Kinematic mechanism of the modulation of the spectral intensity in the spatially uniform system of Hubbard fermions

Using the exact representation of the Green’s function constructed in terms of the Hubbard operators, it has been shown that the kinematic interaction that induces the spin-fluctuation processes in the spatially uniform system of Hubbard fermions leads to significant variations in the spectral intensity A(k, ω) in the Brillouin zone. As a result, the modulation of A(k, ω) appears in the Fermi contour. The sign of the hopping integral within the first coordination sphere is determined by the contour section, where A(k, ω) decreases according to the angle-resolved photoemission spectroscopy data.     

Magnetization of optically polarized gas atoms by an optical pulse train

The properties of the density matrix and the multipole moments arising in oriented and aligned atoms with zero nuclear spin through the interaction with strong resonant ultrashort pulses with wave vector k ₀ and circular or linear polarization have been found. Calculations have been made for the time-dependent light-induced magnetization μ(t′) of a gas of pre-oriented and prealigned atoms following the passage of a weak resonant elliptically polarized pulse with frequency ω and wave vector k collinear with k ₀. It is shown that for oriented atoms, μ(t′) is an even function of the detuning from resonance, ω-ω _ba, and can be split into two terms whose directions are a consequence of symmetry and are determined by the vectors k ₀ and k as well as by the direction of rotation of the electric fields corresponding to the pulses. For aligned atoms the vector μ(t′) is collinear with k, and the first term is an even function of ω-ω _ba. However, the second term is an odd function of ω-ω _ba and reverses direction when the sign of ω-ω _ba changes, as well as when the orientation of the axes of the polarization ellipse is changed. It is shown that if a series of weak linearly polarized pulses pass through the gas, the light-induced magnetization of the oriented and aligned gas atoms can be decomposed into three factors: the first determines the direction and is a consequence of the symmetry; the second (with the dimensions of magnetic moment) depends on the characteristics of the resonant transitions; and the third is a universal function of t′ and ω-ω _ba that does not depend on the underlying characteristics of the resonant transition. These vector factors and the universal functions are in principle different for oriented and aligned atoms. Zh. éksp. Teor. Fiz. 111, 63–92 (January 1997)     

Symmetry analysis of the monoclinic Pd<Subscript>6</Subscript>B superstructure: Long- and short-range orders

A symmetry analysis of the monoclinic (space group C2/c) Pd₆B superstructure formed in the cubic (with structure B1) boron solid solution PdB _y in palladium has been performed. The formation of this superstructure occurs as a first-order phase transition via the disorder-order transition channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the monoclinic (space group C2) Pd₆B superstructure, the distribution function of boron atoms has been calculated and the interval of admissible values of long-range order parameters has been determined. It has been shown that the found transition channel is identical to the channel of the formation of the monoclinic (space group C2/c) M ₆ X superstructure; therefore, the Pd₆B superstructure can be described with the same accuracy in space group C2. The higher symmetry of the monoclinic (space group C2/c) model suggests that it more accurately describes the structure of the phase Pd₆B (Pd₆B□₅) and mutually inverse phases M ₆ X□₅ and M ₆ X ₅□ than the model with space group C2. It has been demonstrated that there are two types of the nearest environment of metal atoms with non-metal sublattice sites arranged in the first and second coordination spheres in M ₆ X□₅-type superstructures (space groups C2/c, C2, C2/m, and P3₁) and in inverse M ₆ X ₅□-type superstructures with the same space groups.     

An Extension of the HarishChandra-Itzykson-Zuber Integral

 The HarishChandra-Itzykson-Zuber integral over the unitary group U(k) (β=2) is present in numerous problems involving Hermitian random matrices. It is well known that the result is semi-classically exact. This simple result does not extend to other symmetry groups, such as the symplectic or orthogonal groups. In this article the analysis of this integral is extended first to the symplectic group Sp(k) (β=4). There the semi-classical approximation has to be corrected by a WKB expansion. It turns out that this expansion stops after a finite number of terms ; in other words the WKB approximation is corrected by a polynomial in the appropriate variables. The analysis is based upon new solutions to the heat kernel differential equation. We have also investigated arbitrary values of the parameter β, which characterizes the symmetry group. Closed formulae are derived for arbitrary β and k=3, and also for large β and arbitrary k. Received: 15 July 2002 / Accepted: 9 October 2002 Published online: 21 February 2003 RID="*" ID="*" Unité Mixte de Recherche 8549 du Centre National de la Recherche Scientifique et de l'école Normale Supérieure. Communicated by L. Takhtajan     

Monoclinic superstructure V<Subscript>14</Subscript>O<Subscript>6</Subscript> of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure.     

Monoclinic superstructure V14O6 of the tetragonal solid solution of oxygen in vanadium

The monoclinic (space group C2/m) superstructure of V₁₄O₆, which is formed in the atom-vacancy ordering of the tetragonal solid solution of oxygen in vanadium, is studied by the methods of x-ray diffraction and symmetry analysis. It has been found that the channel of the order-disorder phase transition attributed to the formation of the monoclinic suboxide V₁₄O₆ includes six superstructure vectors belonging to three non-Lifshitz stars {k ₁₋₁}, {k ₁₋₂}, and {k _1–3} of one type {k ₁}. The distribution function of the O atoms in the V₁₄O₆ monoclinic superstructure has been calculated. It has been shown that the displacements of V atoms distort the body-centered tetragonal metal sublattice, thus preparing the formation of the fcc sublattice and the transition from the suboxide V₁₄O₆ to the cubic vanadium monoxide with the B1 structure. Original Russian Text ? A.I. Gusev, D.A. Davydov, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 10, pp. 746–751.     

Bloch enhancement of electric field gradient in Fe and Cu host alloys

The Bloch enhancement factor α(k _f ) of the electric field gradient has been evaluated for the half-filledd-core Fe host metal and completely filledd-core Cu host metal in single orthogonalized plane wave (OPW) approximation. For this purpose the radially-dependent antishielding factors,γ(r) have been calculated in non-orthogonal Hartree-Fock perturbation theory (NHFPT). The results show that the contributions of antishielding to α(k _f ) from the plane wave-plane wave part and the core part of the OPW state are individually large but opposite in sign and thereby lead to partial cancellation. The net effect of antishielding on α(k _f ) is found to be − 5.6% in Fe and 14% in Cu.     

Structure of turbulent flows of incompressible fluids and the parametrization of turbulence

The structure of stationary isotropic, homogeneous turbulence in an incompressible fluid with Re ≫ 1 set into motion by a force with amplitude f ₀ and spatial and temporal time scales of r ₀ and τ ₀, respectively, is examined. It is found that, depending on the magnitude of the force that sets the fluid into motion, three fundamentally different turbulent stationary states of the fluid can develop and the dimensionless parameters responsible for transitions from one state to another, γ=f ₀ τ ₀ ² /r ₀ and Γ=γ ^4/3 Re, are determined. It is shown that for γ≪1 and Γ≪1 a Kolmogorov spectrum with E(k)∝1/k ^5/3 develops in the inertial range. During the transition to turbulent flows driven by large amplitude forces f ₀, i.e., during the transition to a regime with γ≪1 and Γ ≫ 1, a segment of the spectrum with E(k)∝1/k ² develops near the viscous range and “detaches” the Kolmogorov spectrum from the viscous range. Further increases in the amplitude f ₀ of the force, i.e., approaching the parameter range with γ≫1 and Γ≫1, causes the entire inertial range to be “occupied” by a spectrum E(k)∝1/k ², and outside the inertial range, large scale structures with a characteristic size extending to γ ^2/5 r ₀ begin to be generated. In the regime with Γ≪1, the power dissipated per unit mass of fluid is independent of the viscosity, but on going to turbulent regimes with Γ≫1, the viscous losses begin to depend on the viscosity of the fluid. The “turn-off” of viscous dissipation for Γ≫1 shows that a drag crisis can occur simply as the source power is increased, without any further conditions. With this method for the excitation of turbulence, the Loitsyanskii integral diverges for arbitrary values of γ and Γ. A physical mechanism is proposed to explain the readjustment of the spectrum of the turbulent fluctuations at different γ and Γ. These results have all been obtained neglecting intermittency. Zh. éksp. Teor. Fiz. 116, 1630–1647 (November 1999)     

An approximate expression for the galvanomagnetic tensor

Using the iterative solution to the Boltzmann equation for electrons in d.c. electric and magnetic fields, an expression for the resistivity tensor can be obtained in the form of an infinite series. This series can be approximated by retaining only the first two terms. In the cases where relaxation times exist — in the sense that the collision term in the Boltzmann equation can be written asg(k)/τ(k), whereτ(k) is the relaxation time, andf (k) = f _E(ɛ k) + [∂f _E(εk)/∂ε]·g(k) the distribution function for electrons with wavevectork — this approximation is exact. For polyvalent metals in the one-OPW approximation, the complete galvanomagnetic tensor can be obtained using this approximation and the result differs from that obtained by using a time of relaxation given by an expression suggested byZiman. A calculation for a simple model Fermi surface, with screened Coulomb scattering, is carried out and the results compared with those of the relaxation time approximation.     

Long- and short-range order in the Pd<Subscript>6</Subscript>B monoclinic superstructure and M<Subscript>6</Subscript>X<Subscript>5</Subscript> and M<Subscript>6</Subscript>X allied superstructures

Symmetry analysis of the Pd₆B monoclinic superstructure (space group C2/c) formed in the cubic (with the B1 structure) solid solution of boron in palladium (PdB _y ) has been carried out. The formation of this superstructure proceeds as a first-order phase transition via the disorder-order channel including nine nonequivalent superstructure vectors of four stars {k ₁₀}, {k ₄}, {k ₃}, and {k ₀}. For the Pd₆B monoclinic super-structure (space group C2/c), the distribution function for boron atoms is calculated and the interval of admissible values of the long-range order parameters is defined. It is shown that the transition channel determined in this way coincides with the channel in which the M₆X monoclinic superstructure (space group C2) is formed; therefore, the Pd₆B superstructure can also be described in space group C2 to the same degree of accuracy. The higher symmetry of the monoclinic model (space group C2/c) suggests that it describes the structure of the Pd₆B phase (Pd₆B□₅), as well as of mutually inverse phases M₆X□₅ and M₆X₅□, more adequately than the model with space group C2. It is shown that superstructures of the M₆X□₅ type (space groups C2/c, C2, C2/m, and P3₁) and inverse superstructures of the M₆X₅□ type with the same space groups have the positions of the nearest surrounding of metal atoms by two types of nonmetallic sublattice sites located in the first and second coordination spheres.     

Noncommuting limits of oscillator wave functions

Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite—Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry. The text was submitted by the authors in English. On sabatical leave from Physics Department, Ben Gurion University of the Negev, Beer Sheva, Israel. on leave from the Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, Russia.     

Raman scattering in YBa2Cu3O7 single crystals: Anisotropy in normal and superconductivity states

Precise temperature and polarization dependences of Raman spectra have been investigated for fully oxygenated twin-free YBa₂Cu₃O₇ single crystals. We have found a striking superconductivity-induced x−y anisotropy in the temperature behavior of the 340 cm⁻¹ line: the magnitudes of the softening and broadening are quite different in the xx-and yy-polarizations. This anisotropy suggests a contribution of the CuO-chain superconductivity with a pairing symmetry different from that for the CuO₂ plane, or indicates that the superconducting gap amplitudes are different in the k _x and k _y directions. The d+s gap symmetry is the only realistic symmetry in the case of Δ_x≠Δ_y. Fiz. Tverd. Tela (St. Petersburg) 40, 403–412 (March 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

Spectrum of Kelvin-wave turbulence in superfluids

We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum E _LN(k) ∝ k ^−5/3 must replace in future theory (e.g., in finding the quantum turbulence decay rate) the previously used spectrum E _KS(k) ∝ k ^−7/5, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.     

Antiferromagnetic conical refraction of elastic waves in hematite

Conical refraction, which is due to the renormalization of the elastic moduli by the effective magnetoelastic interaction and depends on the static magnetic field, has been experimentally observed in an α-Fe₂O₃ trigonal easy-plane antiferromagnet in addition to the usual internal conical refraction of transverse elastic waves propagating along the trigonal C ₃ axis. It has been shown that the deviation angle θ_η of the energy flux from the C ₃ axis at the internal conical refraction is independent of the magnetic field applied in the basal plane (H ⊥ C ₃) and is a constant determined by the ratio of the elastic moduli C ₁₄ and C ₄₄. The deviation angle of the energy flux at the antiferromagnetic conical refraction increases with the magnetic field and approaches the value θ_η at large H values. The results are well described by the theory of this phenomenon developed by E.A. Turov and confirm its basic conclusions.     

Effect of interlayer single-particle hoppings on the superconducting transition temperature

It is well known that the superconducting transition temperature of high-T _c cuprates depends on the number of CuO₂ planes in the unit cell. The multilayer structure implies the possibility of interlayer hopping. Under the assumption that the interlayer hopping can be specified by the parameter t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))², the quasiparticle excitation spectrum for the bilayer cuprate in the superconducting state has been determined in the framework of the t − t′ − t″ − t _⊥ − J* model using the generalized mean-field approximation. It turns out that the interlayer hoppings does not create any additional mechanism of the Cooper paring and does not lead to an increase in T _c . The splitting of the upper Hubbard quasiparticle band attributed to the interlayer hoppings is manifested as two peaks in the doping dependence of the superconducting transition temperature at temperatures below the maximum T _c value for a single-layer cuprate. It has been found that antiferromagnetic interlayer correlations suppress the interlayer splitting. This probably leads to the common doping dependence of T _c for both single-layer and bilayer cuprates.     

The Threshold Effects for the Two-Particle Hamiltonians on Lattices

For a wide class of two-body energy operators h(k) on the d-dimensional lattice ℤ^d, d≥3, k being the two-particle quasi-momentum, we prove that if the following two assumptions (i) and (ii) are satisfied, then for all nontrivial values k, k≠0, the discrete spectrum of h(k) below its threshold is non-empty. The assumptions are: (i) the two-particle Hamiltonian h(0) corresponding to the zero value of the quasi-momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and (ii) the one-particle free Hamiltonians in the coordinate representation generate positivity preserving semi-groups.     

Distribution of the conductance of a linear chain of tunnel barriers with fractal disorder

Distributions of the conductance G of a long quantum wire with the fractal distribution of barriers have been obtained in the successive incoherent tunneling regime. The asymptotic behavior (in the limit L → ∞) of moments 〈G ^k (L)〉, average power of the shot noise 〈S(L)〉, and Fano factor agree with the results of the work [C. W. J. Beenakker et al., Phys. Rev. B 79, 024204 (2009)], and the distributions themselves describe well the Monte Carlo simulation results. The equation that has been obtained for the distributions of the resistance and conductance agrees with the recent fractional differential generalization of the Dorokhov-Mello-Pereyra-Kumar equation for the quasi-one-dimensional multichannel disordered semiconductors with a self-similar distribution of scatterers.     

Dependence of the critical temperature of high-temperature cuprate superconductors on hoppings and spin correlations between CuO<Subscript>2</Subscript> planes

The influence of interlayer hoppings on the superconducting transition temperature (T _c) in bilayer cuprates has been studied. The parameter of hopping between layers is expressed as t _⊥(k) = t _⊥(cos(k _x ) − cos(k _y ))² and treated as a small perturbation for the states of two CuO₂ planes described by the t-t′-t″-J* model. In the generalized mean field approximation for d_{x² - y²}{d_{{x^2} - {y^2}}} symmetry of the superconducting gap, neither the interlayer hopping or exchange interaction, nor the pair hopping between CuO₂ layers provides an additional mechanism of Cooper pair formation or an increase in T _c. In the concentration dependence of T _c, the bilayer splitting of the upper Hubbard band of quasi-holes is manifested as two peaks with temperatures slightly lower than the maximum T _c for a single-layer cuprate. Interlayer antiferromagnetic spin correlations suppress bilayer splitting.