Numerical estimate of the phase diagram of finite ANNNI chains in transverse field

We have estimated numerically the phase diagram of a one dimensional spin 1/2 quantum Ising model with competing nearest and next nearest neighbour interactions in presence of a transverse field. The method essentially is to diagonalise exactly the Hamiltonian for finite (10 spins) open chains and calculate the spin-spin correlations from the ground state eigenvector. The results obtained confirm the transition between ferromagnetic and paramagnetic phases for <0.5 and between antiphase and paramagnetic phase for >0.5. ( is the ratio of next nearest and nearest neighbour interactions.) The results perhaps indicate furthermore that (i) there is a disorder line passing through =0.5; (ii) the zero point quantum fluctuations destroy the order near =0.5 as the transverse field is switched on; and (iii) there is probably also a floating phase with slowly decayling correlation near the order-disorder phase boundary for >0.5.     

The basic equations of the dynamics of the continuous distribution of dislocations I. General theory

The basic equations of the dynamics of the continuous distribution of dislocations analogical to Maxwell's equations are derived in a series of papers I, II, III. The analogy of the elastic and electromagnetic fields is analyzed. In part I the basic equations of the continuous distribution of dislocations are derived for the dynamic case (especially for small deformations and for the Poisson ratio equal to zero in a continuum, infinite with respect to space and time, from the variational problem by means of the formal apparatus of the special theory of relativity.

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I.

, . . , , .

     

Über den Einfluss von Stickstopf auf die Exoelektronenemission von Germanium

Zusammenfassung Es wurde der Einfluß eines Bombardements mit Stickstoffionen vor der Erregung untersucht und gezeigt, daß die Stiekstoffatome eine große Rolle bei der Entstehung des Emissionsmaximums bei 150° spielen.

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, 150°C.

     

Charge Fluctuations in the Two-Dimensional One-Component Plasma

We study, via computer simulations, the fluctuations in the net electric charge in a two-dimensional, one component plasma (OCP) with uniform background charge density –e in a region inside a much larger overall neutral system. Setting e=1, this is the same as the fluctuations in N , the number of mobile particles of charge e. As expected, the distribution of N has, for large , a Gaussian form with a variance which grows only as ^||, where || is the length of the perimeter of . The properties of this system depend only on the coupling parameter =kT, which is the same as the reciprocal temperature in our units. Our simulations show that when the coupling parameter increases, ^() decreases to an asymptotic value ^()^(2)/2 which is equal (or very close) to that obtained for the corresponding variance of particles on a rigid triangular lattice. Thus, for large , the characteristic length _L=2^/ associated with charge fluctuations behaves very differently from that of the Debye length, _D1/ , which it approaches as 0. The pair correlation function of the OCP is also studied.     

D=2 and D=4 realization of κ-conformal algebra

We describe the generators of-conformal transformations leaving invariant the-deformed d'Alembert equation. For the case D=4 the algebraic structure of the conformal extension of the off-shell spin zero realization of-Poincaré algebra is discussed. Then the D=2 off-shell realization of-conformal algebra for arbitrary spin and its commutation relations are studied.Presented at the 4th Colloquium Quantum Groups and Integrable Systems, Prague, 22–24 June 1995.Supported by KBN grant 2P 302 087 06.     

Group velocity difference effect on incoherent sum-frequency generation spectrum

The spectral distribution of optical sum-frequency generation (SFG) by incoherent non-linear mixing of two chaotic beams with identical spectral width is calculated theoretically in the first approximation of the iterative method including dispersion of the non-linear medium and the difference between the group velocity of the input beams. It is shown that for the same group velocities (=0) of the input beams in non-linear medium the resultant field has a spectral width narrower than , and if a phase mismatch is present the spectral maximum of the resultant field is shifted towards lower or higher frequencies according to the sign of the phase mismatch. If the input beams have different group velocities (0) in the non-linear medium, then the spectral distribution of SFG is strongly dependent on . For small the spectral distribution of SFG is the same irrespective of . For large the difference in group velocities broadens the spectrum of SFG and for very large differences in group velocity the SFG has a spectral width identical to that of the input beams.     

