Theory of decaying states based on a method of coupled equations: Kapur–Peierls and Siegert resonant states and the ‘extended’ Hellmann–Feynman theorem

1997 ◽  
pp. 530-543
Author(s):  
AKITOMO TACHIBANA ◽  
TOKIO YAMABE ◽  
KENICHI FUKUI
Keyword(s):  
Coupled Equations ◽  
Resonant States ◽  
Decaying States ◽  
Feynman Theorem

scholarly journals THE FRIEDRICHS-MODEL WITH FERMION-BOSON COUPLINGS II

2007 ◽  
Vol 16 (01) ◽  
pp. 169-178 ◽  
Author(s):  
O. CIVITARESE ◽  
M. GADELLA ◽  
G. P. PRONKO
Keyword(s):  
Degrees Of Freedom ◽  
Formal Solution ◽  
Extended Version ◽  
Simultaneous Treatment ◽  
Standard Methods ◽  
Coupled Equations ◽  
Resonant States ◽  
Friedrichs Model

In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the fermions with the discrete and continuous sectors of the bosonic degrees of freedom leads to a system of coupled equations, whose solutions are found by applying standard methods of representation of bound and resonant states.

scholarly journals Numerical Continuation of Resonances and Bound States in Coupled Channel Schrödinger Equations

2012 ◽  
Vol 11 (2) ◽  
pp. 435-455 ◽  
Author(s):  
Przemysław Kłosiewicz ◽  
Jan Broeckhove ◽  
Wim Vanroose
Keyword(s):  
Schrödinger Equation ◽  
Bifurcation Theory ◽  
Schrodinger Equation ◽  
Bound States ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Coupled Equations ◽  
Resonant States ◽  
The Subject ◽  
Coupled Channel

AbstractIn this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states of the quantum mechanical Schrödinger equation. We extend previous work on the subject [1] to systems of coupled equations.Bound and resonant states of the Schrödinger equation can be determined through the poles of the S-matrix, a quantity that can be derived from the asymptotic form of the wave function. We introduce a regularization procedure that essentially transforms the S-matrix into its inverse and improves its smoothness properties, thus making it amenable to numerical continuation. This allows us to automate the process of tracking bound and resonant states when parameters in the Schrödinger equation are varied. We have applied this approach to a number of model problems with satisfying results.

Towards quantitative simulations of inelastic electron diffraction patterns and images

1992 ◽  
Vol 50 (2) ◽  
pp. 1170-1171
Author(s):  
Z. L. Wang
Keyword(s):  
Phonon Scattering ◽  
Incident Beam ◽  
Dynamical Theory ◽  
Inelastic Electron ◽  
Additional Advantage ◽  
Coupled Equations ◽  
Atomic Vibrations ◽  
Diffraction Patterns ◽  
Primary Advantage ◽  
The One

A new dynamical theory has been developed based on Yoshioka's coupled equations for describing inelastic electron scattering in thin crystals. Compared to existing theories, the primary advantage of this theory is that the incoherent summation of the diffracted intensities contributed by electrons after exciting vast numbers of different excited states has been evaluated before any numerical calculation. An additional advantage is that the phase correlations of atomic vibrations are considered, so that full lattice dynamics can be combined in the phonon scattering calculation. The new theory has been proven to be equivalent to the inelastic multislice theory, and has been applied to calculate energy-filtered diffraction patterns and images formed by phonon, single electron and valence scattered electrons.A calculated diffraction pattern of elastic and phonon scattered electrons for a parallel incident beam case is in agreement with the one observed (Fig. 1), showing thermal diffuse scattering (TDS) streaks and Kikuchi pattern.

