Logarithmic Energy Dependence Research Articles

Microscopic Mechanism of the Heat-Induced Blueshift in Phosphors and a Logarithmic Energy Dependence on the Nearest Dopant-Vacancy Distance.

Heat-induced blueshift (HIB) observed in many luminescent materials is a puzzling phenomenon that has remained unexplained for decades. By using the high-throughput first-principles calculations and energy-screening techniques, we generated a number of model structures for five phosphors, RbLi[Li3 SiO4 ]2 :Eu2+ , Na[Li3 SiO4 ]:Eu2+ , K[Li3 SiO4 ]:Eu2+ , Sr[LiAl3 N4 ]:Eu2+ , and Ca[LiAl3 N4 ]:Eu2+ . Our analyses suggest, to a first approximation, a logarithmic energy dependence on the nearest distance between the dopant and the metal-cation vacancy. By identifying the transition energies from the electronic structures calculated for the screened model structures, we show that the vibration of the Eu2+ ion lying in an asymmetric and anharmonic potential well couples with the electronic states, leading to their HIB phenomena.

Microscopic Mechanism of the Heat‐Induced Blueshift in Phosphors and a Logarithmic Energy Dependence on the Nearest Dopant–Vacancy Distance

Heat-induced blueshift (HIB) observed in many luminescent materials is a puzzling phenomenon that has remained unexplained for decades. By using the high-throughput first-principles calculations and energy-screening techniques, we generated a number of model structures for five phosphors, RbLi[Li3SiO4]2:Eu2+, Na[Li3SiO4]:Eu2+, K[Li3SiO4]:Eu2+, Sr[LiAl3N4]:Eu2+, and Ca[LiAl3N4]:Eu2+. Our analyses suggest, to a first approximation, a logarithmic energy dependence on the nearest distance between the dopant and the metal-cation vacancy. By identifying the transition energies from the electronic structures calculated for the screened model structures, we show that the vibration of the Eu2+ ion lying in an asymmetric and anharmonic potential well couples with the electronic states, leading to their HIB phenomena.

Fate of a multiple-band Fermi liquid that is coupled with critical ϕ4 bosons

Multiple-band nature of electronic energy bands leads to novel physical effects in solids. In this paper, we clarify physical properties of a Fermi system with a pair of electron and hole Fermi surfaces (FSs), whose coupling is mediated by a critical U(1) boson field. By using a one-loop renormalization group analysis, we show that when the boson field undergoes a quantum phase transition with broken U(1) symmetry, the multiple-band Fermi system shows a non-Fermi liquid (non-FL) behaviour in its thermodynamic and magnetic properties. At a quantum critical point (QCP), Fermi velocities of the two FSs are renormalized into a same critical velocity as a boson velocity, and the fermion's density of states (DOS) shows a pseudo-gap behaviour with a logarithmic energy dependence at the QCP.

Solar neutrinos, helicity effects and new affine gravity with torsion

New f(R,T) model of gravitation, introduced previously by the author, is considered. It is based on an affine geometrical construction in which the torsion is a dynamical field, the coupling is minimal and the theory is Lorentz invariant by construction. It was shown that the Dirac equation emerges from the same space time and acquires a modification (coupling-like) of the form γαj1-ddγ5hα, with hα the torsion axial vector, j a parameter of pure geometrical nature and d, the spacetime dimension. In the present work it is shown that this interaction produces a mechanism of spin (helicity) flipping, with its consequent weak symmetry violation. The cross section of this process is explicitly calculated and a logarithmic energy dependence (even at high energies) is found. This behavior is reminiscent of similar computations made by Hans Bethe in the context of neutrino astrophysics. These results are applied to the solar neutrino case and compared with similar results coming from a gravitational model with torsion of string theory type and within the standard model context respectively.

