Related papers: On parameterizations of the Nordheim function
In this paper, we generalize the partial fraction decomposition which is fundamental in the theory of multiple zeta values, and prove a relation between Tornheim's double zeta functions of three complex variables. As applications, we give…
The work concerns relativistic effects and the influence of an external magnetic field on the transmission coefficient. The Fowler-Nordheim equation has been relativistically generalized and effect of the Lorentz contraction of a potential…
Field emission data are often represented on a Fowler--Nordheim plot but a new empirical equation has been recently proposed to better analyze experiments. Such an equation is based on approximations of the Murphy and Good model and…
In this work we combine density functional theory and quantum transport calculations to study the influence of atomic--scale defects on the work function and field emission characteristics of metal surfaces. We develop a general methodology…
Field emission formulae, current-voltage characteristics and energy distribution of emitted electrons, are derived analytically for a nonplanar (hyperboloidal) metallic emitter model. The traditional Fowler-Nordheim formulae, which are…
Representing field emission data on a Fowler--Nordheim plot is both very common and strongly not recommended. It leads to a spurious estimation of the emitter parameters despite a very good data fit. There is a lack of a reliable method of…
The commonest method of characterizing a cold field electron emitter is to measure its current-voltage characteristics, and the commonest method of analysing these characteristics is by means of a Fowler-Nordheim (FN) plot. This…
Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…
Vertical-arrow fluctuations near the boundaries in the six-vertex model on the two-dimensional $N \times N$ square lattice with the domain wall boundary conditions are considered. The one-point correlation function (`boundary polarization')…
Poynting theorem plays a very important role in analyzing electromagnetic phenomena. The electromagnetic power flux density is usually expressed with the Poynting vector. However, since Poynting theorem basically focuses on the power…
An important parameter used to characterize large-area field electron emitters (LAFEs) is the characteristic apex field enhancement factor {\gamma}_C. This parameter is normally extracted from the slope of a Fowler-Nordheim (FN) plot.…
We intimate deeper connections between the Riemann zeta and gamma functions than often reported and further derive a new formula for expressing the value of $\zeta(2n+1)$ in terms of zeta at other fractional points. This paper also…
In this paper, we introduce a new two-parameter deformation of the Gamma function that generalizes some existing Gamma-type functions in the literature. We study properties of this function that depend on the parameters. We also prove some…
The Riemann theta function is a complex-valued function of g complex variables. It appears in the construction of many (quasi-) periodic solutions of various equations of mathematical physics. In this paper, algorithms for its computation…
In this article, we explore a natural extension of the quadratic parametrization introduced in our previous work. By replacing the integer $n$ by $n^s$ ($ s\in\mathbb{R}, s>1$) and allowing the parameters to be real, we obtain for each…
The main object of this paper is to present generalizations of gamma, beta and hypergeometric functions. Some recurrence relations, transformation formulas, operation formulas and integral representations are obtained for these new…
These notes have been triggered by physicist's considerations on (1)'Pre-quantized wave equations' for matter fields, (2) Conservation laws, (3) Gauge Field extensions. All starting from variational principles. These notes do not contain…
For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the…
A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…
We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant…