Equation for the Landauer resitivity in the case of multichannel scattering

Generalization of the Landauer resistivity ρ _N ^L is given for the case of multichannel scattering of a particle by the system of nonoverlapped N random potentials, depending on x − x _i and y, which are localized near the points x _i (i = 1,2,…N). It is shown that in this case a new resistivity ρ _N ^S appears, which is a power function of N. A recurrent equation is obtained for definition of the Landauer resistivity ρ _N ^L .     

The Landauer resistance of a one-dimensional metal with periodically spaced random impurities

We find the dependence of the ensemble-averaged resistance, 〈ρ _L〉, of a one-dimensional chain consisting of periodically spaced random delta-function potentials of the chain length L, the incident-electron energy, and the chain disorder parameter w. We show that generally the 〈ρ _L〉 vs L dependence can be written as a sum of three exponential functions, two of which tend to zero as L℩∞. Hence the asymptotic expression for 〈ρ _L〉 is always an exponential function of L. Such an expression for 〈ρ _L〉 means that the electronic states are indeed localized and makes it possible (which is important) to find the dependence of the localization radius on the incident-electron energy and the force with which an electron interacts with the sites of the chain. We also derive a recurrence representation for 〈ρ _L〉, which proves convenient in numerical calculations. Zh. éksp. Teor. Fiz. 111, 575–584 (February 1997)     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

A relation between circular 1/2 BPS ’t Hooft operators in 4d N=4{{\mathcal N}=4} SYM and instantonic solutions in 2D Yang-Mills theory (YM₂) has recently been conjectured. Localization indeed predicts that those ’t Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM₂, belonging to representations of the dual group ^L G. This conjecture has been tested in the case G = U(N) =  ^L G and for fundamental representations. In this paper, we examine this conjecture for the case of the groups G = SU(N) and ^L G = SU(N)/Z _N and loops in different representations. Peculiarities when groups are not self-dual and representations not “minimal” are pointed out.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.     

Solution of approximate gluon evolution equation for small-x at fixed ‘ρ’

A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x ₀/x)/ln[ln(Q ²/Λ²)/ln(Q ₀ ² /Λ²)]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.     

<Emphasis Type="Italic">ρρ</Emphasis>N and <Emphasis Type="Italic">ρρ</Emphasis>Δ molecules with J<Superscript>P</Superscript> = 5/2<Superscript>+</Superscript> and J<Superscript>P</Superscript> = 7/2<Superscript>+</Superscript>

The ρρN and ρρΔ three-body systems have been studied within the framework of the fixed center approximation of Faddeev equation. The ρρ interaction in isospin I = 0 , spin S = 2 is strongly attractive, and so are the N ρ, ρΔ interactions. This leads to bound states of both ρρN and ρρΔ. We find peaks of the modulus squared of the scattering matrix around 2227 MeV for ρρN, and 2372 MeV for ρρΔ. Yet, the strength of the peak for the ρρN amplitude is much smaller than for ρρΔ, weakening the case for a ρρN bound state, or a dominant ρρN component. A discussion is made on how these states can be searched for in present programs looking for multimeson final states in different reactions.     

Magnetic, electrical, and optical properties of Ca1 ? x Ce x MnO3 ( x ≤ 0.12) single crystals

The magnetic, electrical, and optical properties of Ca_{1 − x} Ce _x MnO₃ (x≤0.12) manganite single crystals are investigated with the aim of revealing the specific features of the multiphase electronic and magnetic state as a function of the cerium concentration and the atmosphere used for growing single crystals. It is found that the concentration dependence of the low-temperature magnetization M(x) of the single crystals is shifted toward the high-concentration range as compared to the corresponding dependence of the polycrystals, which is explained by the predominant cation deficiency. The electrical resistivity and the reflection spectra of the single crystals in the infrared spectral range indicate that charge carriers exhibit a band nature at temperatures close to room temperature. The temperature dependence of the electrical resistivity of the single crystal with x = 0.08, which has the maximum magnetization in the studied series of Ca_{1 − x} Ce _x MnO₃ compounds, unlike polycrystals, exhibits a metallic behavior over the entire temperature range. The G-type antiferromagnetic phase with the Néel and Curie temperatures T _N(G) = T _C = 100 K is characterized by maxima of the electrical resistivity ρ and the magnetoresistance Δρ/ρ = |(ρ₀ − ρ _H )/ρ₀| = 38% in the magnetic field H = 90 kOe. The magnetoresistance Δρ/ρ of the single crystals at cerium concentrations x = 0.10 and 0.12 with variations in temperature exhibit three specific features: near the temperature of charge ordering T _co, near the temperature of the magnetic phase transition to the C-type antiferromagnetic phase T _N(C), and near the temperature of the phase transition to the magnetic charge-ordered phase T _N(MCO). An anomalous temperature dependence of the magnetization is revealed for a single crystal with x = 0.10 grown in oxygen at a pressure of 5 atm, which is explained by the presence of regions with hole conductivity due to cation deficiency. The inhomogeneous electronic and magnetic state is associated with the interrelation of the charge, orbital, and spin orderings. Original Russian Text ? N.N. Loshkareva, A.V. Korolev, N.I. Solin, E.V. Mostovshchikova, S.V. Naumov, N.V. Kostromitina, A.M. Balbashov, 2009, published in Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 135, No. 1, pp. 98–107.     