Second-harmonic generation at periodic second-order susceptibility gratings with self-phase and cross-phase modulation

Quasi-phase-matched second-harmonic generation at periodic quadratic susceptibility gratings with self-phase and cross-phase modulation owing to Kerr nonlinearities is investigated. A model of interaction of monochromatic plane travelling waves is considered. The solution assumes a nondepleted pump and results for a numerical computation of second-harmonic conversion efficiency for a highly efficient process are presented. It is shown that for high spatial-frequency gratings the efficiency of second-harmonic generation depends on the reduced detuning and the Kerr-nonlinearity coefficient only. In some cases, if the signs of and are opposite, the Kerr nonlinearity can enhance the second-harmonic conversion efficiency due to the compensation of the phase mismatch attained in the below-half-conversion stage by the reversed phase mismatch in the above-half-conversion stage of the process. The computed maximum conversion efficiencies for various values of and are plotted in a contour map on the - plane.     

Structural relaxation effects on the low-temperature properties of vitreous silica

Measurements of the low-temperature specific heatC and thermal conductivity of vitreous silica after heat treatment at temperaturesT _a between 900°C and 1,400°C are reported. A decrease ofC and an increase of are observed over the whole temperature range studied (C0.06K<T<6K; 0.5 K<T<20 K). Below 1 K the changes inC and (10%) are attributed to a dependence of the density of tunneling states on the fictive temperature. Measurements of the thermal conductivity show that these changes are reversible, thus strongly supporting the evidence for a connection between the tunneling states and the quasi-equilibrium state which is frozen in when an undercooled liquid drops out of thermal equilibrium. Our results are compared to predictions of the free-volume theory of the glass transition. At higher temperaturesC decreases by roughly the same amount as below 1 K while increases by up to 30%. The dependence ofC and onT _a cannot be explained unambigously in terms of a phonon-fraction crossover in the vibrational density of states. Instead, a recently proposed model of coupled SiO₄ rotations is favored.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Effect of electrolytically deposited nickel films on the magnetic properties of iron-silicon alloy

The effect of electrolytically deposited nickel films on the magnetostriction, coercive force, residual induction, and the position with respect to each other of the magnetic susceptibility maxima _max. _max of specimens of iron-silicon alloy is investigated. It is shown that elastic extensions lead to a reduction in the spacing between the maxima _max, _max , and for certain loads this spacing disappears and only one maximum is observed.     

Nonlocal structures: Bilocal photon

As a starting point, it is postulated that all particles and fields are built from a single primitive field, which must then be a massless fermion with a spin of one-half. Two helicities are embodied in a spin of one-half. The vacuum is an open Fermi sea whose height is a wave number . Elementary particles are structures having the form of standing-wave systems floating on the vacuum sea, with the height providing both the scale of inner structural size and the mass unit for the elementary particle mass spectrum. A bilocal photon starts with a function describing two primitive quanta with parallel spin and opposite spin. A centroid-time wave equation then couples-in an infinite set of orthogonal functions. The introduction of an operatorQ permits the reduction of the infinite secular determinant to a finite six-by-six determinant. Solutions (for the infinite expansion) are obtained describing photons with right-handed and left-handed polarizations. Superpositions of these give linearly polarized photons. Electric and magnetic field vectors, satisfying the vacuum Maxwell equations, are obtained from a bilocal Hertz vector given by = (2/³ c)(/t _r)_r(1,2), where (1,2) is the bilocal wave function, and t_r and r are the relative time and relative position variables.     

Grassmann-Cartan algebra and Klein-Gordon equations

Given a Riemannian structure (M, g), a hypothesis is investigated that if= _p=0 ⁿ _p (M) is submitted to the differential condition (g++)=0, =mc/—which implies that each component of fulfills the Klein-Gordon equation (- ²) _p =0, ought to be interpreted as a natural complex of the bosonic fields. Then it is found that the complex admits the interpretation in the sense of first quantization with (M) being a convex set of states, with the structure of a Hilbert space over . The definite spin states of bosons are then pure states which are not conserved by the temporal evolution.     

