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.     

Theoretical studies of ground and excited states in a series of Zn(II) complexes,derived from thiourea and thiosemicarbazide

Theoretical studies for a series of mono- and binuclear zinc (II) complexes Zn(CH₃COO)₂(H₂L)₂ [H₂L = N-2-propenyl-N ^′-2-pyridinylthiourea] (A), Zn₂(CH₃COO)₂(H₃L-a)₂ [H₃L-a = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-phenylcarbothioamide] (B), and Zn(H₃L-b)₂ [H₃L-b = 2-[(2-hydroxy phenyl)methylene]hydrazine-N-(2-propenyl)carbothioamide] (C) have been performed on their structures and excited-state absorption spectra. The singlet ground-state geometries are fully optimised at three DFT levels, i.e., B3LYP, B3PW91, and M06. Different geometries, i.e., strongly distorted tetrahedral coordination environment in complex A, distorted square-pyramidal environment in complex B, and irregular octahedral mode in complex C are identified. Consequently, the spectroscopic properties are calculated by means of time-dependent density functional theory (TDDFT) with the Polarisable Continuum Model (PCM) based on the optimised gas-phase geometries. Three absorption peaks are identified for every complex, which are in good agreement with the experimental ones. For complex A, all three absorption peaks centered at 280.33 nm, 268.09 nm, and 250.87 nm, respectively, are ascribed to the (p,π) → π* transition with a mixed intraligand charge-transfer (ILCT)/ligand-ligand charge-transfer (LLCT) character. The composition of frontier orbitals involved in major absorption bands for the three complexes shows similarities, which results in the almost homologous transition attributions and characteristics. A remarkable bathochromic shift in the lowest-lying absorption band is observed for complexes B and C as compared with complex A, which is attributed to the decreased H (HOMO)-L (LUMO) energy gap (ΔE |HOMO-LUMO|) by the formation of conjugate metallocycles in complexes B and C.     

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.     

Quantum Bundle Description of Quantum Projective Spaces

We realise Heckenberger and Kolb??s canonical calculus on quantum projective (N ? 1)-space C _q [C p ^N?1] as the restriction of a distinguished quotient of the standard bicovariant calculus for the quantum special unitary group C _q [SU _N ]. We introduce a calculus on the quantum sphere C _q [S ^2N?1] in the same way. With respect to these choices of calculi, we present C _q [C p ^N?1] as the base space of two different quantum principal bundles, one with total space C _q [SU _N ], and the other with total space C _q [S ^2N?1]. We go on to give C _q [C p ^N?1] the structure of a quantum framed manifold. More specifically, we describe the module of one-forms of Heckenberger and Kolb??s calculus as an associated vector bundle to the principal bundle with total space C _q [SU _N ]. Finally, we construct strong connections for both bundles.     

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.     

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.     

Theory of spatial dispersion of dielectric and magnetic constants in magnetic uniaxial gyrotropic crystals

The theory of spatial dispersion of dielectric and magnetic constants of magnetic uniaxial crystals based on generalized Maxwell’s equations D = ε?E = (ε + inγ E = ?ns ^× H and B = μ?H = (μ + inδ)H = ns ^× E with spatial dispersion parameters γ and δ is considered. Generalized Fresnel’s and polarization equations for the obtained vectors E, D, H, and B are analyzed for the wave normal direction s ⊥ C (where C is the optic axis of a crystal). The possibility of the existence of a third natural wave in a crystal is proved.     

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.

     

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.     

Power Series Representations for Bosonic Effective Actions

We develop a power series representation and estimates for an effective action of the form $$\ln\frac{\int e^{f(\phi,\psi)}d\mu(\phi)}{\int e^{f(\phi,0)}d\mu(\phi)}$$ Here, f(φ,ψ) is an analytic function of the real fields φ(x),ψ(x) indexed by x in a finite set X, and d μ(φ) is a compactly supported product measure. Such effective actions occur in the small field region for a renormalization group analysis. The customary way to analyze them is a cluster expansion, possibly preceded by a decoupling expansion. Using methods similar to a polymer expansion, we estimate the power series of the effective action without introducing an artificial decomposition of the underlying space into boxes.     

A Pulsed EPR and DFT Investigation of the Stabilization of Coordinated Phenoxyl Radicals in a Series of Cobalt Schiff-Base Complexes

We recently demonstrated how the aerobic addition of acetic acid to N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexane-diamino Co^II, [Co(1)], leads to the formation of an unusual coordinated Co^III-phenoxyl radical. In this work, some of the structural aspects associated with the Schiff-base-derived ligand (1) that are crucial for the acid-mediated formation of the phenoxyl radical are investigated. For comparison with [Co(1)], we therefore studied the influence of acetic acid on two complexes: (1) the N,N′-bis(3,5-di-tert-butylsalicylidene)-1,2-ethane-diamino Co^II complex, [Co(2)], that lacks the cyclohexyl group of [Co(1)], and (2) the N′-disalicylidene-ethylenediamine Co^II salen complex, [Co(3)], that lacks both the tertiary butyl groups and the cyclohexyl groups. It is shown that the cyclohexyl group of [Co(1)] is not involved in the formation or stabilization of the phenoxyl radical, whereas the tertiary butyl groups of [Co(1)] play a crucial role. In addition, the characteristics of the phenoxyl radical, formed after aerobic addition of acetic acid to [Co(2)], are analyzed in detail by pulsed electron paramagnetic resonance, in combination with isotopic labeling. The experimental data are compared to density functional theory computations and to previous data on the acid-mediated phenoxyl radical of [Co(1)].     

