Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

The series of three papers is focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention paid to the influence of an external magnetic field. In the present paper, various aspects of the Landauer formalism (relating conductances to transmission coefficients) are reviewed. The one-dimensional case is discussed in detail. Some views on its generalization to higher dimensionality are presented. The connection to the linear response theory is briefly discussed. A short account of the Büttiker formalism for systems with more than two probes is given. Further the Landauer formalism is generalized for two-dimensional systems in quantizing magnetic fields. Particular attention is paid to the role of ideal leads where edge states occur.The author wishes to thank Professors P. Steda and L. Smrka for their encouragement and discussion.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

The paper of three parts is focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous part the total conductance of such a system was shown to be proportional to the transmission current. In the present part we give a detailed proof, based on the linear response theory, to the last statement. The value of the magnetic field may be arbitrary and possible inhomogeneity of the electric field is also considered.The author wishes to thank to Professor P. Steda and Professor L. Smrka for discussions and encouragement.     

The effect of low-temperature electron irradiation on the transition temperature of YBa2Cu3O7−δ superconductors

Measurements of the complex susceptibility =–i of electron-irradiated YBa₂Cu₃O_7– show a strong influence of the electron irradiation dose, ·t on the transition temperatureT _c . For irradiation doses of ·t=2.2·10¹⁹ e^–/cm² we find a damage rate of T _c /(·t)=–1.6·10^–19 K/(e^–/cm²). It is assumed that the decrease ofT _c is mainly a bulk effect due to the production of atomic defects like vacancies and interstitials in the Cu–O–Cu chains and in the basal planes of the unit cells.     

Renormalized boson expansion for the 2νββ decay

Two neutrino double beta (2) Gamow-Teller transitions, and , are treated with a many-body Hamiltonian involving a Bonn-type realistic two-body interaction. The states involved in these transitions are described by a pnRQRPA approach. Transition operators are expanded in first order in terms of renormalized bosons. For illustration the formalism is applied to the case Kr.     

Hypernuclear production induced by in-flight K and π

The development in treating K- and -induced hypernuclear production reactions is reviewed, including the application of DWIA to the (K^–, K⁺) reaction to produce ^–. After summarizing the conventional DWIA treatment without spin-dependence, we discuss the calculational method of strength functions up to the continuum. Finally the process is reformulated starting from the elementary amplitudes with the spin-flip component as well as the spin-nonflip one. The new treatment is shown to be powerful and the emphasis is put on the production of polarized hypernuclei, which provides a useful spectroscopic tool for the weak-decay mechanism.Dedicated to our distinguished collaborator, Professor Jan ofka (1943–1991), to the memory of his inspiration in hypernuclear physics and his wide, friendly activities in our community.The authors are very grateful to the late Professor Jan ofka who was a distinguished collaborator for a long time. He coordinated many collaborations between e and Japan. We will miss his scientific and organizational activities in hypernuclear physics. The authors express their thanks to O. Richter, M. Sotona, R. Wünsch, H. Ejiri and T. Kishimoto for collaboration and discussion on several parts of the calculated results. This work has been supported by the Grant-in-Aid for Scientific Research (C) and also by A Grant under The Monbusho International Scientific Research program (Joint Research 1990–1991).     

Anomalous dimensions in local and non-local light cone expansion

Anomalous dimensions of operator products are considered in the general case of non-diagonal matrix elements both in local and in non-local version of light cone expansion for quantum chromodynamics. Results are reviewed shortly.Presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.     

Lorentz boosts in de Sitter and anti-de Sitter space-times

Symmetries of de Sitter and anti-de Sitter space-times are discussed. In particular, Lorentz boosts, which appear to be given previously only in the infinitesimal form, are presented here in closed finite forms.Dedicated to the memory of Professor Jozef Kvasnica.I would like to thank Prof. Jií Biák and Dr. Hans-Jürgen Schmidt for useful discussions.     

