Length-independent voltage fluctuations in small conductors

The mean-squared voltage fluctuation of a disordered conductor of lengthL smaller than the phase coherence lengthL _ϕ, is independent of the distance between the probes. We obtain this result using the voltage additivity and the known results for the conductance fluctuation. Our results complement the recent theoretical and experimental findings.     

Partition function zeros and the three-dimensional Ising spin glass

We have computed the exact partition function of the 3D Ising spin glass on lattices of effective size 3×3×L_z, 4×4×L_z, and 5×5×L_z forL _z up to 9, and several random bond configurations. Studying the distribution of zeros of the associated partition functions, we find further evidence that these systems have a singularity in the thermodynamic limit.     

Analytic scattering theory for many-body systems below the smallest three-body threshold

We consider the Schrödinger operatorH=H ₀+V of a many-body system, whereV is a sum of dilation-analytic, short range (not necessarily local) two-body interactions, together with the associated self-adjoint analytic familyH(z), |Argz|<a, of complex-dilated operators. For eachz we construct the local wave operators and the S-matrix below the smallest 3-body threshold, using abstract stationary scattering theory and the Weinberg-van Winter equation. The diagonal element of the inverse S-matrix describing scattering within the channel in the lowest energy range is proved to be the boundary value of a meromorphic functionL (z)(z), –az<0, whereL (z) is the S-matrix forH(z) on the corresponding cut. Generally, the poles ofL (z) are resolvent resonances, but a resolvent resonance may not be a pole ofL (z), if it is embedded as an eigenvalue in the continuum ofH(z ₀) for a suitablez ₀.     

Structure investigation of liquid crystals composed of terminally polar molecules

Summary Recent experimental studies of X-ray scattering in mesogenic compounds with polar endgroups are discussed. The evidence of different types of layering in the nematic and smecticA phases was found. The lamellar packing in smeticA phases corresponds to either the monolayersA ₁ with an interlayer distance equal to the molecular lengthd≈L, or a bilayerA ₂ withd≈2L, or partially bilayerA _d phase whose period is incommensurate with the molecular lengthL<d<2L. The influence of the molecular structure of terminally polar molecules on the stability of layered structures of different types is discussed. The smectic ? phase with bilayer density wave modulated along the direction perpendicular to the directorn is described. The properties of liquid crystals consisting of polar molecules are discussed in terms of frustrated smectics with competing length scales. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Scattering of acoustic phonons by rare earth substitutional atoms in yttrium aluminum garnets

The diffusive maxima of phonon signals, and in particular their arrival timest _m are examined for a number of solid solutions of rare earth atoms in yttrium aluminum garnets. The phonon pulses are generated by metallic films of the characteristic lengthl _h heated by current pulses to the temperatureT _h slightly higher than the ambient temperatureT. The injected phonons travel in wafers of the thicknessL _z. They are scattered by substitutional atoms of rare earth occupying the yttrium dodecahedral sites, rare earth and yttrium atoms occupying the aluminum octahedral sites and by another lattice imperfections generated in the process of sample growing. The qualitative analysis based on our exact formula for the diffusion coefficientD allows us to extract the contribution of rare earth atoms substituting the Y atoms toD. Considering the dependence oft _m/L _z ² on the temperature and the ratiol _h/L_z we conclude thatD∼T _h ⁻⁴ and that the energy of phonons forming the diffusive maxima ranges from 3.2k _BT_H to 4.2k _BT_H, which is in reasonable agreement with the existing estimates.     

Dynamic topological solitons in a two-dimensional ferromagnet

It is shown that stable, skyrmion-type, dynamic solitons can be constructed for a wide class of two-dimensional models of anisotropic ferromagnets. These solitons are stabilized as a result of the conservation of various integrals of motion: the z projection of the total spin S _z or the orbital angular momentum L _z of the magnetization field. A class of two-parameter solitons with quite complicated (almost periodic) magnetization-field dynamics exists for a purely uniaxial model (in the sense of both spin and spatial rotations) with maximum symmetry. Stable solitons with periodic magnetization dynamics exist for ferromagnets with lower symmetry (only S _z or L _z or the total angular momentum J _z =L _z +S _z is conserved). Zh. éksp. Teor. Fiz. 115, 1511–1530 (April 1999)     