ALPHA-PARTICLE RESONANT STATES IN MEDIUM WEIGHT NUCLEI

1971 ◽  
Vol 32 (C6) ◽  
pp. C6-185-C6-187
Author(s):  
A. DUDEK ◽  
P. E. HODGSON
Keyword(s):  
Alpha Particle ◽  
Resonant States ◽  
Medium Weight

Decay of resonant states and determination of their quantum numbers

1970 ◽  
Vol 101 (8) ◽  
pp. 655-696 ◽  
Author(s):  
M.S. Dubovikov ◽  
Yurii A. Simonov
Keyword(s):  
Quantum Numbers ◽  
Resonant States

Ciliary Flow of Casson Nanofluid with the Influence of MHD having Carbon Nanotubes

2020 ◽  
Vol 16 ◽  
Author(s):  
Adel Alblawi ◽  
Saba Keyani ◽  
S. Nadeem ◽  
Alibek Issakhov ◽  
Ibrahim M. Alarifi
Keyword(s):  
Carbon Nanotubes ◽  
Velocity Profile ◽  
Pressure Gradient ◽  
Volume Fraction ◽  
Solid Volume Fraction ◽  
Pressure Rise ◽  
Shear Stresses ◽  
Left Wall ◽  
Coupled Equations ◽  
The Right

Objective: In this paper, we consider a model that describes the ciliary beating in the form of metachronal waves along with the effects of Magnetohydrodynamic fluid over a curved channel with slip effects. This work aims at evaluating the effect of Magnetohydrodynamic (MHD) on the steady two dimensional (2-D) mixed convection flow induced in carbon nanotubes. The work is done for both the single wall nanotube and multiple wall nanotube. The right wall and the left wall possess a metachronal wave that is travelling along the outer boundary of the channel. Methods: The wavelength is considered as very large for cilia induced MHD flow. The governing linear coupled equations are simplified by considering the approximations of long wavelength and small Reynolds number. Exact solutions are obtained for temperature and velocity profile. The analytical expressions for the pressure gradient and wall shear stresses are obtained. Term for pressure rise is obtained by applying Numerical integration method. Results: Numerical results of velocity profile are mentioned in a table form, for various values of solid volume fraction, curvature, Hartmann number [M] and Casson fluid parameter [ζ]. Final section of this paper is devoted to discussing the graphical results of temperature, pressure gradient, pressure rise, shear stresses and stream functions. Conclusion: Velocity profile near the right wall of the channel decreases when we add nanoparticles into our base fluid, whereas an opposite behaviour is depicted near the left wall due to ciliated tips whereas the temperature is an increasing function of B and ߛ and decreasing function of ߶.

scholarly journals Novel semi-analytical optoelectronic modeling based on homogenization theory for realistic plasmonic polymer solar cells

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Zahra Arefinia ◽  
Dip Prakash Samajdar
Keyword(s):  
Solar Cells ◽  
Active Layer ◽  
Analytical Modeling ◽  
High Efficiency ◽  
Polymer Solar Cells ◽  
Scattered Light ◽  
Homogenization Theory ◽  
Computational Time ◽  
Coupled Equations ◽  
Long Time

AbstractNumerical-based simulations of plasmonic polymer solar cells (PSCs) incorporating a disordered array of non-uniform sized plasmonic nanoparticles (NPs) impose a prohibitively long-time and complex computational demand. To surmount this limitation, we present a novel semi-analytical modeling, which dramatically reduces computational time and resource consumption and yet is acceptably accurate. For this purpose, the optical modeling of active layer-incorporated plasmonic metal NPs, which is described by a homogenization theory based on a modified Maxwell–Garnett-Mie theory, is inputted in the electrical modeling based on the coupled equations of Poisson, continuity, and drift–diffusion. Besides, our modeling considers the effects of absorption in the non-active layers, interference induced by electrodes, and scattered light escaping from the PSC. The modeling results satisfactorily reproduce a series of experimental data for photovoltaic parameters of plasmonic PSCs, demonstrating the validity of our modeling approach. According to this, we implement the semi-analytical modeling to propose a new high-efficiency plasmonic PSC based on the PM6:Y6 PSC, having the highest reported power conversion efficiency (PCE) to date. The results show that the incorporation of plasmonic NPs into PM6:Y6 active layer leads to the PCE over 18%.

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