On the sign of cos θ at the branch points of a partial wave amplitude in thes-plane

The sign of the cosine of the scattering angle, cos, at the branch points of a relativistic two-body partial wave amplitude with arbitrary masses in the complexs-plane is determined. The results yield that as to the tops-sheet, (i) the sign of cos is the same at the complex conjugated branch points which lie off the reals-axis, and (ii) cos changes sign at the (direct channel) thresholds. The difference between the elastic and inelastic cases is emphasized. It is pointed out that in certain physical energy ranges, for some collisions (e.g. + N + N), the directions near the backward direction can be considered as the most important ones, while for several other collisions (e.g. + N + N) the directions into the forward hemisphere have the strongest influence.The author would like to thank Professor G. Höhler for his kind hospitality at the Institut für theoretische Kernphysik, University of Karlsruhe. He is grateful to him and to the members of that Institute for valuable discussions. Correspondence with Dr. Jens Lyng Petersen, which gave rise to the present investigation, is also acknowledged.     

π0 → γγ in the Spinor Strong Interaction Theory

An expression for the decay rate (⁰ ) has been derived in the frameworkof the spinor strong interaction theory, a first-principles strong interaction theoryproposed some years ago as an alternative to low-energy QCD. The startingpoint is the SO(3) gauge-invariant action for two quark mesons which has beensuccessful in accounting for confinement, ^{+ +} , e⁺, and ⁰ e⁺, nonexistenceof the Higgs boson, and other low-energy mesonic phenomena. The quasi-four-quarkmeson equations developed for the decay of a vector meson into twopseudoscalar mesons V PP has been taken over here to apply to P(⁰) VV(^{+ –}) (plus ⁺ and ^– which annihilate each other). This mechanismin principle agrees with that of the assumption of vector meson dominance inthe literature. It, together with the effect of form factors, arises naturally in theformalism and need not be assumed. Equations for the perturbed vector mesonwave functions cannot be simply solved and an assumption has been made toobtain an estimate of their magnitude. Together with a constant associated withthe strong coupling obtained earlier from V() PP(K⁺K^–), the estimated decayrate is 19.2 eV, in order-of-magnitude agreement with data (7.74 eV).     

Second-quantization representation and diagrammatic technique for systems of composite particles

A second-quantization formalism for systems of interacting free elementary particles and their bound clusters is presented. A modified version of the Feynman-Goldstone diagrammatic technique is used for the classification and evaluation of individual terms appearing in this formalism. The resulting effective Hamiltonian naturally includes such processes as Coulomb and exchange interactions between bound composite particles, their breakup and recombination reactions, etc. For simplicity, a system of hydrogen atoms, protons, and electrons is studied. The method can easily be generalized to any species of composite particles.Dedicated to Professor Alexander Tká on the occasion of his sixtieth birthday.     

A finite size analysis of the structure factor in the antiferromagnetic Heisenberg (AFH) model

From a finite size analysis we extract the structure factorS(p, N=) of the one dimensional AFH-model in the groundstate: The gross structure is well described byL (p) = –ln(1– ^p ). The fine structure which only contributes a few percent reveals a pronounced non-linear behavior inL(p) with a maximum atp=0.20 and a minimum atp=0.82.     

Spatial Spectrum of Artificial Ionospheric Irregularities Induced by Powerful HF Radiowaves