Convergence Radii for Eigenvalues of Tri-Diagonal Matrices

Consider a family of infinite tri-diagonal matrices of the form L + zB, where the matrix L is diagonal with entries L _kk  = k ², and the matrix B is off-diagonal, with nonzero entries B _k,k+1 = B _k+1,k  = k ^α , 0 ≤ α < 2. The spectrum of L + zB is discrete. For small |z| the nth eigenvalue E _n (z), E _n (0) = n ², is a well-defined analytic function. Let R _n be the convergence radius of its Taylor’s series about z = 0. It is proved that

Growth of resistance with density of scatterers in one dimensional wave propagation

We study wave propagation in a one-dimensional disordered array of scattering potentials. We consider three different ensembles of scatterer configurations: anN-ensemble with a fixed numberN of scatterers, anL-ensemble with a varying number of scatterers distributed over a fixed lengthL, and anNL-ensemble where bothN andL are fixed. The latter ensemble allows a detailed study of the mean resistance and its variance for a fixed lengthL as the number of scatterersN increases. We find that the Landauer result, which predicts an exponential increase of the mean resistance withN, is valid only in the low-density regime. At high density the mean resistance grows exponentially with N and the concept of optical potential applies. In the crossover regime we find an interesting resonance.     

Influence of boundaries on dissipative structures in the Schlögl model

The stationary spatial structures arising in the Schlögl model of first order nonequilibrium phase transitions are investigated for a one-dimensionals system of finite length.The solution manifold and the occurring bifurcations are analysed systematically by varying the type of boundary condition, the boundary valuev _R ,the system lengthL and the control parameterg. It is shown by plotting appropriate state diagrams that the bistability range of the infinite system is shifted to larger values ofg for small fixedv _R and to smaller values ofg for largev _R ,and that the shift depends sensitively uponL.     

Analyticity properties and a convergent expansion for the inverse correlation length of the low-temperatured-dimensional Ising model

We show that the inverse correlation lengthm(z) of the truncated spin-spin correlation function of theZ ^d Ising model with + or — boundary conditions admits the representationm(z) = –(4d–4)ln z(1–_d1) + r(z) for smallz=e ^–, i.e., large inverse temperatures is ad-dependent analytic function atz = 0, already known in closed form ford = 1 and 2; ford = 3 b_n can be computed explicitly from a finite number of the Z^d limits of z = 0 Taylor series coefficients of the finite lattice correlation function at a finite number of points ofZ ^d.     

First-order phase transitions in finite-size strips with interfaces

Finite-size rounding of the magnetization discontinuity at the magnetic phase transition atH=0 (T<T _c ) in 2d Ising-type strips of sizeL ×L , with ± boundary conditions alongL inducing an interface of lengthL , is studied by phenomenological considerations and transfer matrix techniques. Scaling expressions are derived forL =O(L ) and also in the infinite strip limitL . Most of the results can be extended to the 3d case.     

Anomalous electron diffusion in irradiated thin gold films

We report on topographical and electrical properties of an evaporated (as-prepared) thin gold film before and after irradiation with 200 keV Ar⁺ ions. TEM-investigations reveal for the as-prepared film voids and channels of small size, and a pronounced percolative structure with large scale inhomogeneities after irradiation. Magnetoresistance measurements carried out before and after irradiation yield the temperature dependence of the phase coherence lengthL , when analysing the experimental data within current theories for 2-dimensional (2d) weak localization. The results can be explained by normal electron diffusion if-for the as-prepared film-L is larger than the size of structural inhomogeneities, and-for the irradiated film-by anomalous electron diffusion ifL becomes smaller. The analysis ofL (T) for the irradiated film yields critical exponents for 2d-percolation, in good agreement with predictions of percolation theory.     

Percolation of chains and jamming coverage in two dimensions by computer simulation

A computer simulation model is used to study the percolation of random chains with a self-avoiding constraint. The percolation threshold is found to decay with the chain lengthL _c with a power lawL _c ^–0.1 , while the jamming coverage varies asL _c ^–1/3 .     