Semiclassical position and momentum information entropy for sech2 and a family of rational potentials

The classical and semiclassical position and momentum information entropies for the reflectionless sech2 potential and a family of rational potentials are obtained explicitly. The sum of these entropies is of interest for the entropic uncertainty principle that is stronger than the Heisenberg uncertainty relation. The analytic results relate the classical period of the motion, total energy, position and momentum entropy, and dependence upon the principal quantum number n. The logarithmic energy dependence of the entropies is presented. The potentials considered include as special cases the attractive delta function and square well. PACS Nos.: 03.67–a, 03.65.Sq, 03.65.Ge, 03.65.–w

Small-xBehavior of Parton Distributions from the Observed Froissart Energy Dependence of the Deep-Inelastic-Scattering Cross Sections

We fit the reduced cross section for deep-inelastic electron scattering data to a three parameter ln2s fit, A + beta ln2(s/s0), where s = (Q2/x)(1-x) + m2, and Q2 is the virtuality of the exchanged photon. Over a wide range in Q2 (0.11 < or = Q2 < or = 1200 GeV2) all of the fits satisfy the logarithmic energy dependence of the Froissart bound. We can use these results to extrapolate to very large energies and hence to very small values of Bjorken x-well beyond the range accessible experimentally. As Q2-->infinity, the structure function F2(p)(x,Q2) exhibits Bjorken scaling, within experimental errors. We obtain new constraints on the behavior of quark and antiquark distribution functions at small x.

Gauge Theories in AdS5 and Fine-Lattice Deconstruction

The logarithmic energy dependence of gauge couplings in AdS5 emerges almost automatically when the theory is deconstructed on a coarse lattice. Here we study the theory away from the coarse-lattice limit. While we cannot analytically calculate individual KK masses for a fine lattice, we can calculate the product of all non-zero masses. This allows us to write down the gauge coupling at low energies for any lattice-spacing and curvature. As expected, the leading log behavior is corrected by power-law contributions, suppressed by the curvature. We then turn to intermediate energies, and discuss the gauge coupling and the gauge boson profile in perturbation theory around the coarse-lattice limit.

Logarithmic contribution to the density of states of rectangular Andreev billiards

We demonstrate that the exact quantum mechanical calculations are in good agreement with the semiclassical predictions for rectangular Andreev billiards and therefore for a large number of open channels it is sufficient to investigate the Bohr-Sommerfeld approximation of the density of states. We present exact calculations of the classical path length distribution $P(s)$ which is a non-differentiable function of $s$, but whose integral is a smooth function with logarithmically dependent asymptotic behavior. Consequently, the density of states of rectangular Andreev billiards has two contributions on the scale of the Thouless energy: one which is well-known and it is proportional to the energy, and the other which shows a logarithmic energy dependence. It is shown that the prefactors of both contributions depend on the geometry of the billiards but they have universal limiting values when the width of the superconductor tends to zero.

High energy field theory in truncated anti-de Sitter space.

In this Letter we show that in five-dimensional anti-de Sitter (AdS) space truncated by boundary branes, effective field theory techniques are reliable at high energy (much higher than the scale suggested by the Kaluza-Klein mass gap), provided one computes suitable observables. We argue that in the model of Randall and Sundrum for generating the weak scale from the AdS warp factor, the high energy behavior of gauge fields can be calculated in a cutoff independent manner, provided one restricts Green's functions to external points on the Planck brane. Using the AdS/CFT (conformal field theory) correspondence, we calculate the one-loop correction to the Planck brane gauge propagator due to charged bulk fields. These effects give rise to nonuniversal logarithmic energy dependence for a range of scales above the Kaluza-Klein gap.

Dimensional Transmutation and Dimensional Regularization in Quantum Mechanics: II. Rotational Invariance

A thorough analysis is presented of the class of central fields of force that exhibit: (i) dimensional transmutation and (ii) rotational invariance. Using dimensional regularization, the two-dimensional delta-function potential and the D-dimensional inverse square potential are studied. In particular, the following features are analyzed: the existence of a critical coupling, the boundary condition at the origin, the relationship between the bound-state and scattering sectors, and the similarities displayed by both potentials. It is found that, for rotationally symmetric scale-invariant potentials, there is a strong-coupling regime, for which quantum-mechanical breaking of symmetry takes place, with the appearance of a unique bound state as well as of a logarithmic energy dependence of the scattering with respect to the energy.

