Transfer-matrix for the multichannel scattering problem

A transfer-matrix for the multichannel scattering problem is obtained. The elements of this matrix are expressed in terms of transmission and reflection amplitudes. On the basis of the matrix for a system of N localized and nonoverlapped scattering centers the recurrent equations for the transfermatrix elements are derived and the initial conditions are defined.     

Multichannel scattering of a particle in a quantum wire of cylindrical symmetry

The Schrödinger equation for a scattering particle in a quantum wire is considered. We discuss two geometrical forms of cross-section of the wire: the rectangular section and the cylindrical one. It is shown that scattering of the particle on an arbitrary potential V = V (x, y, z,), given in the wire, can be considered as a multichannel scattering, where the index of the channel coincides with the index which determines energy levels of the confined transverse motion of the particle. A method for determination of the amplitudes of transmission T _i and reflection R _i in the case of multichannel scattering is proposed. The case of two-channel scattering is considered in detail and a method for determination of the scattering amplitudes T ₁, T ₂ and R ₁, R ₂ is proposed.     

Temperature dependence of the electrical resistivity of R6(Fe1-xMnx)23 compounds in the temperature range 4.2 to 300 K

The temperature dependence of the electrical resistivity of binary R₆Mn₂₃, R₆Fe₂₃ (R = Y, Dy, Ho, Er, Tm) and pseudobinary R₆(Fe_1-xMn_x)₂₃ (R = Y, Er, Ho) compounds has been determined by a four-probe measuring technique in the temperature range 4 to 400 K.The binary compounds exhibit a prop. T² dependence at low temperatures, while above 100 K a negative curvature of the -T-curves is observed.These experimental results are discussed on the basis of electron-spin wave scattering in the low temperature range and on the basis of s-d scattering in the high temperature range, taking explicitly into account the temperature dependence of the chemical potential.The pseudobinary compounds generally exhibit a decreasing resitivity with increasing temperature, combined with a high residual resistivity. These facts are explained by the so-called strong scattering mechanism and the appearance of “quasilocalized” states.     

T -suppression due to R=Pr,Nd,Eu in (La1?xRx)1.82Sr0.18CuO4

The effect of substitution of rare earth elements (R) on superconductivity and crystal structure is investigated for the samples of (La_1−xR_x)_1.82Sr_0.18CuO₄, R=Pr,Nd,Eu through the measurements of electrical resistivity and lattice parameters. It is revealed thatT _c suppression due to R-elements is not due to their magnetism but can be attributed to two contributions; the reduction of the Madelung site potential at apex sites and the random potential scattering on CuO₂ plane which in effective for pair-breaking in d-wave superconductors, both of which are brought about by the displacement of apex oxygens due to the substitution of R-elements.     

Activation energy and hall-coefficient measurements in lightly dopedn-InP in the thermal freeze-out region

Summary The direct-current resistivity, β, and Hall coefficient,R _H, of lightly dopedn-type InP samples were measured at temperatures (T) down to 12K and magnetic fields up to 4.8 kG. A sharp exponential increase in β, asT was decreased, was observed for temperatures below 80 K. The Hall coefficient showed a similar trend,i.e. R _H increased sharply asT was reduced below 80 K. This is attributed to the freeze-out of conduction electrons onto their donor sites. The donor activation energy,E _d, calculated from the temperature dependence of the resistivity, was less than the theoretical prediction. An enhanced dielectric constant would be a possible candidate for such behaviour. The initial decrease in β (asT is reduced) recorded in the higher-temperature region is due to impurity scattering probably combined with lattice scattering. The authors of this paper have agreed to not receive the proofs for correction.     

Twists in Hopf algebras andRT 1 T 2=T 2 T 1 relations

LetR be a matrix unitary quasi-classical solution of the Yang-Baxter equation. Considering an associative algebra defined by the relationRT ₁ T ₂=T ₂ T ₁ we find a universal twistF such thatR is the image ofR=F ₂₁ F ⁻¹ in the vector representation. Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.     

ThermoElectric Transport Properties of a Chain of Quantum Dots with Self-Consistent Reservoirs

We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions, we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix the boundary values (T _L,μ _L) and (T _R,μ _R), and adjust the parameters (T _i ,μ _i ), for i=1,…,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm and Fourier laws.     

