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.     

Screening of charge in a semiinfinite electron gas

Within linear response and the self-consistent field approximation an equation for the screening of a chargee ^iwt δ(r?r ₀),r ₀=(0, 0,z ₀) by an electrongas confined to the half-spacez>0 is derived. From this 3 cases are discussed: 1. Application to a homogeneous electron gas bounded by an infinite potential. 2. Thomas-Fermi approximation. 3. Image potential approximation.     

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.     

Photoionisation of atoms and Möller operators

The motion of an hydrogenoïd atom in a laser field is usually given by the time-dependent hamiltonian H(t)=[p?A(t)]²/2+V(r) where V(r) is the atomic potential whileA(t) is to be connected with the laser field. The existence and unicity for the Cauchy problem of the solutions of the corresponding Schrödinger equation are established under mild conditions onA(t) and V(r). The existence of Möller operators is investigated in two cases, namely, when the laser field is a function of time only and when it vanishes asymptotically in time. Special attention is paid for the Coulomb case for which a “distorted” Möller operator is derived. Finally, when the laser field vanishes ast→∞, the photoionisation probability is properly defined by means of the Möller operator $$\Omega (H_{At} ,H) = s - \mathop {\lim }\limits_{t \to \infty } U_{At} (t)^{ - 1} U(t)$$ , whereU(t) is the evolution operator for the system whileU _Att (t) is the evolution operator for the atom.     

On the Maximal Excess Charge of the Chandrasekhar–Coulomb Hamiltonian in Two Dimension

We show that for the straightforward quantized relativistic Coulomb Hamiltonian of a two-dimensional atom – or the corresponding magnetic quantum dot – the maximal number of electrons does not exceed twice the nuclear charge. The result is then generalized to the presence of external magnetic fields and atomic Hamiltonians. This is based on the positivity of $$|{\bf x}| T({\bf p}) + T({\bf p} ) |{\bf x}|$$ which – in two dimensions – is false for the non-relativistic case T(p) = p ²/2, but is proven in this paper for T(p) = |p|, i.e., the ultra-relativistic kinetic energy.     

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.     

Pair correlations in a bidisperse ferrofluid in an external magnetic field: theory and computer simulations

The pair distribution function g(r) for a ferrofluid modeled by a bidisperse system of dipolar hard spheres is calculated. The influence of an external uniform magnetic field and polydispersity on g(r) and the related structure factor is studied. The calculation is performed by diagrammatic expansion methods within the thermodynamic perturbation theory in terms of the particle number density and the interparticle dipole-dipole interaction strength. Analytical expressions are provided for the pair distribution function to within the first order in number density and the second order in dipole-dipole interaction strength. The constructed theory is compared with the results of computer (Monte Carlo) simulations to determine the range of its validity. The scattering structure factor is determined using the Fourier transform of the pair correlation function g(r) ? 1. The influence of the granulometric composition and magnetic field strength on the height and position of the first peak of the structure factor that is most amenable to an experimental study is analyzed. The data obtained can serve as a basis for interpreting the experimental small-angle neutron scattering results and determining the regularities in the behavior of the structure factor, its dependence on the fractional composition of a ferrofluid, interparticle correlations, and external magnetic field.     

First-order phase transition from an antiferromagnetic ferroelectric to a cycloidal multiferroic with weak ferromagnetism during the joint action of applied magnetic and electric fields

The thermodynamics of the phase transition in a perovskite-like multiferroic, in which an antiferromagnetic ferroelectric transforms into a new magnetic state where a spiral spin structure and weak ferromagnetism can coexist in applied magnetic field H, is described. This state forms as a result of a first-order phase transition at a certain temperature (below Néel temperature T _N ), where a helicoidal magnetic structure appears due to the Dzyaloshinskii-Moriya effect. In this case, the axes of electric polarization and the helicoid of magnetic moments are mutually perpendicular and lie in the ab plane, which is normal to principal axis c. Additional electric polarization p, which decreases the total polarization of the ferroelectric P, appears in the ab plane. The effect of applied magnetic and electric fields on the properties of a multiferroic with a helicoidal magnetic structure is described. An alternating electric field is shown to cause a field-linear change in magnetic moment m, whose sign is opposite to the sign of the change of electric field E. The detected hysteretic phenomena that determine the temperature ranges of overheating and supercooling of each phase are explained. A comparison with the experimental data is performed.     

Monopole, half-quantum vortex, and nexus in chiral superfluids and superconductors

Two exotic objects are still not identified experimentally in chiral superfluids and superconductors. These are the half-quantum vortex, which plays the part of the Alice string in relativistic theories [A. S. Schwarz, Nucl. Phys. B 208, 141 (1982)], and the hedgehog in the Î field, which is the counterpart of the Dirac magnetic monopole. These two objects of different dimensionality are topologically connected. They form a combined object which is called a nexus [John M. Cornwall, hep-th/9911125; Phys. Rev. D 59, 125015 (1999); Phys. Rev. D 58, 105028 (1998)] or center monopole [N. N. Chernodub, M. I. Polikarpov, A. I. Veselov and M. A. Zubkov, Nucl. Phys. Proc. Suppl. 73, 575 (1999)] in relativistic theories. Such a combination will permit the observation of half-quantum vortices and monopoles in several realistic geometries.     