We present measurement results and spatial-spectrum shapes of the dependence of the relaxation time on the scale across the geomagnetic field for artificial ionospheric irregularities (AIIs) induced in the upper ionosphere by powerful HF radiation of the SURA heating facility. The irregularity diagnostics was based on observing amplitude scintillations of a 243-MHz beacon signal from a quasi-geostationary, solar-synchronous satellite and on measuring field-aligned scattering at frequencies 15 and 20 MHz. The satellite signal was received at the Kazan State University Observatory. The field-aligned scattering signals were received and analyzed by a bistatic HF radar based on the UTR-2 radio telescope located near Kharkov (Ukraine). It is shown that irregularities of the electron density, whose two-dimensional spectrum in the plane perpendicular to the geomagnetic field is the power law æ ^-p with index p2, are developed in the scale range 30–60 l 200–400 m. In this case, the relative fluctuations (N²)^1/2 of the electron density increase with decreasing scale l=2/æ. The estimate N²)^1/2 1–1.5% is obtained for a heating power of 150 MW and irregularity scales l 30–60 m at which the fluctuations are maximum. The measured dependence of the AII relaxation time, defined as the e-folding time of the amplitude-scintillation intensity, has the form _r l . If l 30–60 m, then the index is close to 2, whereas the effective diffusion coefficient D (2–3)· 10^-1 m²/s corresponds to the ambipolar cross-field diffusion coefficient in a magnetized plasma. The time _r for scales l 60–100 m is independent of l and increases with decreasing velocity of regular drift of the plasma. The Doppler-spectrum broadening (²)^1/2 0.6 Hz observed when receiving field-aligned scattered signals can be related to chaotic motions of plasma-density disturbances whose random drift velocities amount to (v²)^1/2 2–3 m/s for scales l 20 m at which the power-law index changes drastically.     

The central limit theorem for the spectrum of the random one-dimensional Schrödinger operator

Let H_L = –d²/dt²+q(t,) be an one-dimensional random Schrödinger operator in ²(–L, L) with the classical boundary conditions. The random potential q(t,) has a form q(t, )=F(x_t), where x_t is a Brownian motion on the Euclidean v-dimensional torus, FS^v R¹ is a smooth function with the nondegenerated critical points, min_s ^v F = 0. Let are the eigenvalues of H_L) be a spectral distribution function in the volume [– L,L] and N() = lim_L(1/2L)N_L() be a corresponding limit distribution function.Theorem 1. If L then the normalized difference N _L ^* ()=[N_L() -2L·N()]2L tends (in the sense of Levi-Prokhorov) to the limit Gaussian process N^*(); N^*()0, 0, and N^*() has nondegenerated finitedimensional distributions on the spectrum (i.e., > 0). Theorem 2. The limit process N^*() is a continuous process with the locally independent increments.     

Mosaic Structure of (001)YBa2Cu3O7-δ/(10.2)Al2O3 Epitaxial Films and Millimeter Waveband Properties of Microstrip Resonators

The c-axis single-phase YBa₂Cu₃O_7- films ( = 0-0.15) on sapphire substrates prepared by the laser ablation technique and the band-pass stripline resonators for 34 GHz-range have been investigated. Increasing disorientation of mosaic block structure of YBa₂Cu₃O_7- films is related to increasing surface resistance R_s at 135 GHz-range and decreasing unloaded quality factor Q_o of linear stripline resonators. The linear dependence between the YBa₂Cu₃O_7- film mosaicity (M) and half-width B₁ of 00.13 reflecting component is determined. The reflection spreading is due to microstrains resulted mainly from the coherent adjustment of the YBa₂Cu₃O_7- film lattice to GdBa₂Cu₃O_7- sub-layer and sapphire substrate. Increasing number of the block characterized by a weak radial lattice adjustment () is demonstrated by spreading of 00.13 reflection. It is found out that depends on the Bragg angle of reflection due to inhomogenity of YBa₂Cu₃O_7- mosaic structure, which resulted from the gradual mosaicity decreasing with the depth.     

The Strange Story of the Concept which Inaugurated Modern Theoretical Physics

The strange Story of the Concept which inaugurated Modern Theoretical Physics is the title of a lecture which I delivered on the invitation of Professor Franco Selleri at the University of Bari about 20 years ago. Since Professor Selleri himself has written several interesting papers on this concept and since the centennial of the birth of modern theoretical physics will be celebrated soon, I found it appropriate to dedicate this essay, containing so far unpublished critical and historical comments on this concept, to Professor Selleri on the occasion of his 70th birthday. It should be emphasized that the critical comments in this essay are not intended to question the validity of the theory initiated by this concept, a theory which in the realm of its applicability is daily corroborated by numerous experiments in high-energy laboratories all over the world. Although these critical remarks refer almost exclusively to the first publication of this theory, a publication which has been hailed as the most important paper written in the 20th century, they discuss profound problems of general importance for the study of the foundations of physics.     

