scholarly journals A computational approach for investigating Coulomb interaction using Wigner–Poisson coupling

2021 ◽  
Author(s):  
Majid Benam ◽  
Mauro Ballicchia ◽  
Josef Weinbub ◽  
Siegfried Selberherr ◽  
Mihail Nedjalkov
Keyword(s):  
Coulomb Interaction ◽  
Spectral Decomposition ◽  
Electron System ◽  
Local Approximation ◽  
Computational Effort ◽  
Computational Approach ◽  
Electron Interaction ◽  
Quantum Particles ◽  
Interacting Electrons ◽  
Poisson Coupling

AbstractEntangled quantum particles, in which operating on one particle instantaneously influences the state of the entangled particle, are attractive options for carrying quantum information at the nanoscale. However, fully-describing entanglement in traditional time-dependent quantum transport simulation approaches requires significant computational effort, bordering on being prohibitive. Considering electrons, one approach to analyzing their entanglement is through modeling the Coulomb interaction via the Wigner formalism. In this work, we reduce the computational complexity of the time evolution of two interacting electrons by resorting to reasonable approximations. In particular, we replace the Wigner potential of the electron–electron interaction by a local electrostatic field, which is introduced through the spectral decomposition of the potential. It is demonstrated that for some particular configurations of an electron–electron system, the introduced approximations are feasible. Purity, identified as the maximal coherence for a quantum state, is also analyzed and its corresponding analysis demonstrates that the entanglement due to the Coulomb interaction is well accounted for by the introduced local approximation.

scholarly journals Interplay of spin–orbit coupling and Coulomb interaction in ZnO-based electron system

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
D. Maryenko ◽  
M. Kawamura ◽  
A. Ernst ◽  
V. K. Dugaev ◽  
E. Ya. Sherman ◽  
...  
Keyword(s):  
Coulomb Interaction ◽  
High Mobility ◽  
Electron System ◽  
Orbit Coupling ◽  
Electron Interaction ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Strong Electron ◽  
Strongly Coupled ◽  
Dimensional Electron System

AbstractSpin–orbit coupling (SOC) is pivotal for various fundamental spin-dependent phenomena in solids and their technological applications. In semiconductors, these phenomena have been so far studied in relatively weak electron–electron interaction regimes, where the single electron picture holds. However, SOC can profoundly compete against Coulomb interaction, which could lead to the emergence of unconventional electronic phases. Since SOC depends on the electric field in the crystal including contributions of itinerant electrons, electron–electron interactions can modify this coupling. Here we demonstrate the emergence of the SOC effect in a high-mobility two-dimensional electron system in a simple band structure MgZnO/ZnO semiconductor. This electron system also features strong electron–electron interaction effects. By changing the carrier density with Mg-content, we tune the SOC strength and achieve its interplay with electron–electron interaction. These systems pave a way to emergent spintronic phenomena in strong electron correlation regimes and to the formation of quasiparticles with the electron spin strongly coupled to the density.

SPIN SPLITTING IN A TWO DIMENSIONAL ELECTRON SYSTEM DETERMINED BY NUCLEAR MAGNETIC RELAXATION AND MAGNETOTRANSPORT ACTIVATION MEASUREMENTS

1993 ◽  
Vol 07 (01n03) ◽  
pp. 474-479 ◽  
Author(s):  
A. BERG ◽  
D. WEISS ◽  
K. V. KLITZING ◽  
R. NÖTZEL
Keyword(s):  
Energy Transport ◽  
Lattice Relaxation ◽  
Electron System ◽  
Spin Lattice Relaxation ◽  
Spin Splitting ◽  
Electron Interaction ◽  
Two Dimensional ◽  
Dimensional Electron ◽  
Spin Lattice ◽  
Dimensional Electron System

The spin splitting observed in two-dimensional electron systems at high magnetic fields is not only determined by the single-electron Zeeman energy but also by many-particle effects. Electron-electron interaction results in an enhanced g-factor which can be described by the exchange part of the Coulomb interaction. Nuclear spin lattice relaxation experiments analysing the Overhauser Shift in Electron Spin Resonance (ESR) measurements reveal that the exchange term is dominant. The spin splitting is strongly dependent on magnetic field and temperature. Numerical simulations enable the quantitative determination of the exchange part of the spin split energy. Transport activation measurements verify that the exchange part is proportional to the spin polarization of the electrons.

Piledriver Noise: Acoustic Radiation From a Cylindrical Pipe Pile Under Periodic Axial Impacts

1975 ◽  
Vol 97 (4) ◽  
pp. 1219-1222
Author(s):  
Jeffrey J. Fredberg ◽  
Jerome E. Manning
Keyword(s):  
Boundary Condition ◽  
Finite Length ◽  
Axial Velocity ◽  
Spectral Decomposition ◽  
Acoustic Radiation ◽  
Linear Process ◽  
Cylindrical Pipe ◽  
Pipe Pile ◽  
Power Radiation ◽  
Poisson Coupling

The acoustic radiation caused by periodic axial impacts on a cylindrical pipe pile of finite length is calculated. The axial velocity at all points on the pile surface is specified in terms of the excitation, the pile properties, and the ground impedance. It is assumed that the reflection of the structural wave at the pile-ground interface is a linear process, and that the radial pile velocity is simply related to the axial velocity through Poisson coupling. The pile motion is then used as a boundary condition for the acoustical space and the total acoustical power radiation and its spectral decomposition are predicted. Possible methods of noise control are discussed.

A Comparison between Three Meta-Modeling Optimization Approaches to Design a Tube Hydroforming Process

2012 ◽  
Vol 504-506 ◽  
pp. 607-612 ◽  
Author(s):  
Giuseppe Ingarao ◽  
Laura Marretta ◽  
Rosa di Lorenzo
Keyword(s):  
Polynomial Regression ◽  
Tube Hydroforming ◽  
Local Approximation ◽  
Computational Effort ◽  
Optimization Techniques ◽  
Optimization Approach ◽  
Modeling Techniques ◽  
Hydroforming Process ◽  
Meta Modeling ◽  
Research Challenge

Computer aided procedures to design and optimize forming processes have become crucial research topics as the industrial interest in cost and time reduction has been increasing. A standalone numerical simulation approach could make the design too time consuming while meta-modeling techniques enables faster approximation of the investigated phenomena, reducing the simulation time. Many researchers are, nowadays, facing such research challenge by using various approaches. Response surface method (RSM) is probably the most known one, since its effectiveness was demonstrated in the past years. The effectiveness of RSM depends both on the definition of the Design of Experiments (DoE) and the accuracy of the function approximation. The number of numerical simulations can be strongly reduced if a proper optimization approach is implemented: one of the main issues about optimization techniques is related to the design necessity of performing either global or local approximation. This paper aims to test the efficacy of some meta-modeling techniques in the optimization of a T-shaped hydroforming process. In this paper three optimization approaches based on different meta-modeling techniques are implemented. In particular, classical Polynomial Regression approach (PR), Moving Least Squares approximation (MLS) and Kriging method are applied. The results showed that, thanks to the peculiarities of MLS and Kriging methods, it is possible to strongly reduce the computational effort in sheet metal forming optimization, particularly in comparison with a classical PR approach. Differences were highlighted and quantified.

COEXISTENCE OF SUPERCONDUCTIVITY AND FERROMAGNETISM IN UGe2

2003 ◽  
Vol 17 (26) ◽  
pp. 1385-1389 ◽  
Author(s):  
JE HUAN KOO ◽  
GUANGSUP CHO
Keyword(s):  
Transition Temperature ◽  
Exchange Interaction ◽  
Coulomb Interaction ◽  
High Transition Temperature ◽  
Previous Model ◽  
Electron Interaction ◽  
Electron Pairs ◽  
High Transition

We investigate the coexistence of ferromagnetism and superconductivity in UGe 2 and Sr 2 RuO 4 in analogy with our previous model3 for high transition temperature superconductivity (HTSC). The Coulomb interaction for triplet electron pairs is reduced by a difference of the exchange interaction. If the electron–electron interaction Usf for UGe 2 and Usd for Sr 2 RuO 4 are larger than the reduced Coulomb interaction, superconductivity must happen. Under the same conditions, the coexistence of superconductivity and ferromagnetism is impossible in the case of our scheme, but changing phonons by pressures makes the coexistence possible for UGe 2.

scholarly journals A Comprehensive Study of the Thermal and Magnetic Properties of Two-Harmonically Interacting Electrons Confined in a Parabolic GaAs Quantum Dot in a Magnetic Field

2019 ◽  
Vol 11 (3) ◽  
pp. 76 ◽  
Author(s):  
A. A. Shukri ◽  
F. S. Nammas
Keyword(s):  
Magnetic Field ◽  
Heat Capacity ◽  
Magnetic Properties ◽  
Quantum Dot ◽  
Electron Interaction ◽  
Double Peak Structure ◽  
Peak Structure ◽  
Interacting Electrons ◽  
Gaas Quantum Dot ◽  
Spinless Case

