scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

LOCAL MOMENT ORDERING IN PERIODIC ANDERSON MODEL

2001 ◽  
Vol 15 (19n20) ◽  
pp. 2583-2594 ◽  
Author(s):  
A. RAMAKANTH ◽  
W. NOLTING ◽  
G. G. REDDY ◽  
D. MEYER ◽  
S. SCHWIEGER
Keyword(s):  
Magnetic Properties ◽  
Spectral Density ◽  
Anderson Model ◽  
Magnetic Ordering ◽  
High Energy ◽  
Localized States ◽  
Periodic Anderson Model ◽  
Self Energy ◽  
Atomic Limit ◽  
Comparison Of The Results

Strongly correlated electron systems are studied with the help of periodic Anderson model (PAM). The PAM in which highly correlated nondegenerate localized states form a subsystem is considered and the focus of study is on magnetic ordering of electrons in these localized states. In order to study the PAM, which is not amenable to exact solution, two approximate schemes are proposed. The first one is called the spectral density approximation (SDA). Guided by the atomic limit, a two-pole ansatz is made for the localized electron spectral density. The spectral weights and the quasiparticle energies are determined by a moment method. From the spectral density, the spin and energy dependent self-energy is evaluated. A principal limitation of this method is that per ansatz, the quasiparticles are of infinite lifetime. To introduce a finite lifetime, a second approximation scheme is proposed where coherent potential approximation (CPA) is applied to PAM. In order to do CPA, an alloy analogy (AA) is required. In the conventional AA, the concentrations α and the atomic levels E of the fictitious alloy are taken from the atomic limit. Since the interest is in the magnetic properties, this AA is not appropriate. Therefore, a modified AA (MAA) is proposed. In MAA, α and E are obtained using the high energy expansion of the Green's function and the self-energy. In both the approximations, the density of states and the magnetization are selfconsistently evaluated and a phase diagram is obtained. Comparison of the results of the two schemes brings out the effect of quasiparticle damping on the magnetic properties.

P20 phosphor on polyimide as a large area high-resolution transmission screen for slow scan CCD systems

1995 ◽  
Vol 53 ◽  
pp. 20-21
Author(s):  
C. C. Ahn ◽  
S. Karnes ◽  
M. Lvovsky ◽  
C. M. Garland ◽  
H. A. Atwater ◽  
...  
Keyword(s):  
Mechanical Stability ◽  
High Energy ◽  
Practical Implementation ◽  
Line Pair ◽  
Modulation Transfer ◽  
Large Area ◽  
Ccd Imaging ◽  
Transmission Electron ◽  
The One ◽  
Beam Broadening

The bane of CCD imaging systems for transmission electron microscopy at intermediate and high voltages has been their relatively poor modulation transfer function (MTF), or line pair resolution. The problem originates primarily with the phosphor screen. On the one hand, screens should be thick so that as many incident electrons as possible are converted to photons, yielding a high detective quantum efficiency(DQE). The MTF diminishes as a function of scintillator thickness however, and to some extent as a function of fluorescence within the scintillator substrates. Fan has noted that the use of a thin layer of phosphor beneath a self supporting 2μ, thick Al substrate might provide the most appropriate compromise for high DQE and MTF in transmission electron microcscopes which operate at higher voltages. Monte Carlo simulations of high energy electron trajectories reveal that only little beam broadening occurs within this thickness of Al film. Consequently, the MTF is limited predominantly by broadening within the thin phosphor underlayer. There are difficulties however, in the practical implementation of this design, associated mostly with the mechanical stability of the Al support film.

RENORMALIZATION OF FERMI VELOCITY IN A COMPOSITE TWO DIMENSIONAL ELECTRON GAS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 87-94 ◽  
Author(s):  
M. WEGER ◽  
L. BURLACHKOV
Keyword(s):  
Electron Gas ◽  
Fermi Velocity ◽  
Bohr Radius ◽  
Dimensional Electron ◽  
Temperature Dependent ◽  
Two Dimensional Electron Gas ◽  
Self Energy ◽  
2D System ◽  
Dimensional Electron Gas ◽  
The One

We calculate the self-energy Σ(k, ω) of an electron gas with a Coulomb interaction in a composite 2D system, consisting of metallic layers of thickness d ≳ a 0, where a 0 = ħ2∊1/ me 2 is the Bohr radius, separated by layers with a dielectric constant ∊2 and a lattice constant c perpendicular to the planes. The behavior of the electron gas is determined by the dimensionless parameters k F a 0 and k F c ∊2/∊1. We find that when ∊2/∊1 is large (≈5 or more), the velocity v(k) becomes strongly k-dependent near k F , and v ( k F ) is enhanced by a factor of 5-10. This behavior is similar to the one found by Lindhard in 1954 for an unscreened electron gas; however here we take screening into account. The peak in v(k) is very sharp (δ k/k F is a few percent) and becomes sharper as ∊2/∊1 increases. This velocity renormalization has dramatic effects on the transport properties; the conductivity at low T increases like the square of the velocity renormalization and the resistivity due to elastic scattering becomes temperature dependent, increasing approximately linearly with T. For scattering by phonons, ρ ∝ T 2. Preliminary measurements suggest an increase in v k in YBCO very close to k F .

scholarly journals Absence of high-energy spectral concentration for Dirac systems with divergent potentials

2005 ◽  
Vol 135 (4) ◽  
pp. 689-702 ◽  
Author(s):  
M. S. P. Eastham ◽  
K. M. Schmidt
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Regularity Conditions ◽  
Absolutely Continuous Spectrum ◽  
Absolutely Continuous ◽  
One Dimensional ◽  
Local Maxima ◽  
Dirac Systems ◽  
Additional Regularity ◽  
Spectral Concentration

It is known that one-dimensional Dirac systems with potentials q which tend to −∞ (or ∞) at infinity, such that 1/q is of bounded variation, have a purely absolutely continuous spectrum covering the whole real line. We show that, for the system on a half-line, there are no local maxima of the spectral density (points of spectral concentration) above some value of the spectral parameter if q satisfies certain additional regularity conditions. These conditions admit thrice-differentiable potentials of power or exponential growth. The eventual sign of the derivative of the spectral density depends on the boundary condition imposed at the regular end-point.