Liouville Type Equations with Singular Data¶and Their Applications to Periodic Multivortices¶for the Electroweak Theory

Motivated by the study of multivortices in the Electroweak Theory of Glashow–Salam–Weinberg [33], we obtain a concentration-compactness principle for the following class of mean field equations: on M, where (M,g) is a compact 2-manifold without boundary, 0 < a≤K(x)≤b, x∈M and λ > 0. We take with α _i > 0, δ _{p i} the Dirac measure with pole at point p _i ∈M, i= 1,…,m and ψ∈L ^∞(M) satisfying the necessary integrability condition for the solvability of (1)_λ. We provide an accurate analysis for solution sequences of (1)_λ, which admit a “blow up” point at a pole p _i of the Dirac measure, in the same spirit of the work of Brezis–Merle [11] and Li–Shafrir [35]. As a consequence, we are able to extend the work of Struwe–Tarantello [49] and Ding–Jost–Li–Wang [21] and derive necessary and sufficient conditions for the existence of periodic N-vortices in the Electroweak Theory. Our result is sharp for N= 1, 2, 3, 4 and was motivated by the work of Spruck–Yang [46], who established an analogous sharp result for N= 1, 2. Received: 24 September 2001 / Accepted: 7 December 2001     

Experimental investigation of the angular dependence of photon-induced differential cross-sections of L X-rays from U,Th and Bi at 59.5 keV

Summary The differential cross-sections for the emission of L_ρ, L_α, L_β and L_γ groups of L X-ray lines from U, Th and Bi have been measured at different angles varying from 45° to 135° at intervals of 15°. The vacancies were created by 59.5 keV γ-rays from²⁴¹Am source and L X-rays were measured using a Si(Li) detector. It is found that the L_γ and L_β groups of L X-rays are isotropic, the L_ρ and L_α groups are anisotropic in the spatial distribution. The authors of this paper have agreed to not receive the proofs for correction.     

Harness Processes and Non-Homogeneous Crystals

We consider the Harmonic crystal, a measure on with Hamiltonian H(x)=∑ _i,j J _i,j (x(i)−x(j))²+h∑ _i (x(i)−d(i))², where x, d are configurations, x(i), d(i)∈ℝ, i,j∈ℤ ^d . The configuration d is given and considered as observations. The ‘couplings’ J _i,j are finite range. We use a version of the harness process to explicitly construct the unique infinite volume measure at finite temperature and to find the unique ground state configuration m corresponding to the Hamiltonian.     

Note on the natural system of units

We propose to substitute Newton’s constant G _N for another constant G ₂, as if the gravitational force would fall off with the 1/r law, instead of the 1/r ²; so we describe a system of natural units with G ₂, c and ℏ. We adjust the value of G ₂ so that the fundamental length L = L _Pl is still the Planck’s length and so G _N = L × G ₂. We argue for this system as (1) it would express longitude, time and mass without square roots; (2) G ₂ is in principle disentangled from gravitation, as in (2 + 1) dimensions there is no field outside the sources. So G ₂ would be truly universal; (3) modern physics is not necessarily tied up to (3 + 1)-dim. scenarios and (4) extended objects with p = 2 (membranes) play an important role both in M-theory and in F-theory, which distinguishes three (2, 1) dimensions. As an alternative we consider also the clash between gravitation and quantum theory; the suggestion is that non-commutative geometry [x _i , x _j ] = Λ² θ _ij would cure some infinities and improve black hole evaporation. Then the new length Λ shall determine, among other things, the gravitational constant G _N.     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

Influence of grain boundaries on resistivity of manganites La1 − x K x MnO3

Results of investigation of resistivity and magnetoresistance of manganites La_{1 − x} K _x MnO₃ (x = 0.050–0.175) are presented. Behavior of resistivity ρ(T) in the paramagnetic and ferromagnetic phases has been described. To describe ρ(T) near the phase-transition temperature, notions of the percolation theory have been used. Two maxima have been found in the dependence ρ(T); their appearance has been attributed to the ceramic nature of the studied samples. The observed increase in magnetoresistance with a decrease in temperature is caused by intergranular spin-polarized tunneling of charge carriers.     

