scholarly journals The critical transition of Coulomb impurities in gapped graphene

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
M. Asorey ◽  
A. Santagata
Keyword(s):  
Boundary Conditions ◽  
Bound States ◽  
Energy Levels ◽  
Bound State ◽  
Negative Energy ◽  
Spectral Flow ◽  
Supercritical Regime ◽  
Gapped Graphene ◽  
Critical Charge ◽  
Common Framework

AbstractThe effect of supercritical charge impurities in graphene is very similar to the supercritical atomic collapses in QED for Z > 137, but with a much lower critical charge. In this sense graphene can be considered as a natural testing ground for the analysis of quantum field theory vacuum instabilities. We analyze the quantum transition from subcritical to supercritical charge regimes in gapped graphene in a common framework that preserves unitarity for any value of charge impurities. In the supercritical regime it is possible to introduce boundary conditions which control the singular behavior at the impurity. We show that for subcritical charges there are also non-trivial boundary conditions which are similar to those that appear in QED for nuclei in the intermediate regime 118 < Z < 137. We analyze the behavior of the energy levels associated to the different boundary conditions. In particular, we point out the existence of new bound states in the subcritical regime which include a negative energy bound state in the attractive Coulomb regime. A remarkable property is the continuity of the energy spectral flow under variation of the impurity charge even when jumping across the critical charge transition. We also remark that the energy levels of hydrogenoid bound states at critical values of charge impurities act as focal points of the spectral flow.

1.37 - 2.90 Micron Intersubband Transitions in GaN/AlN Superlattices

2006 ◽  
Vol 955 ◽  
Author(s):  
Eric Anthony DeCuir ◽  
Emil Fred ◽  
Omar Manasreh ◽  
Jinqiao Xie ◽  
Hadis Morkoc ◽  
...  
Keyword(s):  
Quantum Wells ◽  
Bound States ◽  
Energy Levels ◽  
Three Dimensional ◽  
Blue Shift ◽  
Bound State ◽  
Peak Position ◽  
Multiple Quantum ◽  
Intersubband Transitions ◽  
Photovoltaic Mode

ABSTRACTIntersubband transitions in the spectral range of 1.37-2.90 °Cm is observed in molecular beam epitaxy grown Si-doped GaN/AlN multiple quantum wells using a Fourier-transform spectroscopy technique. A blue shift in the peak position of the intersubband transition is observed as the well width is decreased. A sample with a well width in the order of 2.4 nm exhibited the presence of three bound states in the GaN well. The bound state energy levels are calculated using a transfer matrix method. An electrochemical capacitance voltage technique is used to obtain the three dimensional carrier concentrations in these samples which further enable the calculation of the Fermi energy level position. Devices fabricated from these GaN/AlN quantum wells are found to operate in the photovoltaic mode.

scholarly journals Quantum speedup, non-Markovianity and formation of bound state

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Bahram Ahansaz ◽  
Abbas Ektesabi
Keyword(s):  
Bound States ◽  
Decisive Role ◽  
Bound State ◽  
Negative Energy ◽  
Quantum Evolution ◽  
Level System ◽  
System Environment ◽  
Speed Up ◽  
The Relationship ◽  
Quantum Speedup

Abstract In this paper, we investigate the relationship between the quantum speedup, non-Markovianity and formation of a system-environment bound state. Previous results show a monotonic relation between these three such that providing bound states with more negative energy can lead to a higher degree of non-Markovianity, and hence to a greater speed of quantum evolution. By studying dynamics of a dissipative two-level system or a V-type three-level system, when similar and additional systems are present, we reveal that the quantum speedup is exclusively related to the formation of the system-environment bound state, while the non-Markovian effect of the system dynamics is neither necessary nor sufficient to speed up the quantum evolution. On the other hand, it is shown that only the formation of the system-environment bound state plays a decisive role in the acceleration of the quantum evolution.

scholarly journals Energy levels in muonic helium

2019 ◽  
Vol 222 ◽  
pp. 03009
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Hyperfine Structure ◽  
Bound States ◽  
Energy Levels ◽  
Computer Code ◽  
Bound State ◽  
Relativistic Correction ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.

SUPERSYMMETRY APPROACHES TO THE BOUND STATES OF THE GENERALIZED WOODS–SAXON POTENTIAL

2004 ◽  
Vol 19 (08) ◽  
pp. 615-625 ◽  
Author(s):  
H. FAKHRI ◽  
J. SADEGHI
Keyword(s):  
Differential Equation ◽  
Quantum Mechanics ◽  
Bound States ◽  
Differential Operators ◽  
Energy Levels ◽  
Negative Energy ◽  
Saxon Potential ◽  
First Order ◽  
Jacobi Differential Equation ◽  
Algebraic Solutions

Using the associated Jacobi differential equation, we obtain exactly bound states of the generalization of Woods–Saxon potential with the negative energy levels based on the analytic approach. According to the supersymmetry approaches in quantum mechanics, we show that these bound states by four pairs of the first-order differential operators, represent four types of the laddering equations. Two types of these supersymmetry structures, suggest the derivation of algebraic solutions by two different approaches for the bound states.

