Quantum size effects in the fermi energy and electronic density of states in a finite square well thin film model

The dependence of the Fermi energy, E_F, and the electronic density of states, ρ(E), of thin metallic films (L_z ≲ 50 Å) on film thickness, electron density, and potential well depth, is systematically investigated in a free-electron, finite square well model. Two size-dependent effects are observed: (1) oscillations in E_F and ρ(E) due to the size-quantization of the energy levels, and (2) changes in the mean values of these quantities, averaged over several oscillation periods, relative to their bulk values. The mean value of E_F is increased relative to its bulk value by as much as 5%–10% for physically reasonable well depths and typical metallic electron densities. For the special case in which the top energy level in the well is occupied, the mean value of E_F is equal to its bulk value. The mean value ofρ(E_F) can be either greater than or less than its bulk value, depending on the well depth. In contrast to the small amplitude oscillations in E_F, the oscillations in ρ(E_F) may have an amplitude as large as 25% of the mean value for sufficiently thin films. Accurate analytic expressions for the thickness dependence of the Fermi energy and density of states are derived.     

The effect of screening on the x and Q2 behaviour of F2 slopes

A systematic study of ϖF₂(x, Q²)/ϖ ln Q² and ϖ ln F₂(x, Q²)/ϖ ln(1/x) is carried out in pQCD taking screening corrections into account. The result of calculations, which are different from the non-screened DGLAP prediction, are compared and shown to agree with the available experimental data as well as a pseudo data base generated from the ALLM'97 parameterization. This pseudo data base allows us to study in detail our predictions over a wider kinematic region than is available experimentally, and allows us to make suggestions for future experiments. Our results are compared with the GRV'94 parameterization (which is used as an input for our calculations) as well as the recently proposed MRST structure functions.     

Simulation and optimization of deep violet InGaN double quantum well laser

The performance characteristics of a deep violet InGaN double quantum well laser diode (LD) such as threshold current (I_th), external differential quantum efficiency (DQE) and output power have been investigated using the Integrated System Engineering Technical Computer Aided Design (ISE-TCAD) software. As well as its operating parameters such as internal quantum efficiency (η_i), internal loss (α_i) and transparency threshold current density (J₀) have been studied. Since, we are interested to investigate the mentioned characteristics and parameters independent of well and barrier thickness, therefore to reach a desired output wavelength, the indium mole fraction of wells and barriers has been varied consequently. The indium mole fractions of well and barrier layers have been considered 0.08 and 0.0, respectively. Some important parameters such as Al mole fraction of the electronic blocking layer (EBL) and cavity length which affect performance characteristics were also investigated. The optimum values of the Al mole fraction and cavity length in this study are 0.15 and 400 μm, respectively. The lowest threshold current, the highest DQE and output power which obtained at the emission wavelength of 391.5 nm are 43.199 mA, 44.99% and 10.334 mW, respectively.     

On a class of nonstandard quantum algebras and their representations

The nonstandardU _z sl(2, IR) quantum algebra is considered together with other nonstandard algebras sharing the same universalR-matrix as well as a fixed Hopf subalgebra. Some boson realizations for these nonstandard algebras are obtained which are later used in order to compute in a simplified way their (finite and infinite dimensional) representations. In the limit when the deformation parameterz vanishes these realizations turn into the well known (one or two-boson) Gelfand-Dyson realizations for the corresponding classical Lie algebras.     

Infinite dimensional geometry and quantum field theory of strings. III. Infinite dimensional W-geometry of a second quantized free string

The present paper is devoted to various objects of the infinite dimensional W-geometry of a second quantized free string. Our purpose is to include the W-symmetries into the general infinite dimensional geometrical picture related to the quantum field theory of strings, which was described in part I of this series of papers. It is done by replacing the Lie algebra of all infinitesimal reparametrizations of a string world-sheet by the Lie quasi(pseudo)algebra of classical W-transformations (Gervais-Matsuo quasi(pseudo)algebra) as well as the Virasoro algebra by the central extended enlarged Gervais-Matsuo quasi(pseudo)algebra. A way to obtain W-algebras from the classical W-transformations (i.e. Gervais-Matsuo Lie quasi(pseudo)algebra) is proposed. A relationship between Gervais-Matsuo differential W-geometry and the Batalin-Weinstein-Karasev-Maslov approach to the geometry of nonlinear Poisson brackets as well as L.V. Sabinin's program of “nonlinear geometric algebra” is mentioned.     