On the number of negative eigenvalues for a Schrödinger operator with magnetic field

We consider the Schrödinger operator with magnetic field $$H = \sum\limits_{j = 1}^n {\left( {\frac{1}{i}\frac{\partial }{{\partial x_j }} - a_j } \right)^2 + Vin\mathbb{R}^n .} $$ Under certain conditions on the magnetic fieldB=curla, we generalize the Fefferman—Phong estimates (Bull. A. M. S.9, 129–206 (1983)) on the number of negative eigenvalues for ?Δ+V to the operatorH. Upper and lower bounds are established. Our estimates incorporate the contribution from the magnetic field. The conditions onB in particular are satisfied if the magnetic potentialsa _j (x) are polynomials.     

Synthesis and Spectroscopy of Novel Branched Fluorescent Dyes Containing Benzophenone Parts and the Possibility as Fluorescence Probes

This paper describes a new fluorescent family of branched dyes containing benzophenone unit including 4-N, N-diphenylamino-4??-phenacyl-stilbene (C1), 4,4??-di(4-benzoylphenylethylene)yl-triphenylamine (C2) and 4,4??,4??-tri(4-benzoylphenylethylene)yl-triphenylamine (C3). Benzophenone part is coupled with core through C?CC double bond. The chemical structures of the derivatives are characterized with ¹H and ¹³C nuclear magnetic resonance and elemental analysis. Strong ?ШC?? stacking interactions are discovered with the analysis of the X-ray crystallographic data of C1. The absorption maxima and emission maxima of the derivatives exhibit gradual bathochromic shift from C1 to C3. The optical density of C1, C2 and C3 are shown to be related to the number of branches. The changes of dipole moments between the excited and ground states for C1, C2 and C3 were estimated to be 4.356, 8.091 and 8.479 Derby, respectively by Lippert equation, confirming that the internal charge transfer (ICT) dominates the process of excited singlet state. The possibility as fluorescence probes of the derivatives on the estimation of what region of micelles interacting with samples was evaluated.     

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.     

Phase diagram of a surface superconductor in parallel magnetic field

The universal phase diagram of a 2D surface superconductor with generic Rashba interaction in a parallel magnetic field is found. In addition to the uniform BCS state, we find two inhomogeneous superconductive states, the stripe phase with Δ (r) ∝ cos(Qr) at high magnetic fields, and a new “helical” phase with Δ(r) ∝ exp(iQr) which intervenes between the BCS state and stripe phase at an intermediate magnetic field and temperature. We prove that the ground state for helical phase carries no current.     

Mössbauer absorption by soft ferromagnets in radio-frequency magnetic field

The simultaneous influence of periodical magnetic field reversals at the nucleus between the values ±h ₀ and of magnetostrictive vibrations on the shape of the Mössbauer absorption spectrum is analyzed. The effect of a constant external magnetic field is taken into account by assuming unequal durations of the states ?h ₀ and +h ₀. It is shown that such asymmetric reversals of the magnetic field lead to splitting of the absorption lines into Zeeman patterns corresponding to the time-averaged magnetic field h ₀ R, where R is the asymmetry parameter of the reversals. The calculations agree well with experiment.     

Sum rules for the bound-free transition form factors in hydrogenlike atoms

The product of two bound-free transition form factors of the type 〈k¦exp(i q·r)¦nlm〉 is analytically summed-up over all the degenerate stateslm. Using the genuine Coulomb wave 〈r¦k〉, together with the hydrogenlike wavefunction 〈r¦nlm〉, exact analytical expressions are derived for the sum rule. The results are conveniently expressed in terms of the finite linear combination of easily generated Appell and Lauricella hypergeometric polynomials of two and three variables. This highly desirable sum rule is most frequently required in broad applications within the distorted wave theory of particle-atom scattering.     

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.     

Über eine Näherung für Gitterelektronen in äußeren Feldern

The Hamilton operator of an electron in a periodic lattice potential under influence of external electric and magnetic fields with potentialsV(r) andA(r) resp. is often replaced by an approximate operatorW ⁰ (?i?+A(r))+V(r) for one single energy bandW ⁰(k) which means a renormalization of the kinetic energy by the lattice. The validity of this replacement is examined and the magnitude of its error is roughly estimated. Neglecting other bands one obtains an error term proportional to the derivative of the electric field strengthF, if one takes a suitable position of the “raster” of the replacement operator, and to the square of the magnetic field strengthB resp. The decoupling from the other energy bands leads to error terms proportionalF ² andB ² resp. which however in the general case increase rapidly in the vicinity of overlapping energy bands.     

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.     

Specific features of the thermal electromotive force in Bi quantum wires in transverse magnetic and electric fields

The thermal electromotive force (emf) in Bi quantum wires has been calculated in the model of potential in the form of a paraboloid of revolution in a uniform magnetic field H, which is normal to the axis of the studied nanostructure, and in a direct-current (dc) electric field E ‖ H. It has been shown that, with an increase in E, the thermal emf α _xx is described by a nonmonotonic function at different values of H. A physical interpretation of this behavior of α _xx as a function of E is proposed with account for the interaction between carriers and the rough surface of the nanowire.