Intrinsic inhomogeneities of low-doped lanthanum manganites in the paramagnetic temperature range

The nature of the electrical resistivity for low-doped lanthanum manganites is elucidated. The electrical resistivity is described by the Efros-Shklovskii law (lnρ √ (T ₀/T)^−1/2, where T ₀ √ 1/R _ls) in the temperature range from T* ≈ 300 K ≈ T _C (T _C is the Curie temperature for conducting manganites) to their T _C and is explained by the tunneling of carriers between localized states. The magnetoresistance is explained by a change in the size of localized states R _ls in a magnetic field. The patterns of change in R _ls with temperature and magnetic field strength determined from magnetotransport properties are satisfactorily described in the model of phase separation into small-radius metallic droplets in a paramagnetic matrix. The sizes R _ls and their temperature dependence have been estimated through magnetic measurements. The results confirm the existence of a Griffith phase. The intrinsic inhomogeneities produced by thermodynamic phase separation determine the electrical resistivity and magnetoresistance of lanthanum manganites.     

Polarization Phenomena in Elastic Electron-Proton Scattering

A unified treatment is given by using the scattering matrix in the Pauli spin spaces and polarization density matrices. Various quantities such as polarization P, asymmetry A, spin correlation parameters C_αβ, double polarization asymmetry A_αβ, polarization transfer parameters D_t, A_t, R_t and depolarization and spin rotation parameters D, A, R are expressed in terms of six coefficients which appear in the scattering matrix. Some explicit expressions as well as numerical results for these quantities are also given in the one photon exchange approximation.     

Implications of time-reversal symmetry for the band structure of single-wall carbon nanotubes

When electron states in carbon nanotubes are characterized by two-dimensional wave vectors with the components K ₁ and K ₂ along the nanotube circumference and cylindrical axis, respectively, then two such vectors symmetric about a M-point in the reciprocal space of graphene are shown to be related by the time-reversal operation. To each carbon nanotube there correspond five relevant M-points with the following coordinates: K ₁⁽¹⁾ = N/2R, K ₂⁽¹⁾= 0; K ₁⁽²⁾ = M/2R, K ₂⁽²⁾= −π/T; K ₁⁽³⁾= (2N −M)/2R, K ₂⁽³⁾= π/T; K ₁⁽⁴⁾= (M + N)/2R, K ₂⁽⁴⁾= -π/T, and K ₁⁽⁵⁾= (N − M)/2R, K ₂⁽⁵⁾= π/T, where M and N are the integers relating the chiral, C _h , symmetry, R, and translational, T, vectors of the nanotube by N R = C _h + M T, T = |T|, and R is the nanotube radius. The states at the edges of the one-dimensional Brillouin zone, which are symmetric about the M-points with K ₂ = ±π/T, are shown to be degenerate due to the time-reversal symmetry.     

On the relationship betweenT 1 andT 2 for stochastic relaxation models

We consider the relaxation dynamics of two quantum levels coupled to a stochastic bath. We emphasize that even if the matrix elements of the fluctuating Hamiltonian are Gaussian, a second-order cumulant truncation is not exact. For various stochastic models, including the case of a spin-1/2 particle in a fluctuating magnetic field, we calculate 1/T ₁, the population relaxation rate, and 1/T ₂, the phase relaxation rate, up to fourth order in perturbation theory. We show that unlike the commonly accepted second-order result that 1/T ₂1/2T ₁, when fourth-order terms are included, in some instances 1/T ₂<1/2T ₁.     

Concerning the two magnetic correlation lengths above T c in an Invar iron-nickel alloy

The magnetic phase transition in the Invar alloy Fe₇₀Ni₃₀ is investigated by means of small-angle neutron scattering over a wide range of momentum transfer. This method was used to measure two magnetic correlation lengths R _c 1 and R _c 2 which coexist in the alloy above the phase transition temperature T _c . The critical correlations with correlation length R _c 1 are described well by an Ornstein-Zernicke expression, and the critical correlations with the second correlation length, an order of magnitude larger than R _c 2, are described well by a squared Ornstein-Zernicke expression. The temperature dependences obtained for the correlation lengths R _c 1 and R _c 2 satisfy the power law R _c ∼((T−T _c )/T _c ) ^−υ with critical exponents υ₁=0.65±0.05 and υ₂=1.3±0.1 for the shorter and longer scales, respectively. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 1, 53–57 (10 July 1997)     