Multiparameter deformed and non-standard Y(glM) Yangian symmetry in a novel class of spin Calogero-Sutherland models

It is well known through a recent work of Bernard, Gaudin, Haldane and Pasquier (BGHP) that the usual spin Calogero-Sutherland (CS) model, containing particles with M internal degrees of freedom, respects the Y(gl_M) Yangian symmetry. By following and suitably modifying the approach of BGHP, in this article we construct a novel class of spin CS models which exhibit multiparameter deformed or ‘non-standard’ variants of Y(gl_M) Yangian symmetry. An interesting feature of such CS Hamiltonians is that they contain many-body spin-dependent interactions, which can be calculated directly from the associated rational solutions of the Yang-Baxter equation. Moreover, these spin-dependent interactions often lead to ‘anyon-like’ representations of the permutation algebra on the combined internal space of all particles. We also find the general forms of conserved quantities as well as Lax pairs for the above-mentioned class of spin CS models, and describe the method of constructing their exact wave functions.     

Magnetization and dynamically induced finite densities in three-dimensional Chern-Simons QED

In (2 + 1)-dimensional QED with a Chem-Simons term, we show that spontaneous magnetization occurs in the context of finite density vacua, which are the lowest Landau levels fully or half occupied by fermions. Charge condensation is shown to appear so as to complement the fermion anti-fermion condensate, which breaks the flavor U(2N) symmetry and causes fermion mass generation. The solutions to the Schwinger-Dyson gap equation show that the fermion self-energy contributes to the induction of a finite fermion density and/or fermion mass. The magnetization can be supported by charge condensation for theories with the Chem-Simons coefficient κ = Ne²2gp, and κ = Ne²/4π, under the Gauss law constraint. For κ = Ne²/4π, both the magnetic field and the fermion mass are simultaneously generated in the half-filled ground state, which breaks the U(2N) symmetry as well as the Lorentz symmetry.     

Radiation force of acoustical tweezers on a sphere: The case of a high-order Bessel beam of quasi-standing waves of variable half-cone angles

Using the partial-wave series for the acoustic scattering of a high-order Bessel beam (HOBB) of counterpropagating quasi-standing waves of variable half-cone angles, a generalized radiation force expression is obtained. The radiation force function, which is the radiation force per unit cross-sectional surface and unit characteristic energy density, is expressed in terms of the order m of the HOBB, the quasi-standing waves’ amplitudes Φ₀ and Φ₁, as well as the variable half-cone angles β₁ and β₂. The features of the theory include the ability to suppress two resonances as well as exploring a broad range of parameters related to the beam shape and mechanical properties of the spherical target.     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

Effect of disorder and isotope on the properties of a two orbital double exchange system

A two-site single electron double exchange model incorporating orbital degeneracy, superexchange and electron-phonon (e-ph) interaction is studied using exact diagonalization method. The core spins are treated quantum mechanically. We study the ground state phase diagram as well as the magnetic susceptibility and the kinetic energy of the system as a function of temperature. Effect of difference in site energies, which mimics the role of site-diagonal disorder, is investigated. The susceptibility shows a peak at a characteristic temperature which we have referred to as T₀. The variation of T₀ with e-ph coupling and that of the isotope-shift exponent (α) with T₀ are obtained. We also investigate the field-induced change in the kinetic energy, which is related to the colossal magnetoresistance (CMR) of the system, and find that the disorder enhances the CMR even for the two-site system.     

Inflationary models with exponential potentials

In this paper we consider cosmological models containing a self-interacting scalar field possessing a potential of the form V(φ) = Λ exp(−λφ). We investigate the inflationary nature of the model in an (N + 1)-dimensional Friedman space-time as well as in some (3 + 1)-dimensional anisotropic cosmological models. We determine the conditions under which power-law inflation occurs by a detailed stability analysis which determines all possible asymptotic behaviour. We also present some new exact solutions which exhibit the transition to power-law inflation. We determine the range of evolutionary behaviours in each case for all λ ⩾ 0 and find the range of λ values for which power-law inflation occurs. We also discuss how potentials of the exponential type may arise in realistic models of the early universe.     

Statistics of event by event fluctuations

Following Hwa and Wu [R.C. Hwa, Y. Wu, Phys. Rev. C 60 (1999) 0544904], we characterize the fluctuation behavior of the hadron density produced during quark-hadron phase transition, as modeled by a 2D Ising model. Using a recently developed discrete wavelet based approach, the scaling behavior is studied at temperatures below, at and above T_c. At T_c, we find the Hurst exponent H?1, as observed in a recent experimental finding [L. Qin, M. Ta-chung, Phys. Rev. D 72 (2005) 014011]. However, as compared to the R/S analysis, which yields only the Hurst exponent, our local approach finds a correlation behavior and multifractal properties at temperatures below, at and above T_c. We find evidence for a transition from Brownian to fractional Browian motion near T_c. The correlation behavior compares well with the results obtained from a continuous wavelet based average wavelet co-efficient method, as well as with Fourier power spectral analysis.     