Occurrence of superconductivity in R2-z Ce z CuO4 and related compounds

The facts concerning the occurrence of superconductivity in R_2-z Ce _z CuO₄ and in R_2-z Th _z CuO₄ are studied using a combination of simple tools: a hard-sphere model, the self-consistent bond-valence-sum method and Madelung potential calculations. Doping by isolated substitutional Ce should produce Ce³⁺, and not Ce⁴⁺, causing us to conclude that the dopants are not isolated, but (Ce, O_interstitial) pairs, which make the material p type and not n type. The L = 0 magnetic rare-earth ions Gd and Cm are unsplit pair breakers, unlike the other magnetic rare-earth ions which lead to superconductivity. As the rare-earth ions become smaller, the c-axis length shortens; then the O ions rotate after they come into contact with one another. Eu_1.85Th_0.15CuO₄ does not superconduct because quadrivalent Th is too large to fit at the dopant site, but Eu_1.85Ce_0.15CuO₄ does superconduct because Ce fits.     

Extraordinary photons with unusual angular momentum

A series of novel state-vector functions (SVFs), which is the general solution of the Schrödinger equation for a photon, are constructed. Each set of these functions consists of a triplet of eigen-SVFs: The triplet can be broken down into a pair of nonzero l-order functions and a single zero-order function. The photons, described with a triplet of eigen-SVFs, possess all the quantum characteristics of a photon: In addition to common attributes like energy E = ? _ω , and momentum p _z = ? _κ , they also exhibit different angular momenta (AM) L _z+ = l?, L _z? = l?, and L _z0 = 0, where l?1. In other words, in addition to usual eigenvalues L _z±= ±?, there are unusual nonzero l-order eigenvalues L _z± = ±l? and a zero-order eigenvalue L _z0 = 0 for AM of a photon. By a series of SVFs, the pattern from nonzero l-order and zero-order Laguerre-Gaussian modes of a laser beam is explained well from a quantum mechanical point of view.     

Simplified components of the spin-other-orbit interaction near the middle of the atomic f shell

To honour the memory of Brian Garner Wybourne, an analysis is presented of three components of the spin-other-orbit interaction for f electrons using the kind of Lie groups he would have been familiar with. The components have been named z ₆, z ₈ and z ₁₀. They all belong to the irreducible representation (IR) (30) of Racah’s group G₂. Near the middle of the f shell it is often found that fewer independent blocks of numbers are needed to express their matrix elements than the Wigner–Eckart theorem, generalized to the IRs U of G₂, would indicate. Each block corresponds to a given U and U?′, and possesses rows and columns labelled by the angular momenta L and L′. The number of independent blocks would be expected to be given by Racah’s multiplicity function c(UU?′ (30)); but near the middle of the shell the number c(UU?′ (20)) (or less) often suffices. For this to occur, z ₈ and z ₁₀ have to be replaced by linear combinations corresponding to IRs of the types (20)×(10) and (21)×(10) of the direct product group G_2A×G_2B, where A and B refer to electrons with their spins up (A) and spins down (B). A detailed example is provided by the IR (31) of G₂, which occurs in the configurations f ⁵ through f ⁹. In addition, two antiHermitian operators (z _a6 and z _a7) that also belong to the IR (30) of G₂ are discussed.     

Anderson localization in different one-dimensional systems with off-diagonal disorder and spin-dependence

The localization properties of certain spin-dependent, one-dimensional electronic systems with only off-diagonal disorder are studied. In higher dimensions (d=2,3) the models considered would correspond to different universality classes, whereas ford=1 no qualitative difference is found: ForE=0, all eigenstates are exponentially localized, whereas forE0 the localization length diverges logarithmically, such that exactly atE=0 the geometric average of the transmission coefficient would decay with increasing chain lengthL as exp (-const. ·L ^1/2), instead of the usual, exponential decay.ForE=0, in the interior of the band, the localization lengthr ₀ diverges W ₂ ^–2 in the limit of weak disorder (W ₂0), whereas just at the band edge one has roughlyr ₀W ₂ ^–2/3. A universal recursion relation, depending only on the energy and on certain randomly distributed determinants, determines the localization length and the density of states for all systems considered.     

