Application of the Method of Standard Comparison Problems to Perturbations of the Coulomb Field. The Discrete Spectrum

1971 ◽  
pp. 113-121
Author(s):  
S. Yu. Slavyanov
Keyword(s):  
Discrete Spectrum ◽  
Coulomb Field

Some Aspects of Discrete Relaxation Time Spectra as Obtained from Dynamic Moduli Data

1995 ◽  
Vol 60 (11) ◽  
pp. 1815-1829 ◽  
Author(s):  
Jaromír Jakeš
Keyword(s):  
Relaxation Time ◽  
Least Squares ◽  
Discrete Spectrum ◽  
Integral Transform ◽  
Time Spectrum ◽  
Relaxation Time Spectrum ◽  
Dynamic Moduli ◽  
Best Fitting ◽  
Discrete Spectra ◽  
Well Posed

The problem of finding a relaxation time spectrum best fitting dynamic moduli data in the least-squares sense is shown to be well-posed and to yield a discrete spectrum, provided the data cannot be fitted exactly, i.e., without any deviation of data and calculated values. Properties of the resulting spectrum are discussed. Examples of discrete spectra obtained from simulated literature data and experimental literature data on polymers are given. The problem of smoothing discrete spectra when continuous ones are expected is discussed. A detailed study of an integral transform inversion under the non-negativity constraint is given in Appendix.

scholarly journals From the Vector to Scalar Perturbations Addition in the Stark Broadening Theory of Spectral Lines

Universe ◽  
2021 ◽  
Vol 7 (6) ◽  
pp. 176
Author(s):  
Valery Astapenko ◽  
Andrei Letunov ◽  
Valery Lisitsa
Keyword(s):  
Spectral Line ◽  
Stark Effect ◽  
Coulomb Field ◽  
Spectral Lines ◽  
Alternative Methods ◽  
Scalar Perturbation ◽  
Numerical Comparison ◽  
Line Shapes ◽  
Stark Effects ◽  
The Impact

The effect of plasma Coulomb microfied dynamics on spectral line shapes is under consideration. The analytical solution of the problem is unachievable with famous Chandrasekhar–Von-Neumann results up to the present time. The alternative methods are connected with modeling of a real ion Coulomb field dynamics by approximate models. One of the most accurate theories of ions dynamics effect on line shapes in plasmas is the Frequency Fluctuation Model (FFM) tested by the comparison with plasma microfield numerical simulations. The goal of the present paper is to make a detailed comparison of the FFM results with analytical ones for the linear and quadratic Stark effects in different limiting cases. The main problem is connected with perturbation additions laws known to be vector for small particle velocities (static line shapes) and scalar for large velocities (the impact limit). The general solutions for line shapes known in the frame of scalar perturbation additions are used to test the FFM procedure. The difference between “scalar” and “vector” models is demonstrated both for linear and quadratic Stark effects. It is shown that correct transition from static to impact limits for linear Stark-effect needs in account of the dependence of electric field jumping frequency in FFM on the field strengths. However, the constant jumping frequency is quite satisfactory for description of the quadratic Stark-effect. The detailed numerical comparison for spectral line shapes in the frame of both scalar and vector perturbation additions with and without jumping frequency field dependence for the linear and quadratic Stark effects is presented.

Effect of the coulomb field in 16O-16O elastic scattering

2008 ◽  
pp. 439-439
Author(s):  
S. Mukherjee ◽  
D. C. Agrawal ◽  
C. Maheshwari ◽  
P. C. Sood
Keyword(s):  
Elastic Scattering ◽  
Coulomb Field

Localization of Discrete Spectrum of Multiparticle Schrödinger Operators

1985 ◽  
Vol 40 (10) ◽  
pp. 1052-1058 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Discrete Spectrum ◽  
Lower Bounds ◽  
Upper Bound ◽  
Schrödinger Operators ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators

An upper bound on the dimension of eigenspaces of multiparticle Schrödinger operators is given. Its relation to upper and lower bounds on the eigenvalues is discussed.

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

scholarly journals Polarization Coulomb field scattering with the electron systems in AlGaN/GaN heterostructure field-effect transistors

AIP Advances ◽  
2020 ◽  
Vol 10 (7) ◽  
pp. 075212
Author(s):  
Guangyuan Jiang ◽  
Yuanjie Lv ◽  
Zhaojun Lin ◽  
Yongxiong Yang ◽  
Yang Liu ◽  
...  
Keyword(s):  
Field Effect ◽  
Field Effect Transistors ◽  
Coulomb Field ◽  
Electron Systems ◽  
Polarization Coulomb Field Scattering ◽  
Heterostructure Field Effect Transistors ◽  
Gan Heterostructure
Sign in / Sign up

Export Citation Format

Share Document