Electrooptical modulation in the Stark-ladder regime

A direct measurement of the in-plane birefringence below the absorption edge of a GaAs/AlAs superlattice (SL) under electric fields shows a unique type of electrooptical modulation. The SL is sandwiched between two doped AlGaAs alloy layers, which play the simultaneous role of positive (p ⁺) and negative (n ^?) contacts, as well as clad layers, to achieve optical waveguiding. The p-(SL)-n structure is chosen so that, as a function of the externally applied bias, it displays Stark-ladder localization and the quantum confined Stark effect at low and high fields, respectively. We show that this results in an electrooptical modulation, in which the built-in birefringence of the SL initially decreases and shows a crossover to a quadratic increase for larger fields.     

A grand unified wave function

A variant of wave functions describing all fundamental fermions (quarks and leptons) is presented. It represents a peculiar pattern of generations, of which the first consists of (v_e, e, u, d; v_μ, μ, c, s) and the second contains quarks and leptons with unorthodox electric charges as well as τ, v_τand b.     

Correlated states and transparency of a barrier for low-energy particles at monotonic deformation of a potential well with dissipation and a stochastic force

The features of the formation of correlated coherent states of a particle in a parabolic potential well at its monotonic deformation (expansion or compression) in finite limits have been considered in the presence of dissipation and a stochastic force. It has been shown that, in both deformation regimes, a correlated coherent state is rapidly formed with a large correlation coefficient |r| → 1, which corresponds at a low energy of the particle to a very significant (by a factor of 10⁵⁰–10¹⁰⁰ or larger) increase in the transparency of the potential barrier at its interaction with atoms (nuclei) forming the “walls” of the potential well or other atoms located in the same well. The efficiency of the formation of correlated coherent states, as well as |r|, increases with an increase in the deformation interval and with a decrease in the deformation time. The presence of the stochastic force acting on the particle can significantly reduce the maximum |r| value and result in the fast relaxation of correlated coherent states with |r| → 0. The effect of dissipation in real systems is weaker than the action of the stochastic force. It has been shown that the formation of correlated coherent states at the fast expansion of the well can underlie the mechanism of nuclear reactions at a low energy, e.g., in microcracks developing in the bulk of metal hydrides loaded with hydrogen or deuterium, as well as in a low-pressure plasma in a variable magnetic field in which the motion of ions is similar to a harmonic oscillator with a variable frequency.     

Parity-violating excitation of the Δ(1232): hadron structure and new physics

We consider prospects for stydying the parity-violating (PV) electroweak excitation of the Δ(1232) resonance with polarized electron scattering. Given present knowledge of Standard Model parameters, such PV experiments could allow a determination of the N → Δ electroweak helicity amplitudes. We discuss the experimental feasibility and theoretical interpretability of such a determination as well as the prospective implications for hadron structure theory. We also analyze the extent to which a PV N → Δ measurement could constrain various extensions of the Standard Model.     

Ordering and phase transitions in ising systems with competing short range and dipolar interactions

As a simple model of order-disorder ferroelectrics or dipolar magnets we consider a simple cubic Ising-system with nearest neighbor exchangeJ and dipolar interaction of strengthµ ²/a ³. ForJa ³/µ ²Ja ³/µ ²<0.1270 the ground state consists of ferromagnetic rows (in spin direction) arranged antiferromagnetically in the plane perpendicular to it. AtJa ³/µ ²=0.1279 the structure changes to a layered antiferromagnetic structure with a twocomponent order parameter, while forJa ³/µ ²>0.16429 the ferromagnetic phase becomes stable (with domain arrangements depending on the shape of the sample). For all critical values ofJa ³/µ ² where the bulk energies of two phases become equal also the interface energy between these phases is found to be zero. The ordering at nonzero temperature is studied by means of mean-field approximations (MFA) and Monte Carlo (MC) calculations. It turns out that forJa ³/µ ² of order unity the MFA overestimates ordering temperatures by about a factor of two, and predicts multicritical points (between the disordered and two ordered phases) at nonzero temperature, including two biaxial Lifshitz points which the MC work suggests to occur atT=0. In contrast to MFA the layered antiferromagnetic structure is found to be stable only at extremely lowT, because a metastable spin-glass phase (with random arrangement of ferromagnetic rows in the spin direction) has only slightly higher energy. The MFA also yields two regimes of helical phases which are “locked in” to the antiferromagnetic phases at uniaxial Lifshitz points occurring at the Brillouin zone boundary. In the MC-work various methods of treating the long-range interaction are investigated. While all kinds of truncations as well as compensating field methods are rather unsatisfactory in our case, Ewald summation techniques yield satisfactory results. Nevertheless strong fluctuations as well as strong finite size effects prevent us from making accurate exponent estimates, but arguments are given that there is no regime of broad visibility of Landaulike critical behavior. Finally the extension of our results to other lattices as well as experimental applications are briefly discussed.     