The thermal and magnetic properties of a parabolic GaAs quantum dot for two-Harmonically interacting electrons when it exposed to an external magnetic field, taking into account the spin-Zeeman energy are investigated using the canonical ensemble approach. The effect of spin on these properties is also investigated. With the possibility of a basic and physically sensible model of electron-electron interaction, the issue is precisely soluble. We found a Schottky-like anomaly in the heat capacity at low temperature, while it saturates to the 4kB value as the temperature increases. Also it is noted that entropy enhances with temperature as expected. However as a function of a magnetic field, a peak structure is observed in heat capacity at very low values of magnetic field, while it saturates to the 2kB value as magnetic field increases. Also we noticed that these peaks are not presented in the spinless case. Moreover magnetic field does not show a significant effect on the entropy at high temperatures, but at relatively lower temperatures, the entropy shows a monotonic increase with magnetic field. As a function of the Lande g* factor, we found a local minima and a double peak-structure in the susceptibility and in the heat capacity at g*=0. It is demonstrated that the favored state for both magnetization and susceptibility is the diamagnetic state. The significant effect of the spin on the magnetic properties of quantum dot is seen at low values of temperature and magnetic field. Moreover, our results showed a very good agreement with reported previous works.

scholarly journals Field-Angle Dependence of Interlayer Magnetoresistance in Organic Dirac Electron System α-(BEDT-TTF)2I3

Crystals ◽  
2019 ◽  
Vol 9 (4) ◽  
pp. 212 ◽  
Author(s):  
Takehiro Tani ◽  
Naoya Tajima ◽  
Akito Kobayashi
Keyword(s):  
Magnetic Field ◽  
Coulomb Interaction ◽  
Electron System ◽  
Landau Levels ◽  
Spin Splitting ◽  
Organic Conductor ◽  
Angle Dependence ◽  
Dirac Electron ◽  
The Magnetic Field ◽  
Theory And Experiments

The effect of the Coulomb interaction in interlayer magnetoresistance is elucidated in collaboration with theory and experiments for the Dirac electron system in organic conductor α -(BEDT-TTF) 2 I 3 under a strong magnetic field. It is found that the effective g-factor enhanced by Coulomb interaction depends on the angle of the magnetic field, resulting in the field-angle dependence of a characteristic magnetic field in which interlayer resistance has a minimum due to spin splitting N = 0 Landau levels. The qualitative agreement between the theory and experimental results for the field-angle dependence of interlayer magnetoresistance is obtained.

A VARIATIONAL THEORY OF QUASI-PARTICLES IN A 3D N x N x N CUBIC LATTICE

2014 ◽  
Vol 5 (1) ◽  
pp. 712-725
Author(s):  
Enaibe A. Edison ◽  
Akpata Erhieyovwe ◽  
Osafile Omosede
Keyword(s):  
Hubbard Model ◽  
Coulomb Interaction ◽  
Interaction Strength ◽  
Finite Size ◽  
Electron System ◽  
Single Band ◽  
Variational Theory ◽  
S Wave ◽  
Cubic Lattice ◽  
Hubbard Hamiltonian

The single-band Hubbard Hamiltonian study faces a serious limitation and difficulty as we move away from finite - size lattices to larger N - dimensional lattices. Thus there is the needto develop the means of overcoming the finite - size lattice defects as we pass on to a higher dimension.In this work, a quantitative approximation to the one-band Hubbard model is presented using a variational analytic approach. The goal of this work, therefore, is to explore quantitatively the lowest ground-state energy and the pairing correlations in 3D N x N x N lattices of the Hubbard model. We developed the unit step model as an approximate solution to the single-band Hubbard Hamiltonian to solve variationallythe correlation of two interacting elections on a three-dimensional cubic lattice. We also showed primarily how to derive possible electronic states available for several even and odd3D lattices, although, this work places more emphasis on a 3D 5 x 5 x 5 lattice. The results emerging from our present study compared favourablywith the results of Gutzwillervariational approach (GVA) and correlated variational approach (CVA), at thelarge limit of the Coulomb interaction strength (U/4t). It is revealed in this study, that the repulsive Coulomb interaction which in part leads to the strong electronic correlations, would indicate that the two electron system prefer not to condense into s-wave superconducting singlet state (s = 0), at high positive values of the interaction strength.

A COMPUTATIONAL APPROACH TO THE COINCIDENCE OF EGALITARIAN SOLUTIONS FOR COST-SHARING GAMES

2006 ◽  
Vol 08 (01) ◽  
pp. 169-183 ◽  
Author(s):  
REINER WOLFF
Keyword(s):  
General Solution ◽  
Cost Sharing ◽  
Cost Allocation ◽  
Solution Concept ◽  
Computation Time ◽  
Computational Effort ◽  
Solution Algorithm ◽  
Computational Approach ◽  
Operational Conditions ◽  
Egalitarian Solution

The pre-nucleolus is a popular egalitarian solution concept for cost-sharing games. A drawback of this concept is that an associated cost allocation often cannot be calculated in polynomial time. Therefore, it would be convenient to know whether the pre-nucleolus of a particular game coincides with the outcome of a cost-allocation method which is computationally less demanding. We provide operational conditions for a coincidence of the pre-nucleolus (point) of a cost-sharing game and the center of the game's imputation set (CIS vector). These conditions can be checked with little computational effort as compared to the potential savings in terms of computation time of a general solution algorithm.

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