Some Applications of Elliptic Integrals of First Kind

2013 ◽  
Vol 65 (1) ◽  
Author(s):  
Yasamin Barakat ◽  
Nor Haniza Sarmin
Keyword(s):  
Algebraic Function ◽  
High Accuracy ◽  
Elliptic Integrals ◽  
Definite Integrals ◽  
Engineering Mathematics ◽  
Optimal Values ◽  
Complete Elliptic Integrals

One of the most important applications of elliptic integrals in engineering mathematics is their usage to solve integrals of the form  (Eq. 1), where  is a rational algebraic function and  is a polynomial of degree  with no repeated roots. Nowadays, incomplete and complete elliptic integrals of first kind are estimated with high accuracy using advanced calculators.  In this paper, several techniques are discussed to show how definite integrals of the form (Eq. 1) can be converted to elliptic integrals of the first kind, and hence be estimated for optimal values. Indeed, related examples are provided in each step to help clarification.

Remarks on generalized elliptic integrals

2009 ◽  
Vol 139 (2) ◽  
pp. 417-426 ◽  
Author(s):  
Xiaohui Zhang ◽  
Gendi Wang ◽  
Yuming Chu
Keyword(s):  
Elliptic Integrals ◽  
Complete Elliptic Integrals

We study the monotonicity for certain combinations of generalized elliptic integrals, thus generalizing analogous well-known results for classical complete elliptic integrals, and prove a conjecture put forward by Heikkala, Vamanamurthy and Vuorinen.

scholarly journals Closed Analytic Formulas for the Approximation of the Legendre Complete Elliptic Integrals of the First and Second Kinds

2021 ◽  
Vol 8 ◽  
pp. 23-28
Author(s):  
Richard Selescu
Keyword(s):  
Normal Form ◽  
Asymptotic Expansions ◽  
Elliptic Integrals ◽  
Analytic Study ◽  
Regression Functions ◽  
Complete Elliptic Integrals ◽  
The Right ◽  
Approximate Formulas

The author proposes two sets of closedanalytic functions for the approximate calculus of thecomplete elliptic integrals of the first and secondkinds in the normal form due to Legendre, therespective expressions having a remarkablesimplicity and accuracy. The special usefulness of theproposed formulas consists in that they allowperforming the analytic study of variation of thefunctions in which they appear, by using thederivatives. Comparative tables including theapproximate values obtained by applying the two setsof formulas and the exact values, reproduced fromspecial functions tables are given (all versus therespective elliptic integrals modulus, k = sin ). It is tobe noticed that both sets of approximate formulas aregiven neither by spline nor by regression functions,but by asymptotic expansions, the identity with theexact functions being accomplished for the left end k= 0 ( = 0) of the domain. As one can see, the secondset of functions, although something more intricate,gives more accurate values than the first one andextends itself more closely to the right end k = 1 ( =90) of the domain. For reasons of accuracy, it isrecommended to use the first set until  = 70.5 only,and if it is necessary a better accuracy or a greaterupper limit of the validity domain, to use the secondset, but on no account beyond  = 88.2.

scholarly journals High-resolution late Holocene sedimentary cores record the long history of the city of Cádiz (south-western Spain)

2020 ◽  
Vol 27 ◽  
pp. 35-47
Author(s):  
Ferréol Salomon ◽  
Darío Bernal-Casasola ◽  
José J. Díaz ◽  
Macarena Lara ◽  
Salvador Domínguez-Bella ◽  
...  
Keyword(s):  
Western Europe ◽  
High Energy ◽  
Mitigation Strategies ◽  
Urban Centre ◽  
Archaeological Data ◽  
Lisbon Earthquake ◽  
History Of ◽  
Western Spain ◽  
The One ◽  
The City

Abstract. Today, coastal cities worldwide are facing major changes resulting from climate change and anthropogenic forcing, which requires adaptation and mitigation strategies to be established. In this context, sedimentological archives in many Mediterranean cities record a multi-millennial history of environmental dynamics and human adaptation, revealing a long-lasting resilience. Founded by the Phoenicians around 3000 years ago, Cádiz (south-western Spain) is a key example of a coastal resilient city. This urban centre is considered to be one of the first cities of western Europe and has experienced major natural hazards during its long history, such as coastal erosion, storms, and also tsunamis (like the one in 1755 CE following the destructive Lisbon earthquake). In the framework of an international, joint archaeological and geoarchaeological project, three cores have been drilled in a marine palaeochannel that ran through the ancient city of Cádiz. These cores reveal a ≥50 m thick Holocene sedimentary sequence. Importantly, most of the deposits date from the 1st millennium BCE to the 1st millennium CE. This exceptional sedimentary archive will allow our scientific team to achieve its research goals, which are (1) to reconstruct the palaeogeographical evolution of this specific coastal area; (2) to trace the intensity of activities of the city of Cádiz based on archaeological data, as well as geochemical and palaeoecological indicators; and (3) to identify and date high-energy event deposits such as storms and tsunamis.

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