Transverse Shubnikov–de Haas effect and the manifestation of quantum diffraction

2020 ◽  
Vol 34 (05) ◽  
pp. 2050016
Author(s):  
Yu. A. Berezhnoy ◽  
A. S. Molev
Keyword(s):  
Matrix Element ◽  
Electron Transition ◽  
Amplitude Distribution ◽  
Fraunhofer Diffraction ◽  
Initial State ◽  
Final State ◽  
Quantum Diffraction ◽  
The Matrix ◽  
Transverse Conductivity ◽  
Haas Effect

A quantum diffraction interpretation of the transverse Shubnikov–de Haas effect is presented. Within the framework of the conventional theory of this effect, we show that the matrix element for the electron transition from an initial state to a final state used in calculating the transverse electrical conductivity can be represented as a diffraction-type amplitude distribution. The squared modulus of this matrix element under certain conditions exhibits the Fraunhofer diffraction pattern. It is shown that the oscillating part of the transverse conductivity has the same form as the amplitude for Fraunhofer diffraction by an annular aperture.

Free Energy Calculations of Precipitate Nucleation

2007 ◽  
Vol 539-543 ◽  
pp. 2395-2400 ◽  
Author(s):  
Shigeto R. Nishitani ◽  
Atsuto Seko ◽  
Koretaka Yuge ◽  
Isao Tanaka
Keyword(s):  
Free Energy ◽  
Energy Barrier ◽  
Harmonic Approximation ◽  
Free Energy Calculations ◽  
Free Energy Barrier ◽  
Initial State ◽  
Final State ◽  
The Matrix ◽  
Predicted Values ◽  
Vibrational Free Energy

Our recently proposed calculating method reliably predicts the nucleation free energy barrier of the homogeneous and coherent precipitations. Helmholtz free energy change is clearly defined and calculated by the purely enthalpic and entropic contributions between the initial state of the isolated solute atoms scattering around the matrix and the final state of the cluster of size n traveling around the matrix. The enthalpic term is calculated by the reliable first principles method and the entropic term is estimated by the ideal solution model. The vibrational free energy is also included by the quasi-harmonic approximation. The model calculation was performed on bcc Cu precipitations in the Fe-Cu system. The predicted values of the critical number of 12 atoms and the critical free energy barrier of 0.6eV show good agreement with the experimentally estimated ones for the annealing temperature of 773K and the initial concentration of 1.4at%Cu.

scholarly journals Measurement of spin correlations in tt‾ production using the matrix element method in the muon+jets final state in pp collisions at s=8 TeV

2016 ◽  
Vol 758 ◽  
pp. 321-346 ◽  
Author(s):  
V. Khachatryan ◽  
A.M. Sirunyan ◽  
A. Tumasyan ◽  
W. Adam ◽  
E. Asilar ◽  
...  
Keyword(s):  
Matrix Element ◽  
Pp Collisions ◽  
Final State ◽  
Spin Correlations ◽  
Matrix Element Method ◽  
The Matrix ◽  
8 Tev ◽  
Element Method

scholarly journals Peculiarities of Matrix-Element Calculations with Few Coulomb Functions for Particles’ Scattering Processes

2018 ◽  
Vol 173 ◽  
pp. 03007 ◽  
Author(s):  
Ochbadrakh Chuluunbaatar ◽  
Konstantin Kouzakov ◽  
Yuri Popov
Keyword(s):  
Matrix Element ◽  
Momentum Space ◽  
Space Representation ◽  
Coulomb Interactions ◽  
Fast Proton ◽  
Final State ◽  
The Matrix ◽  
Coulomb Singularity ◽  
Parameter Values ◽  
He Atom

Specific features of the matrix-element calculations in the momentum-space representation are discussed for the single ionization of the He atom by fast proton impact in the case when the Coulomb interactions of all three charged fragments in the final state are taken into account. It is shown that a “soft” smoothing of the Coulomb singularity does not affect the accuracy of the calculations in a certain region of the smoothing parameter values.

scholarly journals Band gap manipulation of viscoelastic functionally graded phononic crystal