Spatial representation of groups of automorphisms of von Neumann algebras with properly infinite commutant

Theorem. Let a topological groupG be represented (a→φ _a ) by *-automorphisms of a von Neumann algebraR acting on a separable Hilbert spaceH. Suppose that

1. G is locally compact and separable,
2. R′ is properly infinite,
3. for anyT∈R,x,y∈H the function

$$a \to \left\langle {\phi _a (T)x,y} \right\rangle _H $$ is measurable onG. Then there exists a strongly continuous unitary representation ofG onH,a→U _a , such that forT∈R,a∈G, $$\phi _\alpha (T) = U_a TU_a *.$$ .     

Analytische Näherung für elastische Wellen in anisotropen kubischen Kristallen

It is shown that the frequencies ω_α(k) and the polarisation vectorse _α(k) (α=1, 2, 3) of the elastic waves in anisotropic cubic crystals can be described exactly as Taylor series in the parameter \(\delta = \frac{{c_{11} - c_{12} - 2c_{44} }}{{c_{12} + c_{44} }}\) for all wave number vectorsk. As the expansion functions of these series include no elastic constants, δ is taken as the proper anisotropy parameter. The series are converging very fast for almost all substances and may be broken off after the third expansion term.     

Dynamic model for alpha particle emission during fission

We investigate the motion of anα-particle in the average time depencent potentialV(R _α ,t) of a fissioning nucleus. The emission process is treated quantum mechanically via a numerical solution of the one-body Schroedinger equation withV(R _α ,t). This solution yields the distribution of initial conditions for classical trajectories describing theα-particles outside the Coulomb barrier. The time and shape dependence ofV(R _α,t) is shown to have significant influence on the observable angle and energy distribution of theα-particles emitted during fission.     

Some exact solutions of the local induction equation for the motion of a vortex in a Bose–Einstein condensate with a Gaussian density profile

The dynamics of a vortex filament in a Bose–Einstein condensate whose equilibrium density in the reference frame rotating at the angular velocity Ω is Gaussian with the quadratic form r·D?r has been considered. It has been shown that the equation of motion of the filament in the local-induction approximation permits a class of exact solutions in the form R(β, t) = βM(t) + N(t) of a straight vortex, where β is the longitudinal parameter and is the time. The vortex slips over the surface of an ellipsoid, which follows from the conservation laws N · D?N=C ₁ and M · D?N=C ₀=0. The equation of the evolution of the tangential vector M(t) appears to be closed and has integrals of motion M ·D?M=C ₂ and (|M| ? M· G?Ω) = C, with the matrix G? = 2(I?TrD? ? D?)^?1. Crossing of the respective isosurfaces specifies trajectories in the phase space.     

Propagation of Chaos for a Thermostated Kinetic Model

We consider a system of N point particles moving on a d-dimensional torus $\mathbb{T}^{d}$ . Each particle is subject to a uniform field E and random speed conserving collisions $\mathbf{v}_{i}\to\mathbf{v}_{i}'$ with $|\mathbf{v}_{i}|=|\mathbf{v}_{i}'|$ . This model is a variant of the Drude-Lorentz model of electrical conduction (Ashcroft and Mermin in Solid state physics. Brooks Cole, Pacific Grove, 1983). In order to avoid heating by the external field, the particles also interact with a Gaussian thermostat which keeps the total kinetic energy of the system constant. The thermostat induces a mean-field type of interaction between the particles. Here we prove that, starting from a product measure, in the limit N→∞, the one particle velocity distribution f(q,v,t) satisfies a self consistent Vlasov-Boltzmann equation, for all finite time t. This is a consequence of “propagation of chaos”, which we also prove for this model.     

Analytic Structure of Many-Body Coulombic Wave Functions

We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with \({{\bf x} = (x_{1},\dots, x_{N})\in \mathbb {R}^{3N}}\) denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x ₁ = 0 and the other electron coordinates do not coincide, and differ from 0, ψ can be represented locally as ψ(x) = ψ ⁽¹⁾(x) + |x ₁|ψ ⁽²⁾(x) with ψ ⁽¹⁾, ψ ⁽²⁾ real analytic. A similar representation holds near two-electron coalescence points. The Kustaanheimo-Stiefel transform and analytic hypoellipticity play an essential role in the proof.     

Rotation of the plane of polarization and linear birefringence of sound in hematite below the morin point

The linear antiferromagnetic birefringence of sound in hematite (α-Fe₂O₃) residing in the collinear easy-axis phase (L ‖ C ₃) below the Morin point is experimentally studied. The plane of polarization of a linearly polarized transverse acoustic wave propagating along the trigonal axis C ₃ of a hematite crystal placed in a magnetic field H applied in the basal plane (H ⊥ C ₃, 3.5 ≤ H ≤ 15 kOe) is found to rotate after a temperature-driven orientational phase transition to the easy-axis state. The angle of rotation exhibits a 180° angular dependence on the direction of the magnetic field in the basal plane and varies from zero to ～π/2. Numerical estimates suggest that the conditions necessary for rotation of the plane of polarization through appreciable angles (～π/2) can be satisfied in the easy-axis phase at orientational phase transition temperatures close to the Morin point, which actually takes place in the fields employed. The results obtained are described sufficiently well by the theory of linear antiferromagnetic birefringence of sound (E.A. Turov) and confirm its main conclusions.