Inclusive and diffractive structure functions at small x

In the semiclassical approach, inclusive and diffractive quark and gluon distributions are expressed in terms of correlation functions of Wilson loops. Each Wilson loop integrates the colour field strength in the area between the trajectories of two fast partons penetrating the proton. We introduce a specific model for averaging over the relevant colour field configurations. Within this model, all parton distributions at some low scale Q 0 2 are given in terms of three parameters. Inclusive and diffractive structure functions at higher values of Q 2 are determined in a leading-order QCD analysis. In both cases, the evolution is driven by a large gluon distribution. A satisfactory description of the structure functions F 2( x, Q 2) and F 2 D(3) ( ξ, β, Q 2) is obtained. The observed rise of F 2 D(3) with ξ is parametrized by a non-perturbative logarithmic energy dependence, compatible with unitarity. In our analysis, the observed rise of F 2 at small x is largely due to the same effect.

Unique 6Li-nucleus optical potentials from elastic scattering of 210 MeV 6Li ions by 28Si, 40Ca, 90Zr, and 208Pb.

Differential cross sections for the elastic scattering of /sup 6/Li ions have been measured at a bombarding energy of 210 MeV. Angular distributions for /sup 28/Si (3.6/sup 0/--45.9/sup 0/), /sup 40/Ca (4.6/sup 0/--43.5/sup 0/), and /sup 90/Zr (4.0/sup 0/--43.6/sup 0/) extend sufficiently into the rainbow region to enable the extraction of unique /sup 6/Li potentials. For the /sup 208/Pb target (3.1/sup 0/--36.0/sup 0/), Coulomb scattering dominates with only a slight evidence of nuclear diffraction at the largest angles. The data were analyzed in terms of a six-parameter phenomenological optical-model potential with Woods-Saxon form factors. The unique potentials obtained show a weak target-mass dependence, which allowed the prediction of /sup 208/Pb potential parameters. Using the present results and lower energy analyses, an energy dependence for the /sup 6/Li-nucleus potentials was derived. For all targets, the volume integral per nucleon pair of the real potential seems to satisfy a logarithmic energy dependence of the form J/sub R//6A = J/sup 0//sub R//6A-..beta.. ln E/sub lab/ with J/sub R//sup 0//6A = 830 +- 30 MeV fm/sup 3/ and ..beta.. = 105 +- 5 MeV fm/sup 3/. This result is consistent with elastic scattering of other light ions. By truncating the angular distributions for themore » lighter targets up to the rainbow angle, several discrete potentials, corresponding to the different families found at lower energies, were obtained.« less

Logarithmic energy dependence of the density of states for heavy fermion systems

Logarithmic terms in the energy of Fermi liquids lead to the logarithmic energy dependence of density of states functions. These logarithmic terms account for all anomalies in thermodynamic and transport properties of heavy fermion systems at very low temperatures. The temperature characteristic of these anomalies has nothing to do with the onset of coherence.

Density of states and critical resistivity of strongly disordered systems

Recently we proposed that the anomalous diffusion at short length scales associated with localization is responsible for the unusual sensitivity of the high-${T}_{c}$ superconductors to disorder. We showed that the Coulomb pseudopotential in superconductors is a universal function of $\frac{\ensuremath{\rho}}{{\ensuremath{\rho}}_{c}}$ where $\ensuremath{\rho}$ is the resistivity and ${\ensuremath{\rho}}_{c}$ is a critical resistivity characteristic of the system, and obtained relatively small values of ${\ensuremath{\rho}}_{c}$ from the experimental ${T}_{c}\ensuremath{-}\mathrm{vs}\ensuremath{-}\ensuremath{\rho}$ curves. In the present paper we show that in the strong-disorder region in three dimensions the density of states is also a universal function of the same parameter, so that in the absence of any microscopic calculation of ${\ensuremath{\rho}}_{c}$, a comparison of the density of states and ${T}_{c}$ as function of disorder provides a crucial test of the theory. We find very good agreement with existing data on granular Al. We also find that the density of states has a logarithmic energy dependence in this region, a result independently obtained by Lee. In addition, we make quantitative predictions about where and when to expect this logarithmic correction to be important, and comment on why it has not been observed yet.

