Peculiarities of Stark-phonon Resonance in Two-dimensional Superlattices with Non-additive Energy Spectrum

2016 ◽  
Vol 8 (1) ◽  
pp. 01019-1-01019-3
Author(s):  
D. V. Zav’yalov ◽  
◽  
S. V. Kruchkov ◽  
E. S. Ionkina ◽  
◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Two Dimensional ◽  
Additive Energy

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

1995 ◽  
Vol 09 (01) ◽  
pp. 55-66
Author(s):  
YOUYAN LIU ◽  
WICHIT SRITRAKOOL ◽  
XIUJUN FU
Keyword(s):  
Energy Spectrum ◽  
Density Of States ◽  
Energy Gap ◽  
Fractional Part ◽  
Numerical Results ◽  
Step Height ◽  
Integrated Density Of States ◽  
Two Dimensional

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.

Nonuniversal k−3 energy spectrum in stationary two-dimensional homogeneous turbulence

2001 ◽  
Vol 13 (5) ◽  
pp. 1431-1439 ◽  
Author(s):  
Yukio Kaneda ◽  
Takashi Ishihara
Keyword(s):  
Energy Spectrum ◽  
Homogeneous Turbulence ◽  
Two Dimensional

Dirac oscillator in a uniform electric field: Path integral treatment

2019 ◽  
Vol 34 (30) ◽  
pp. 1950246
Author(s):  
Hassene Bada ◽  
Mekki Aouachria
Keyword(s):  
Energy Spectrum ◽  
Electric Field ◽  
Path Integral ◽  
Uniform Electric Field ◽  
Two Dimensional ◽  
Dirac Oscillator ◽  
Fermionic Model ◽  
Internal Motions ◽  
Integral Treatment ◽  
The One

In this paper, the propagator of a two-dimensional Dirac oscillator in the presence of a uniform electric field is derived by using the path integral technique. The fact that the globally named approach is used in this work redirects, beforehand, our search for the propagator of the Dirac equation to that of the propagator of its quadratic form. The internal motions relative to the spin are represented by two fermionic oscillators, which are described by Grassmannian variables, according to Schwinger’s fermionic model. Once the integration over the anticommuting variables (Grassmannian variables) is accomplished, the problem becomes the one of finding a non-relativistic propagator with only bosonic variables. The energy spectrum of the electron and the corresponding eigenspinors are also obtained in this work.

scholarly journals Accelerated procedure to solve kinetic equation for neutral atoms in a hot plasma

2018 ◽  
Vol 09 (05) ◽  
pp. 1850048 ◽  
Author(s):  
Mikhail Z. Tokar
Keyword(s):  
Monte Carlo ◽  
Kinetic Equation ◽  
Energy Spectrum ◽  
Erosion Rate ◽  
Fusion Reactor ◽  
Two Dimensional ◽  
First Wall ◽  
One Dimensional ◽  
Hot Plasma ◽  
Electrons And Ions

By reaching the first wall of a fusion reactor, charged plasma particles, electrons and ions are recombined into neutral molecules and atoms of hydrogen isotopes. These species recycle back into the plasma volume and participate, in particular, in charge–exchange (cx) collisions with ions. As a result, hot atoms with chaotically directed velocities are generated and some of them hit the wall. Statistical Monte Carlo methods often used to model the behavior of cx atoms are too time-consuming for comprehensive parameter studies. Recently1 an alternative iteration approach to solve one-dimensional kinetic equation2 has been significantly accelerated, by a factor of 30–50, by applying a pass method to evaluate the arising integrals from functions, involving the ion velocity distribution. Here, this approach is used by solving a two-dimensional kinetic equation, describing the transport of cx atoms in the vicinity of an opening in the wall, e.g., the entrance of a duct guiding to a diagnostic installation. To assess the erosion rate and lifetime of the installation, one need to know the energy spectrum of hot cx atoms escaping from the plasma into the duct. Calculations are done for a first mirror of molybdenum under plasma conditions expected in a fusion reactor like DEMO.3,4 The results of kinetic modeling are compared with those found by using a diffusion approximation5 relevant for cx atoms if the time between cx collisions with ions is much smaller than the time till the ionization of atoms by electrons. The present more exact kinetic consideration predicts a mirror erosion rate by a factor of 2 larger than the approximate diffusion approach.

Energy spectrum for two-dimensional periodic potentials in a magnetic field

1993 ◽  
Vol 47 (19) ◽  
pp. 13019-13022 ◽  
Author(s):  
O. Kühn ◽  
V. Fessatidis ◽  
H. L. Cui ◽  
P. E. Selbmann ◽  
N. J. M. Horing
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Two Dimensional ◽  
Periodic Potentials

The energy spectrum in the universal range of two-dimensional turbulence

1988 ◽  
Vol 4 (4) ◽  
pp. 271-301 ◽  
Author(s):  
S Kida ◽  
M Yamada ◽  
K Ohkitani
Keyword(s):  
Energy Spectrum ◽  
Two Dimensional
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