Stability of Schrödinger eigenvalue problems

We derive a general stability criterion for discrete eigenvalues of Schrödinger operators, such asA()=p ²+V(x, ), using only strong continuity ofA() andA*() in the perturbation parameter . The theory is developed for non-selfadjoint operators and illustrated with examples like the anharmonic oscillator, the Stark and the Zeeman effect. The principal tools are Weyl's criterion for the essential spectrum and a construction due to Enss [5]. They are also used to extend the classical invariance theorems for the essential spectrum to certain singular perturbations, including some local perturbations of the Laplacian by differential operators of arbitrary high order.     

First-passage-time approach to overbarrier relaxation of magnetization

We consider the irreversible dynamics of the magnetization vectorM in a single-domain particle. The dynamics is given by a stochastic phenomenological equation due to Gilbert. It contains a damping field proportional toM and a corresponding white noise field component. The probability distribution function satisfies a Fokker-Planck equation derived by Brown. We give the overbarrier decay rate out of a metastable minimum. First we rederive the well-known expression for for an axially symmetric model. We argue that this result is unphysical. For systems of general point symmetry of the magnetic anisotropy energy we give in both the low-damping and intermediate- to high-damping limits.     

Towards κ-deformed D=4 relativistic field theory

We describe free relativistic fields on noncommutative -deformed D=4 Minkowski space. Three possible types of -deformed Fourier transforms are discussed, related with three different -deformed mass-shell conditions.     

Equivalence of vacuum Yang-Mills gravitation and vacuum Einstein gravitation

In the Yang-Mills formulation of gravitational dynamics based uponSL(2,C) spin transformations acting on Dirac spinors, the vacuum field equations are R +C R = 0 and and . HereR is the Ricci curvature andC is the Weyl conformal curvature; is a coupling constant. We show the equivalence between solutions of these equations and the vacuum Einstein equationsR = 0. The proof uses the Newman-Penrose formalism.Supported by a NATO fellowship.Supported by a SRC fellowship.     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

The iteration method in multiple scattering: The transfer equation

Using the iteration method, the author obtains the transfer equation for the scattering of electromagnetic waves in a system comprising a large number of statistically independent particles spherical in shape under the condition c^–1 1 c is the density of the number of particles, the scattering cross section for a single particle, and the wave number. The method is easily extended to the scattering of scalar waves.In conclusion the author expresses his thanks to V. E. Zuev and S. D. Tvorogov for their guidance and observations on the study.     

Time production and spatial distribution of macroscopic space charges in D-C discharge plasma

It is shown for a one-dimensional approximation that, around a disturbance in the ion concentrationn ₊(x, t) in the axial direction of a cylindrical plasma, a corresponding electron distributionn _–(x, t) is established with such a large velocity that under the usual conditions of a discharge plasma this electron distribution follows the relatively slow changes in ion concentration practically without delay. Relation (24) then holds for the electron concentration, the parametersl ₁,l _D being given by Eqs. (15) and (16). As long as the disturbance of the ions isn ₊(x) 0, a space chargeq ₀(n ₊-n_–) is produced and maintained in the plasma even if the disturbance of the equilibrium state of the plasma in the initial stage was electrically neutral (i.e.n ₊(x, t=0)==n _–(x,t=0)). The dimensions of these space charges can be many orders larger than the Debye characteristic lengthl _D ; this is shown on an example of a spatially periodic curven ₊(x). The unique (quasi-stationary) expression of the electron concentrationn _– by means of the deflection of the ion concentrationn ₊(x, t) permits a considerable simplification of the solution of the problems connected with axially disturbing the homogeneous state of a plasma, sincen _–(x, t) can be eliminated from the equations of continuity of the plasma by substituting from (24), and the problem becomes that of determining the curve of the ion concentrationn ₊ from the equations modified in this way.

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, ₊(, t) - _–(, t) , . (24), l ₁ l _D (15) (16). ₊() 0, q ₀(n₊ — n_–), , (..n ₊(x,0)=_–(, 0)). () _{– +}(, t) , , . . _–(, t) n ₊ .

     

Calculation of positron states in the BEDT-TFF based organic superconductors

Positron states in the BEDT-TTF based organic superconductors, namely -Cu(NCS)₂, -CuCN[N(CN)₂] and -Cu[N(CN)₂]Br salts, have been calculated using the superposedatom model and the numerical relaxation technique. For each salt positrons are distributed predominantly around the anion layers and have a little overlap with the TTF skeleton and the outer S atoms which are responsible for the conductivity.