scholarly journals The Landau-Zener Transition and the Surface Hopping Method for the 2D Dirac Equation for Graphene

2017 ◽  
Vol 21 (2) ◽  
pp. 313-357 ◽  
Author(s):  
Ali Faraj ◽  
Shi Jin
Keyword(s):  
Dirac Equation ◽  
Electrostatic Potential ◽  
Numerical Experiments ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Two Dimensional ◽  
Lagrangian Surface ◽  
Surface Hopping ◽  
Asymptotic Models ◽  
Semiclassical Regime

AbstractA Lagrangian surface hopping algorithm is implemented to study the two dimensional massless Dirac equation for Graphene with an electrostatic potential, in the semiclassical regime. In this problem, the crossing of the energy levels of the system at Dirac points requires a particular treatment in the algorithm in order to describe the quantum transition—characterized by the Landau-Zener probability— between different energy levels. We first derive the Landau-Zener probability for the underlying problem, then incorporate it into the surface hopping algorithm. We also show that different asymptotic models for this problem derived in [O. Morandi, F. Schurrer, J. Phys. A:Math. Theor. 44 (2011) 265301]may give different transition probabilities. We conduct numerical experiments to compare the solutions to the Dirac equation, the surface hopping algorithm, and the asymptotic models of [O. Morandi, F. Schurrer, J. Phys. A: Math. Theor. 44 (2011) 265301].

scholarly journals NONCOMMUTATIVE GRAPHENE

2013 ◽  
Vol 28 (16) ◽  
pp. 1350064 ◽  
Author(s):  
CATARINA BASTOS ◽  
ORFEU BERTOLAMI ◽  
NUNO COSTA DIAS ◽  
JOÃO NUNO PRATA
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Dirac Equation ◽  
Energy Levels ◽  
Dirac Fermions ◽  
Two Dimensional ◽  
Dirac System ◽  
Noncommutative Parameter

We consider a noncommutative description of graphene. This description consists of a Dirac equation for massless Dirac fermions plus noncommutative corrections, which are treated in the presence of an external magnetic field. We argue that, being a two-dimensional Dirac system, graphene is particularly interesting to test noncommutativity. We find that momentum noncommutativity affects the energy levels of graphene and we obtain a bound for the momentum noncommutative parameter.

Master Equation for the Dissociation of a Dilute Diatomic Gas. V. Effect of Energy-level Spacing

1971 ◽  
Vol 49 (23) ◽  
pp. 3915-3917 ◽  
Author(s):  
D. L. S. Mcelwain ◽  
H. O. Pritchard
Keyword(s):  
Energy Level ◽  
Master Equation ◽  
Temperature Coefficient ◽  
Numerical Experiments ◽  
Vibrational Energy ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Level Spacing ◽  
Vibrational Energy Levels ◽  
Arrhenius Temperature

Our previous vibration–dissociation coupling calculations for H2 have been repeated for D2. Closer spacing of the vibrational energy levels in D2 leads to increased translation–vibration transition probabilities, and the effect of this is to increase the rate of recombination by the vibrational mechanism at all temperatures. These numerical experiments also clarify two other issues: (i) that the position of the bottleneck does not necessarily occur at that level above which direct collisional dissociation can take place rapidly, and (ii) that there is no simple correspondence between the position of the bottleneck and the Arrhenius temperature coefficient for dissociation.

scholarly journals New Transition and Energy Levels of Three-Times Ionized Krypton (Kr IV)

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 48
Author(s):  
M. Raineri ◽  
M. Gallardo ◽  
J. Reyna Almandos ◽  
A. G. Trigueiros ◽  
C. J. B. Pagan
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Pulsed Discharge ◽  
Core Polarization ◽  
Polarization Effects ◽  
Hartree Fock ◽  
Theta Pinch ◽  
New Energy ◽  
First Time

A capillary pulsed-discharge and a theta-pinch were used to record Kr spectra in the region of 330–4800 Å. A set of 168 transitions of these spectra were classified for the first time. We extended the analysis to twenty-five new energy levels belonging to 3s23p24d, 3s23p25d even configurations. We calculated weighted transition probabilities (gA) for all of the experimentally observed lines and lifetimes for new energy levels using a relativistic Hartree–Fock method, including core-polarization effects.

scholarly journals The influence of Coulomb interaction screening on the excitons in disordered two-dimensional insulators