Phase-transformation-induced microstructure in lead-free ferroelectric ceramics based on (Bi0.5Na0.5)TiO3–BaTiO3–(Bi0.5K0.5)TiO3

Lead-free ferroelectric ceramics with a morphotropic phase boundary (MPB) composition 85.4% (Bi_0.5Na_0.5)TiO₃–2.6%BaTiO₃–12.0% (Bi_0.5K_0.5)TiO₃ (BNT-BT-BKT at a molar ratio of 85.4: 2.6: 12.0) doped with 0.8?mol% Nb₂O₅ were studied for their crystalline phases and microstructure. The crystalline phases were identified using X-ray diffractometry (XRD) with the contents determined using the Rietveld refinement technique. The phase-transformation-induced microstructure was analyzed using transmission electron microscopy (TEM) and the crystal symmetries were determined using the convergent-beam electron diffraction (CBED) technique. Samples sintered at 1200°C contain a mixture of cubic (C-), tetragonal (T-) and rhombohedral (R-) phases at a ratio of C/T/R?=?56.6: 28.4: 15.0?wt%. Two types of grains are produced: one characterized by a featureless contrast consisting of nano-scale T-domains dispersed in a C-phase matrix; the other a core-shell structure with a shell containing twin and anti-phase-boundary (APB) domains coexisting with a (C?+?T)-phase mixture core. The T- and R-twin boundaries are determined to {111}_T and {110}_R, respectively, and the fault vector for T-APB to R?=?1/2?110]_T. The characteristic microstructure is discussed in terms of the reduction in the point group symmetry and changes in the unit cell volume or the Bravais lattice upon phase transformation among the C-, T- and R-phases. The twin and the APB domains are induced and explained.     

Analogs of q-Serre relations in the Yang-Baxter algebras

Yang-Baxter bialgebras, as previously introduced by the authors, are shown to arise from a double crossproduct construction applied to the bialgebra R ₁₂ T ₁ T ₂ = T ₂ T ₁ R ₁₂, E ₁ T ₂ = T ₂ E ₁ R ₁₂, (T)=TT, (E)=ET + 1E and its skew dual, with R being a numerical matrix solution of the Yang-Baxter equation. It is further shown that a set of relations generalizing q-Serre ones in the Drinfeld-Jimbo algebras U _q(g) can be naturally imposed on Yang-Baxter algebras from the requirement of non-degeneracy of the pairing.     

Asymptotic degeneracy of the transfer matrix spectrum for systems with interfaces: Relation to surface stiffness and step free energy

Two- and three-dimensional Ising-type systems are considered in the finite-cross-section cylindrical geometry. An interface is forced along the cylinder (strip in 2d) by the antiperiodic or +– boundary conditions. Detailed predictions are presented for the largest asymptotically degenerate set of the transfer matrix eigenvalues. For rough interfaces, i.e., for 0<T<T _c in 2d,T _R<T<T _c in 3d, the eigenvalues are split algebraically, and the spectral gaps are governed by thesurface stiffness coefficient. For rigid interfaces, i.e., 0<T<T _R in 3d, the eigenvalues are split exponentially, with the gaps determined by thestep free energy.     

The measurement of R2, and R2′ in HIV-infected patients using the prime sequence as a measure of brain iron deposition

Brain iron deposition was assessed at 1.5 T in the caudate nucleus, globus pallidus and frontal and parietooccipital white matter in 28 human immunodeficiency virus (HIV)-infected patients and 15 control subjects with a new Partially Refocussed Interleaved Multi-Echo sequence by measuring 1/T₂, 1/T₂^* and 1/T2′ (i.e., R₂, and R₂′). There were significant differences in the R₂ and of the caudate nucleus (p < 0.0001 and p < 0.05) and the R₂, and R₂′ of the globus pallidus (p < 0.001, p < 0.005 and p < 0.05) in HIV-infected patients compared to control subjects. There was a trend for higher values of R₂, and R₂′ in the globus pallidus and caudate nucleus in HIV-infected patients with later stage HIV disease. These results suggest that there is greater iron deposition in the basal ganglia of HIV-infected patients compared with control subjects, with a predilection for the globus pallidus. The relationship between iron deposition in the brain and various parameters of severity of HIV infection remains uncertain.     

