factor is close to 2 and the optimum inverse pulse duration τ _r ^?1 is used instead of the harmonic pump field frequency ν _r . The largest peak l(τ) height is reached at mutually orthogonal dislocation (L) and magnetic field (B _Earth and $\tilde B$ ) orientations. Pulsed field rotation to the position $\tilde B$ ‖ B _Earth significantly decreases but does not “kill” the effect. For dislocations parallel to the Earth’s field (L ‖ B _Earth), the resonance almost disappears even at $\tilde B$ ⊥ B _Earth. In the optimum geometry of experiments, as the pump field amplitude $\tilde B_m $ decreases from 17.6 to 10 μT, the path peak height l _r = l(τ _r ) decreases only by 7.5%, remaining at the level of l _r ～ 10² μm, and at a $\tilde B_m $ further fall-off to 4 μT, it rapidly decreases to background values. In this case, the relative density of mobile dislocations similarly decreases from ～90 to 40%. Possible physical mechanisms of the observed effect have been discussed.     

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.

     

Nonlinear evolution of the axisymmetric nuclear surface

We consider a uniformly charged incompressible nuclear liquid bounded by a closed surface. It is shown that the evolution of an axisymmetric surface Г(r, t) ≡ σ ? ∑(z, t) = 0, r = (σ, φ, z) can be approximately reduced to the motion of a curve in the (σ, z) plane. A nonlinear integro-diffrerential equation for the contour Σ (z, t) is derived. The contour Σ (z, t) and the local curvature are found to be a direct correspondence, which makes it possible to use methods of differential geometry to analyze the evolution of an axisymmetric nuclear surface.     

Diffraction of electrons in the CubicTi5O5 superstructure of titanium monoxide

Annealed titanium monoxide TiO_1.087 has been studied by the electron diffraction method. A cubic model of the Ti₅O₅ superstructure (Ti₅O₅ (Ti₉₀?₁₈O₉₀??₁₈)) of nonstoichiometric titanium monoxide Ti _x O _z has been proposed on the basis of experimental data and representations about the disorder-order transition channel. It has been shown that reflections observed on the electron diffraction pattern are identified in the space group $Pm\bar 3m$ . The period of the unit cell of the cubic Ti₅O₅ superstructure is larger than that for the B1 basic disordered structure of Ti _x O _z monoxide by a factor of 3. The disorder-order transition channel Ti _x O _z (space group $Fm\bar 3m$ )-Ti₅O₅ (space group $Pm\bar 3m$ ) includes 75 superstructure vectors of seven stars {k ₁₀}, {k ₇}, {k ₆₍₁₎}, {k ₆₍₂₎}, {k ₄₍₁₎}, {k ₄₍₂₎}, and {k ₁}. The distribution functions of Ti and O atoms over the sites of the cubic Ti₅O₅ (space group $Pm\bar 3m$ ) superstructure have been calculated.     

Two-dimensional representation of position, velocity and acceleration by PFG-NMR

A novel view on the presentation of pulsed field-gradient nuclear magnetic resonance experiments to encode position and translational displacements is given. A conventional diffusion or flow experiment employing two magnetic field gradients of effective areak ₁, andk ₂ separated by a time interval Δ can formally be expressed as a means to probek space in a two-dimensional way. While for most applications, a full coverage of the [k ₁,k ₂] space is not necessary, an experiment withk ₁ = ?k ₂ can be regarded as a sampling of the secondary diagonal in [k ₁,k ₂] space. Likewise, the main diagonal is represented by the conditionk ₁ =k ₂ and encodes position. Thus, the [r ₁,r ₂] space conjugate to [k ₁,k ₂], which is obtained by Fourier transformation, can be transferred into a position/displacement correlation plot simply by rotation of the coordinate system by an angle of 45°. While displacementR =r ₂ ?r ₁ corresponds to an average velocity? =R/Δ, an extension towards higher-order derivations such as acceleration is straightforward by modification of the pulse sequence. We discuss this new concept in a general way, treating both the magnetic field and the particle position by Taylor expansions with respect to space and time, respectively, and present examples for fluid flowing through capillary systems in the light of the suggested interpretation.     

Analyzing Power of 3He(n, n)3He Between 1.60 and 5.54 MeV

We report the measurements of the analyzing power A _y (θ) of n-³He elastic scattering with unprecedented accuracy and angular coverage at five incident neutron energies between 1.60 and 5.54 MeV. To this end, we employed the polarization-transfer reactions ³H(p, n)³He and ²H(d, n)³He at 0° for neutron generation and a recently developed high-pressure ³He gas scintillator as an active target, enabling neutron-time-of-flight and ³He recoil-energy determinations. We obtained simultaneously the neutron polarization with a ⁴He-based polarimeter, capitalizing on the well-known n-⁴He A _y (θ). Our n-³He A _y (θ) data are compared to rigorous four-nucleon calculations using high-precision nucleon–nucleon potential models. The agreement between data and calculations is fair at the lower energies and becomes less satisfactory with increasing neutron energy. However, in comparison to the pure isotriplet p-³He system in the same energy region, the agreement between measured and calculated A _y is much better for the mixed (isotriplet and isosinglet) n-³He system, indicating large and somewhat counterintuitive isospin effects. We note that the incorporation of a Δ-mediated three-nucleon force in calculations of n-³He scattering was found to affect A _y (θ) negligibly, suggesting the need for the reconsideration of fundamental interactions in resolving the four-nucleon analyzing power puzzle first established about a decade ago in p-³He scattering.     

Fourier transform microwave spectroscopy of isotopically substituted diacetylenes: rs-structure, quadrupole coupling, and anisotropic nuclear spin-spin interaction

Monodeuterated diacetylene (HCCCCD) and its ¹³C-substituted species H¹³CCCCD, HC¹³CCCD, HCC¹³CCD, and HCCC¹³CD were investigated by Fourier transform microwave spectroscopy. The D nuclear quadrupole splittings were almost completely resolved. For H¹³CCCCD hyperfine splittings caused by the anisotropic nuclear spin-spin interaction between the H and ¹³C nuclei were also observed. The analysis yielded rotational constants, centrifugal distortion constants, and the constants for the nuclear quadrupole coupling and anisotropic nuclear spin-spin interaction. The substitution structure of HCCCCD was calculated as follows: r_s(C-H) = 1.056054(39) Å, r_s(CC) = 1.208631(4) Å, r_s(C-C) = 1.374117(6) Å, r_s(CC) = 1.208116(4) Å, and r_s(C-D) = 1.056231(17) Å, in the order of the arrangement of the bonds. A rough estimate of the equilibrium structure is also presented. The eQq constant for the deuterium nucleus is 0.2061(4) MHz. The anisotropic ¹³C-H spin-spin interaction constant was experimentally determined for the first time as b = −29.2(15) kHz, which is defined as the coefficient of (3I_2zI_3z − I₂ · I₃), where I₂ and I₃ denote the H and ¹³C nuclear spins, respectively, and I_2z and I_3z their components along the molecular axis. The observed b constant is not accounted for by the direct magnetic dipole-dipole interaction only, suggesting a significant contribution from indirect anisotropic interaction.     

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.     

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.