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
E. V. Kirichenko ◽  
V. A. Stephanovich
Keyword(s):  
Coulomb Interaction ◽  
Energy Levels ◽  
Transition Metal Dichalcogenides ◽  
Extreme Case ◽  
Bound State ◽  
Joint Effect ◽  
Two Dimensional ◽  
Inorganic Substances ◽  
Metal Dichalcogenides ◽  
Interaction Screening

AbstractWe study the joint effect of disorder and Coulomb interaction screening on the exciton spectra in two-dimensional (2D) structures. These can be van der Waals structures or heterostructures of organic (polymeric) semiconductors as well as inorganic substances like transition metal dichalcogenides. We consider 2D screened hydrogenic problem with Rytova–Keldysh interaction by means of so-called fractional Scrödinger equation. Our main finding is that above synergy between screening and disorder either destroys the exciton (strong screening) or promote the creation of a bound state, leading to its collapse in the extreme case. Our second finding is energy levels crossing, i.e. the degeneracy (with respect to index $$\mu $$ μ ) of the exciton eigenenergies at certain discrete value of screening radius. Latter effects may also be related to the quantum manifestations of chaotic exciton behavior in above 2D semiconductor structures. Hence, they should be considered in device applications, where the interplay between dielectric screening and disorder is important.

scholarly journals Fast forwad Adiabatic Quantum Dynamics On Two Dimensional Dirac Equation

2021 ◽  
Vol 1842 (1) ◽  
pp. 012057
Author(s):  
I Setiawan ◽  
R Sugihakim ◽  
B E Gunara
Keyword(s):  
Dirac Equation ◽  
Quantum Dynamics ◽  
Two Dimensional

Computational models of filtration gas combustion

2017 ◽  
Vol 32 (2) ◽  
Author(s):  
Yuri M. Laevsky ◽  
Tatyana A. Nosova
Keyword(s):  
Heat Flow ◽  
Numerical Experiments ◽  
Computational Models ◽  
Two Dimensional ◽  
Multidimensional Model ◽  
Gas Combustion ◽  
Total Enthalpy ◽  
Diffusive Flow ◽  
Temperature Heat ◽  
The One

AbstractA multidimensional model of filtration gas combustion is presented. The model is based on the system of conservation laws of ‘temperature – heat flow’, ‘mass–diffusive flow’ types with introducing the concept of total enthalpy flow. Results of numerical experiments are presented for the one- and two-dimensional problems for different conditions and parameters.

scholarly journals Opacities in Strong Magnetic Helds

1995 ◽  
Vol 10 ◽  
pp. 588-590
Author(s):  
Dayal T. Wickramasinghe
Keyword(s):  
Entire Range ◽  
White Dwarfs ◽  
Specific Problem ◽  
Transition Probabilities ◽  
Strong Field ◽  
Energy Levels ◽  
Dipolar Field ◽  
Origin And Evolution ◽  
End Products ◽  
Hydrogen Lines

White dwarfs are one of the most readily studied end products of stellarevolution. Their observed properties have provided and continue to provide important constraints for the theory of stellar evolution. Likewise, a study of magnetism in white dwarfs provides unique insights into the origin and evolution of magnetic fields in stars.Spectacular progress has been made on the specific problem of the structure of the hydrogen atom in strong fields. Energy levels and transition probabilities are now known for all low lying states of hydrogen for the entire range of field strengths appropriate to white dwarfs and neutron stars (104-1013G) (Rosner et al 1984, Forster et al 1984 and Henry and O’Connell 1984). These calculations resulted in the identification of spectral features in the magnetic white dwarf Grw+70°8247 which had remained unidentified for over 50 years (Minkowski 1938), with Zeeman shifted hydrogen lines in a magnetic field of 100 -320 MG ((eg Wickamasinghe and Ferrano 1989). Several other strong field magnetic white dwarfs have since been discovered through hydrogen Zeeman spectroscopy. The data presently at hand show that most hydrogen rich magnetic white dwarfs have complex non-dipolar field structures with strong evidence for higher order multipole components.

scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

scholarly journals Pedestrian Walking Behavior Revealed through a Random Walk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hui Xiong ◽  
Liya Yao ◽  
Huachun Tan ◽  
Wuhong Wang
Keyword(s):  
Numerical Experiments ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Pedestrian Flow ◽  
Alternating Direction Implicit Method ◽  
Walking Behavior ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Continuous Time Random Walks ◽  
High Order Compact Scheme

This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

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