Allowing for Coulomb effects in the effective range expansion for two coupled channels

A Coulomb-modified matrix of scattering amplitudes (an [(F)\tilde]\tilde F matrix) is considered for the case of two coupled channels of elastic scattering of charged particles with different orbital angular momenta (l ₁ and l ₂ = l ₁ + 2). Matrix elements of the [(F)\tilde]\tilde F matrix are expressed in terms of the matrix elements of a [(K)\tilde] ^{- 1}\tilde K^{ - 1} matrix inverse to a modified reaction K matrix. The elements of the [(K)\tilde] ^{- 1}\tilde K^{ - 1} matrix are written as expansions that are generalizations of single-channel effective range expansion with allowance for the Coulomb interaction. If a system of colliding particles involves a bound state, the analytic continuation of these expansions into the region of negative energies makes it possible to obtain both the position of the pole corresponding to the bound state and the scattering amplitude residues in this pole, in terms of which the corresponding vertex constants and asymptotic normalization coefficients are expressed.     

Sum rule estimate of the subleading non-perturbative contributions to Bs–$\bar{ B}_{s}$ mixing

We use QCD sum rules to compute the matrix elements of the ΔB=2 operators appearing in the heavy-quark expansion of the width difference of the B _s mass eigenstates. The main focus of our analysis is on the subleading operators R ₂ and R ₃, which appear at next-to-leading order in the 1/m _b expansion. The matrix elements of these operators are already essential for precise phenomenology, but their calculation in lattice QCD is lacking and the values given here provide a first estimate of their values. We conclude that the violation of the factorization approximation for these matrix elements due to non-perturbative vacuum condensates is as low as 1–2%.     

Investigation of a magnetic phase transition in fcc iron-nickel alloys

A magnetic phase transition in carbon-doped (0.1 and 0.7 at. %) Fe₇₀Ni₃₀ Invar alloys was investigated by the method of depolarization of a transmitted neutron beam and by small-angle scattering of polarized neutrons. It is shown that for both alloys, two characteristic length scales of magnetic correlations coexist above T _c. Small-angle scattering by critical correlations with radius R _c is described well by the Ornstein-Zernike (OZ) expression. The longer-scale (second) correlations, whose size can be estimated from depolarization data, are not described by the OZ expression, and hypothetically can be modeled by a squared OZ expression, which in coordinate space corresponds to the relation 〈M(r)M(0)〉∝exp(−r/R _d), where R _d is the correlation length of the second scale. The temperature dependence of the correlation radius R _c was obtained: R _c ∝ ((T−T _c)/Tc)^−ν , where ν≈2/3 is the critical exponent for ferromagnets, over a wide temperature range up to T _c ^exp , at which the correlation radius becomes constant and equals its maximum value R _c(T _c)=R _c ^max . The maximum correlation radius established (R _c ^max =140 Å and 230 Å for the first and second alloys, respectively) characterizes the length-scale of the fluctuation for which the appearance of critical correlations first results in the formation of a ferromagnetic phase, and the phenomenon itself exhibits a “disruption” of the second-order phase transition at T=T _c ^exp , as a result of which a first-order transition arises. Temperature hysteresis was also detected in the measured polarization of the transmitted beam and intensity of small-angle neutron scattering in the alloy above T _c, confirming the character of this magnetic transition as a first-order transition close to a second-order transition. Zh. éksp. Teor. Fiz. 112, 2134–2155 (December 1997)     

Calculation of high-order rotational centrifugal-distortion matrix elements for a Hund's case (a) basis set

The derivation of explicit expressions for the Hund's case (a) matrix elements of R^2k is discussed, where R is the mechanical rotational angular momentum operator of the molecule. A recursion relation is developed that permits matrix elements of R^2k to be expressed in terms of those of R^2(k?1), thus affording a straightforward means of calculating the case (a) matrix elements of rotational centrifugal-distortion constants D_v, H_v, L_v, M_v, etc., to an arbitrarily high order. The explicit matrix elements of L_v are listed.