Approximate fixed-ρ solution of ‘sea-quark’ evolution equation at small-x and HERA

We found an approximate simple solution of sea-quark evolution equation in terms ofρ(=√ln(x ₀/x)/ln[ln(Q ²/Λ²)/(Q ₀ ² /Λ²)]) andζ(≡ln[ln(Q ²Λ²)/ln(Q ₀ ² /Λ²)]) in the small-x region whenρ is fixed and compared with HERA data. Agreement with data is found for largeQ ² and smallρ. Comparison with double asymptotic scaling prediction is made. We found a critical value ofρ. More data are needed to confirm this point.     

Magnetoresistance and magnetic ordering in praseodymium and neodymium hexaborides

The magnetoresistance Δρ/ρ of single-crystal samples of praseodymium and neodymium hexaborides (PrB₆ and NdB₆) has been measured at temperatures ranging from 2 to 20 K in a magnetic field of up to 80 kOe. The results obtained have revealed a crossover of the regime from a small negative magnetoresistance in the paramagnetic state to a large positive magnetoresistive effect in magnetically ordered phases of the PrB₆ and NdB₆ compounds. An analysis of the dependences Δρ(H)/ρ has made it possible to separate three contributions to the magnetoresistance for the compounds under investigation. In addition to the main negative contribution, which is quadratic in the magnetic field (−Δρ/ρ ∝ H ²), a linear positive contribution (Δρ/ρ ∝ H) and a nonlinear ferromagnetic contribution have been found. Upon transition to a magnetically ordered state, the linear positive component in the magnetoresistance of the PrB₆ and NdB₆ compounds becomes dominant, whereas the quadratic contribution to the negative magnetoresistance is completely suppressed in the commensurate magnetic phase of these compounds. The presence of several components in the magnetoresistance has been explained by assuming that, in the antiferromagnetic phases of PrB₆ and NdB₆, ferromagnetic nanoregions (ferrons) are formed in the 5d band in the vicinity of the rareearth ions. The origin of the quadratic contribution to the negative magnetoresistance is interpreted in terms of the Yosida model, which takes into account scattering of conduction electrons by localized magnetic moments of rare-earth ions. Within the approach used, the local magnetic susceptibility χ_loc has been estimated. It has been demonstrated that, in the temperature range T _N < T < 20 K, the behavior of the local magnetic susceptibility χ_loc for the compounds under investigation can be described with good accuracy by the Curie-Weiss dependence χ_loc ∝ (T − Θ _p )⁻¹.     

Partial suppression of hydrodynamic mixing in profiled shells

The problems of stability and mixing are important in the physics of high-energy densities. Ablation-induced acceleration of foils and compression of liners entail loss of symmetry and the development of instability. The most destructive instability is the fundamental f ⁻ mode, which conserves the pressure in Lagrangian particles. A means has been proposed to eliminate this dangerous mode, based on special profiling of the mass distribution among the subshells. The presence of this mode has led to novel proposals for limiting the degree of instability and optimization of the shells by profiling in the important case of very large density ratios at the ablation front. The solution is based on a class of new polytropes with an inverted density profile and a negative polytrope index N. In this class the density ρ of the material does not decrease towards the boundary with the vacuum, as for ordinary polytropes with N>0, but rather increases. This permits modeling multilayer distributions of ρ typical of inertial confinement fusion systems in which the high-density subshells form an inner core surrounding a low-pressure cavity, and the outer layers are made from low-density materials (plastic, foam type materials, composites). It is emphasized that the distributions are self-similar, and hence both the linear and the turbulent dynamics are scale-invariant. The spectral problem of perturbations in an incompressible fluid has a hidden symmetry. Isospectral deformations of the density profile I{ρ ₀(_y)} are known that leave the spectrum unchanged. It is of interest to apply the transformation I to the invariant f ^± modes, since they are not tied to any specific profile of ρ ₀(y). This paper analyzes a new type of invariant mode obtained in this way. Zh. éksp. Teor. Fiz. 111, 1347–1368 (April 1997)