Integrated nanostrip dipole antennas for coherent 30 THz infrared radiation

We report on the experimental study of infrared nanostrip dipole antennas which are connected to thin-film nanometer Ni-NiO-Ni diodes. The integrated Ni-NiO-Ni diodes are used to detect 30 THz (10 µm) CO₂-laser radiation.The diodes are deposited on 385 µm silicon substrates which are covered with a layer of 1.6 µm SiO₂ on both sides. We have found that in low-power applications 1.6 µm of SiO₂ yields excellent quarter-wave matching layers for wavelengths centered at ₀ = 10.8 µm. By this method 79% of the incident CO₂-laser radiation is transmitted into the Si substrate compared to 48% without SiO₂ layer. The use of SiO₂ quarter-wave matching layers considerably improves the efficiency of infrared nanostrip dipole antennas. This has been confirmed by the study of the laser-induced response of the Ni-NiO-Ni diode detectors as a function of the lengthL of the dipole antenna. Thus, we have observed that the laser-induced response strongly increases for shorter antennas and exhibits a distinct maximum atL=2.8 ± 0.3 µm. For the first time, we have investigated the 30 THz radiation patterns of nanostrip dipole antennas of different lengths. On this occasion, we have observed that the radiation pattern changes when the lengthL of the dipole antenna is varied. This observation indicates that antenna currents propagate on the nanostrip dipole antenna.     

Derivatives of the thiolate-protected gold cluster Au25(SR)18-1

Loss of small fragments (like AuL, Au₂L₃, Au₄L₄) have been found systematically in several MALDI and FAB experiments on thiolate-protected gold clusters of different sizes. When using the cluster Au₂₅L₁₈ ^-1 as parent cluster, the fragmented cluster Au₂₁L₁₄ ^-1 has been reported to be obtained in high proportion (L = SCH₂CH₂Ph). Here we analyse a few possible fragmentation patterns of the well-known parent cluster Au₂₅L₁₈ ^-1 (L = SCH₃). Using DFT calculations we study the different atomic configurations obtained after a AuL fragment is lost from Au₂₅L₁₈ ^-1. We found energetically favourable configurations that can be written as Au₁₃ [Au₂L₃]_6-z [AuL₂] _z ^-1, where the modification can be described as a replacement of the long protecting unit by a short one (Au₂L₃  →  AuL₂). A full replacement (z = 6) gives rise to a protected Au₁₉L₁₂ ^-1 cluster. This mechanism does not modify the super-atomic electronic structure of the gold core, i.e., all these fragments remain an 8 electron super-atom clusters exactly like the parent Au₂₅L₁₈ ^-1. We suggest that the Au₁₉L₁₂ ^-1 cluster could be realized by using a bulky thiolate, such as the tert-butyl thiolate SC(CH₃)₃ .     

Differential Geometry from Differential Equations

We first show how, from the general 3rd order ODE of the form , one can construct a natural Lorentzian conformal metric on the four-dimensional space . When the function satisfies a special differential condition the conformal metric possesses a conformal Killing field, , which in turn, allows the conformal metric to be mapped into a three dimensional Lorentzian metric on the space ) or equivalently, on the space of solutions of the original differential equation. This construction is then generalized to the pair of differential equations, z _ss =S(z,z _s ,z _t ,z _st ,s,t) and z _tt =T(z,z _s ,z _t ,z _st ,s,t), with z _s and z _t the derivatives of z with respect to s and t. In this case, from S and T, one can again, in a natural manner, construct a Lorentzian conformal metric on the six dimensional space (z,z _s ,z _t ,z _st ,s,t). When the S and T satisfy differential conditions analogous to those of the 3^rd order ode, the 6-space then possesses a pair of conformal Killing fields, and which allows, via the mapping to the four-space of (z,z _s ,z _t ,z _st ) and a choice of conformal factor, the construction of a four-dimensional Lorentzian metric. In fact all four-dimensional Lorentzian metrics can be constructed in this manner. This construction, with further conditions on S and T, thus includes all (local) solutions of the Einstein equations. Received: 10 October 2000 / Accepted: 26 June 2001