2020 ◽  
Vol 9 (1) ◽  
pp. 515-523
Author(s):  
Zuguang Bian ◽  
Shuai Yang ◽  
Xiaoliang Zhou ◽  
David Hui
Keyword(s):  
Incident Angle ◽  
Phononic Crystal ◽  
Functionally Graded ◽  
Band Gaps ◽  
Heat Sources ◽  
Initial State ◽  
Final State ◽  
Sh Waves ◽  
Numerical Examples ◽  
The Matrix

AbstractIn this study, band gaps of SH-waves (horizontally polarized shear waves) propagating in a thermal-sensitive viscoelastic matrix are investigated. Metallic films acting as heat sources are periodically embedded into the matrix, which establishes a periodically inhomogeneous thermal field. The homogenous matrix is therefore transformed into functionally gradient phononic crystals (PCs). A three-parameter solid model is employed to describe the viscoelasticity of the present matrix. By virtue of a transfer matrix method incorporated within a laminated model, the dispersion equation of SH-waves is finally obtained, from which the band gaps are determined. The transmission spectra of a finite-periodic PC are also solved to validate the band gaps. In numerical examples, the influences of incident angles of SH-waves and viscoelasticity of matrix on band gaps are discussed first. Then the research focuses on the means to tune the band gaps by manipulating the inputted powers of heat sources. Numerical examples demonstrate that such a strategy is effective and convenient in tuning the positions and widths of band gaps. A viscous parameter, i.e., the ratio of initial-state to final-state storage moduli, significantly affects the band locations and bandwidths, while the locations of low-order band gaps hardly move with the incident angle of SH-waves. Band gaps of several orders are expected to locate in lower-frequency domain, and the total bandwidth becomes larger as the inputted heat flux increases. This paper lays theoretical foundation to manufacture viscoelastic functionally graded PCs which can be used in frequency-selective devices.

PHOTOFIELD EMISSION CALCULATIONS BY USING PROJECTION OPERATOR METHOD

2007 ◽  
Vol 21 (22) ◽  
pp. 1501-1507
Author(s):  
R. K. THAPA ◽  
GUNAKAR DAS ◽  
S. R. GURUNG ◽  
B. I. SHARMA ◽  
P. K. PATRA
Keyword(s):  
Wave Function ◽  
Group Theory ◽  
Matrix Element ◽  
Projection Operator ◽  
Operator Method ◽  
Emission Current Density ◽  
Initial State ◽  
Projection Operator Method ◽  
The Matrix ◽  
Dependent Vector

A model calculation of photofield emission is discussed in which initial state wave function has been deduced by using projection operator method of group theory. A spatial dependent vector potential is used to evaluate the matrix element for calculating the photofield emission current density.

A SIMPLE THEORY OF PHOTOFIELD EMISSION FROM THE SURFACE OF A METAL

2005 ◽  
Vol 19 (19) ◽  
pp. 3141-3149 ◽  
Author(s):  
R. K. THAPA ◽  
GUNAKAR DAS
Keyword(s):  
Differential Equation ◽  
Matrix Element ◽  
Simple Model ◽  
Fermi Level ◽  
Free Electron ◽  
State Energy ◽  
Transmission Probability ◽  
Initial State ◽  
The Matrix ◽  
Electron Wavefunction

A simple model calculation of photofield emission is presented in which the photofield emission current (PFEC) is calculated for metal W. The matrix element for photoexcitation is evaluated by using the free electron wavefunction. The transmission probability D(W) is deduced by solving Airy's differential equation. The variation of PFEC is studied as a function of parameters like the applied high electric field, the photon energy, the initial state energy with reference to the Fermi level. It is found that in addition to D(W), the matrix element Mfi also has effect on the photofield emission.

scholarly journals Dual subtractions

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Renato Maria Prisco ◽  
Francesco Tramontano
Keyword(s):  
Field Theory ◽  
Quantum Field ◽  
Matrix Elements ◽  
Leading Order ◽  
Initial State ◽  
Final State ◽  
Dual Representation ◽  
Subtraction Scheme ◽  
Theoretical Predictions ◽  
Perturbative Quantum

Abstract We propose a novel local subtraction scheme for the computation of Next-to-Leading Order contributions to theoretical predictions for scattering processes in perturbative Quantum Field Theory. With respect to well known schemes proposed since many years that build upon the analysis of the real radiation matrix elements, our construction starts from the loop diagrams and exploits their dual representation. Our scheme implements exact phase space factorization, handles final state as well as initial state singularities and is suitable for both massless and massive particles.

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