Density-of-States Anomalies in a Disordered Conductor: A Tunneling Study

Results of single-particle tunneling experiments performed on films of indium oxide are presented. The zero-bias anomalies change character with decreasing thickness from a three-dimensional behavior to a logarithmic energy dependence. Theoretical consideration suggest a crossover from a $\mathrm{ln}V$ to a ${V}^{\frac{1}{2}}$ correction to the density of states at a thickness-dependent energy. In the ${V}^{\frac{1}{2}}$ range, where the sample exhibits a three-dimensional density-of-states anomaly, its transport properties may still be two dimensional. These expectations are experimentally confirmed.

Elastic scattering of 80-180 MeV protons and the proton-nucleus optical potential

Accurate and extensive measurements have been made of the differential cross sections for the elastic scattering of protons from $^{40}\mathrm{Ca}$, $^{90}\mathrm{Zr}$, and $^{208}\mathrm{Pb}$ targets over an energy range of 80-180 MeV, in the angular range from about 6\ifmmode^\circ\else\textdegree\fi{} to about 90\ifmmode^\circ\else\textdegree\fi{} (to 126\ifmmode^\circ\else\textdegree\fi{} for $^{90}\mathrm{Zr}$ at 135 MeV) in 0.5\ifmmode^\circ\else\textdegree\fi{} to 2.5\ifmmode^\circ\else\textdegree\fi{} steps. The most prominent general feature of the data, namely strong damping of the diffractive oscillations in the mid-angle region (roughly 30-60\ifmmode^\circ\else\textdegree\fi{}), was found to arise from the complex spin-orbit interaction which has a considerably greater influence on the differential cross section at these energies than at lower energies. These data, together with data of comparable quality from other sources in the energy range 60-180 MeV, were analyzed in terms of a 10-parameter phenomenological optical-model potential using relativistic kinematics and a relativistic extension of the Schr\odinger equation. Analyses with various parameter constraints were performed. A logarithmic energy dependence was found for the strengths of the real potentials (central and spin-orbit terms); the corresponding imaginary potentials were found to be essentially independent of energy. While individual model parameters were generally not uniquely defined by the cross section data, volume integrals of the central potentials were well determined. The spin-orbit parameterization was found to be relatively more uncertain, despite the enhanced sensitivity of the cross section to spin dependent terms in the potential at these energies and the inclusion of some existing polarization data in the analysis. Some features of the phenomenological potentials were compared with the predictions of microscopic potential models, and certain aspects of the proton-nucleus interaction at the higher energies have been found to be describable in terms of the free nucleon-nucleon interaction.

On the energy dependence of the real central optical potential for proton-nucleus scattering

The energy dependence of the real central optical potential in the energy range 25–1000 MeV has been determined from optical model analyses of p+ 12C, p+ 16O, p+ 27Al, p+ 40Ca and p+ 208Pb elastic scattering data. The volume integral and the strength can be represented by a relation linear in the incident energy only if a limited energy range is chosen. When the energy range 25–1000 MeV is considered a logarithmic energy dependence gives a better representation of the phenomenological results, especially for the light nuclei.

Shell-Model Combinatorial Calculations of Nuclear Level Densities

Spin-dependent nuclear level densities were calculated for selected nuclides. In each case the numbers and spins of the levels were determined from a computer-generated list of all contributing shell-model configurations. To calculate the energies of the configurations, we assumed the model nucleus to be an infinitely deep spherical well containing fermions that are noninteracting except for pairing forces, for which the BCS theory was used. Comparisons of the calculated results with experimental level densities for odd, even, and odd-mass nuclides show reasonable agreement for nuclides with $Ag50$. The results of calculative investigations of the effects of shell closings, pairing, etc., and the persistence of these effects to high excitation energies and angular momenta are reported and discussed. Comparisons of these results with those obtained from the most commonly used algebraic formula show significant disagreements in the curvature of the logarithmic energy dependence and in the spin distributions.