On the mechanism of the induced anisotropy of magnesium ferrites in the range of higher temperatures

A simple mechanism explaining not only the magnitude but also the type of induced anisotropy on the magnesium ferrite Mg_0·78 Fe_2·22 O_4·026 in the temperature range from 400 to 500°K has been designed. The experimentally estimated values of the microscopic bond energyl _p 7×10^–16 erg of the configuration contributing to theF-type anisotropy and the activation energy _exp = 1·1 eV are in good correspondence with the valuesl _d1·6×10^–16erg and _cal = 1·1₅ eV which have been calculated theoretically.Dedicated to Professor Dr. Jaromír Bro on his sixtieth birthday.The author would like to express his thanks to Dr. S. Krupika for valuable discussions and his interest in this paper.     

Soft mode dynamics and spatio-temporal symmetry breaking in a thermo-convective system

Using neutron scattering we have studied the behaviour of an oscillatory soft mode in a thermoconvective liquid crystal. As a function of an applied vertical temperature difference T the behaviour of the soft-mode frequency defines four regimes, separated by cross-over values at which spatio-temporal symmetry is broken. Breaking of time symmetry manifests itself in different phase relations among localized oscillators. Incomplete softening at the convection threshold T _c is interpreted as anharmonic coupling to low-energy, internal director fluctuations in the nematic. Subtracting the anharmonic contribution, the renormalized frequency squared gives a susceptibility critical index for each of the four regimes. The values range between 1.1 and 2.7, indicative of a change of the spatial dimensionality as TT _c. The widths in T of the regimes converge as the Feigenbaum ratio (4.6), and the meaning of this is discussed.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

On the homology of lattice vibrations of alkali metals

Investigations of the dependence of lattice vibrations of alkali metals on their interatomic distance,r reveal that they satisfy an empirical relation,Mv ² r =(q), a constant which depends on, with q=2·48 ± 0·19 at all wave vectors and hence are homologous. It is shown that the observed crossover of [00] branches of lithium is not an anomalous property, but only manifests itself in alkali metals with smaller interatomic distance due to small variations of . The role played by interatomic distance which is closely related to that of the electron gas constantC in producing a crossover and a possible reason for the observed homology are discussed.The authors are grateful to Professor B. Sharan and Mr. S. B. Rajendraprasad for many valuable and stimulating discussions. One of the authors (M. S.) is greatly indebted to Professor D. M. Sen, principal, and Professor L. V. Sud of Regional Engineering College, Kurukshetra, for granting him study leave.     

Calculation of Out‐of‐Plane Vibrations of a Porphin Molecule

Using the DFT/B3LYP method with the base set 631G^**, we carried out calculation of the frequencies of the normal vibrations of porphin and of its five isotopic types. Scaling of force constants for outofplane vibrations has been performed in independent natural coordinates. The symmetry coordinates are introduced and a force field for outof plane vibrations of a porphin molecule in independent coordinates of symmetry is obtained. A new correlation of the frequencies of vibrations in the type of the symmetry B _1u for the isotopic type of the d ₂ porphin molecule is suggested on the basis of discrete analysis of the distribution of a potential energy.     

Scalar mesons in ππ and K¯K scattering

The s-wave pion scattering amplitude is analysed with the aim to clarify the mass spectrum of scalar mesons and to find evidence of lightest glueball. The S-matrix and K¯K coupled channel formalism is used. The existence of scalar mesons S^* and is implied by the data. The production K¯K and the elastic K¯KK¯K coupled amplitudes are predicted from the scattering data. The couplings c f S^* to and K¯K states are determined.