Energy Levels of One‐ and Two‐Dimensional Anharmonic Oscillators

1967 ◽  
Vol 47 (2) ◽  
pp. 798-799 ◽  
Author(s):  
Paul F. Endres
Keyword(s):  
Energy Levels ◽  
Two Dimensional ◽  
Anharmonic Oscillators

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 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.

scholarly journals Ultrabroadband two-dimensional electronic spectroscopy reveals energy flow pathways in LHCII across the visible spectrum

2019 ◽  
Vol 205 ◽  
pp. 09034
Author(s):  
Minjung Son ◽  
Alberta Pinnola ◽  
Roberto Bassi ◽  
Gabriela S. Schlau-Cohen
Keyword(s):  
Energy Transfer ◽  
Excited States ◽  
Energy Flow ◽  
Energy Levels ◽  
Electronic Spectroscopy ◽  
Visible Region ◽  
Visible Spectrum ◽  
Energy Relaxation ◽  
Two Dimensional ◽  
Flow Pathways

We utilise ultrabroadband two-dimensional electronic spectroscopy to map out pathways of energy flow in LHCII across the entire visible region. In addition to the well-established, low-lying chlorophyll Qy bands, our results reveal additional pathways of energy relaxation on the higher-lying excited states involving the S2 energy levels of carotenoids, including ultrafast carotenoid-to-chlorophyll energy transfer on 90-150 fs timescales.

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].

Quantum states in a nanotube quantum dot

2017 ◽  
Vol 31 (25) ◽  
pp. 1745023
Author(s):  
J. T. Wang ◽  
J. D. Fan
Keyword(s):  
Carbon Nanotube ◽  
High Efficiency ◽  
Energy Levels ◽  
Quantum States ◽  
Semiconductor Surface ◽  
Energy Structure ◽  
Two Dimensional ◽  
Quantum Energy ◽  
Quantum Bit ◽  
Computer Chips

In this paper, we carry out a theoretical calculation of quantum state and quantum energy structure in carbon nanotube embedded semiconductor surface. In this theoretical model, the electrons in the carbon nanotube are considered as in a two-dimensional cylindrical surface. Their motion, therefore, can be described by the Dirac equation. We solve the equation and find that the energy levels are quantized and are linearly dependent on the wave vectors along the [Formula: see text]-direction that is along the direction of the nanotube. This type of energy structure may have potential application for fabricating high efficiency solar cell or quantum bit in computer chips.

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