Supraleitung von Pb- und Sn-Schichten nach Implantation von Mn-Ionen

Ion-implantation is a useful method when preparing dilute alloys, especially of elements with very low solubility like 3d-transition-elements in most non-transition superconductors. A strong decrease inT _c and an increase in the residual resistivity were observed in Pb- and Sn-films doped with Mn-ions. Nonlinearity in theT _c -dependence which was found at very low concentrations (0-100 ppm) is caused by lattice defects. They cannot be avoided if implantation method is used. This was proved by irradiation with nonmagnetic ions of comparable mass (such as Cu or Zn). The linear part in theT _c -depression is compared with results obtained with the quenched film technique by Barth (Pb-Mn) and Schertel (Sn-Mn). A discrepancy to these measurements is found in the case of Sn-Mn. The increase in film resistivity is due to lattice defects as well as magnetic impurities. The magnetic contribution (p/c) _m =(4.5 ± 0.2) μΩ cm/at-% agrees well with a theoretical calculation. Heavily doped Sn-films show a small Kondo-resistance-minimum at 7 K with a depth of 2.5‰ of the residual resistivity.     

Overdamped motion of interacting particles in general confining potentials: time-dependent and stationary-state analyses

By comparing numerical and analytical results, it is shown that a system of interacting particles under overdamped motion is very well described by a nonlinear Fokker-Planck equation, which can be associated with nonextensive statistical mechanics. The particle-particle interactions considered are repulsive, motivated by three different physical situations: (i) modified Bessel function, commonly used in vortex-vortex interactions, relevant for the flux-front penetration in disordered type-II superconductors; (ii) Yukawa-like forces, useful for charged particles in plasma, or colloidal suspensions; (iii) derived from a Gaussian potential, common in complex fluids, like polymer chains dispersed in a solvent. Moreover, the system is subjected to a general confining potential, ??(x)?=?(??|x| ^z )/z (???>?0, z?>?1), so that a stationary state is reached after a sufficiently long time. Recent numerical and analytical investigations, considering interactions of type (i) and a harmonic confining potential (z?=?2), have shown strong evidence that a q-Gaussian distribution, P(x,t), with q?=?0, describes appropriately the particle positions during their time evolution, as well as in their stationary state. Herein we reinforce further the connection with nonextensive statistical mechanics, by presenting numerical evidence showing that: (a) in the case z?=?2, different particle-particle interactions only modify the diffusion parameter D of the nonlinear Fokker-Planck equation; (b) for z????2, all cases investigated fit well the analytical stationary solution P _st(x), given in terms of a q-exponential (with the same index q?=?0) of the general external potential ??(x). In this later case, we propose an approximate time-dependent P(x,t) (not known analytically for z????2), which is in very good agreement with the simulations for a large range of times, including the approach to the stationary state. The present work suggests that a wide variety of physical phenomena, characterized by repulsive interacting particles under overdamped motion, present a universal behavior, in the sense that all of them are associated with the same entropic form and nonlinear Fokker-Planck equation.     

Electronic structure and positron annihilation in alkali metals: Isolation of ionic core contribution and valence high-momentum components

Momentum densities of annihilation pairs from valence as well as from ionic core electrons in alkali metals are calculated ab initio and compared with the experimental results. It is shown that the valence high-momentum components constitute a great deal (23–34% in Na-Cs and probably even more in Li) of the Gaussian part of the angular correlation curves. The average core enhancement factor γ_c ranges from 1.5 (Li) to 7.1 (Cs) and may be well expressed by a logarithmic function of ionic core polarizability. The presented values of γ_c are much higher than the core enhancement factors in the high-momentum (?15 mrad) region which, according to the recent theory of Bonderup, Andersen and Lowy, should not be very different from unity.