Aharonov–Bohm effect in a Coulomb-type potential under the influence of a cutoff point

2021 ◽  
pp. 2150136
Author(s):  
K. Bakke
Keyword(s):  
Electric Fields ◽  
Bound States ◽  
Energy Levels ◽  
Bound State ◽  
Cutoff Point ◽  
Coulomb Type ◽  
Bohm Effect ◽  
Forbidden Region ◽  
Aharonov Bohm ◽  
Type Potential

We analyze the influence of a cutoff point on a Coulomb-type potential that stems from the interaction of an electron with electric fields. This cutoff point establishes a forbidden region for the electron. Then, we search for bound state solutions to the Schrödinger equation. In addition, we consider a rotating reference frame. We show that the effects of rotation break the degeneracy of the energy levels. Further, we discuss the Aharonov–Bohm effect for bound states.

scholarly journals EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN–GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL

2008 ◽  
Vol 19 (09) ◽  
pp. 1425-1442 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Exact Bound ◽  
Pseudoharmonic Potential ◽  
Klein Gordon ◽  
Equal Scalar ◽  
Klein Gordon Equation

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

DETERMINATION OF LINEAR-CHAIN MULTIPLE BOUND STATE RESONANCES IN REFLECTION HIGH-ENERGY ELECTRON DIFFRACTION

1994 ◽  
Vol 01 (02n03) ◽  
pp. 261-271 ◽  
Author(s):  
T.C. ZHAO ◽  
S.Y. TONG ◽  
A. IGNATIEV
Keyword(s):  
Electron Diffraction ◽  
Bound States ◽  
Energy Levels ◽  
Linear Chain ◽  
Bound State ◽  
High Energy ◽  
Dynamical Theory ◽  
Energy Electron ◽  
High Energy Electron ◽  
Discrete Energy

Using the R-matrix dynamical theory of Reflection High-Energy Electron Diffraction (RHEED), we analyze the intensity anomalies commonly observed in RHEED rocking curves. Results for Ag(001) and Pt(111) show that the anomalies are associated with the trapping of particular components of the electron wave field inside the crystal by linear chain potential parallel to the surface. These pseudobound states correspond to minima in the total elastic flux of an ultrathin film (≤10 monolayer) and maxima in the inelastic flux. The discrete energy levels of the bound states in Ag(001) and Pt(111) are determined for the first time and the effect of such bound states on the rocking curves is discussed.

On noninertial effects inducing a confinement of a neutral particle to a hard-wall confining potential

Open Physics ◽  
2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Knut Bakke
Keyword(s):  
Bound States ◽  
Magnetic Dipole Moment ◽  
Neutral Particle ◽  
Energy Levels ◽  
Bound State ◽  
Field Configuration ◽  
Hard Wall ◽  
Confining Potential ◽  
Noninertial Effects

AbstractIn this contribution, we discuss the confinement of a nonrelativistic spin-half neutral particle to a hard-wall confining potential induced by noninertial effects. We show that the geometry of the manifold plays the role of a hard-wall confining potential and yields bound state solutions. We also consider a neutral particle with a permanent magnetic dipole moment interacting with a field configuration induced by noninertial effects, and discuss the behaviour of the induced fields and obtain energy levels for bound states.

scholarly journals Spectral collapse in anisotropic two-photon Rabi model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. F. Lo
Keyword(s):  
Bound States ◽  
Energy Levels ◽  
Energy Difference ◽  
Bound State ◽  
Discrete Energy ◽  
Radiation Mode ◽  
Two Photon ◽  
Rabi Model ◽  
Matter Interaction ◽  
Light Matter Interaction

AbstractIn this communication, based upon a squeezed-state trial wave function, we have performed a simple variational study of the spectral collapse in the anisotropic two-photon Rabi model. Our analysis indicates that the light-matter interaction and the spin-flipping (together with the anisotropy) effectively constitute two competing impacts upon the radiation mode. Whilst the former tries to decrease the radiation mode frequency, the latter may counteract or reinforce it. The light-matter interaction appears to dominate the frequency modulation as its coupling strengths go beyond the critical values, leading to the emergence of the spectral collapse. However, at the critical couplings the dominance of the light-matter interaction is not complete, and incomplete spectral collapse appears. Accordingly, at the critical couplings the eigenenergy spectrum comprises both a set of discrete energy levels and a continuous energy spectrum. The discrete eigenenergy spectrum can be derived via a simple one-to-one mapping to the bound state problem of a particle of variable effective mass in a finite potential well, and the number of bound states available is determined by the energy difference between the two atomic levels. Each of these eigenenergies has a twofold degeneracy corresponding to the spin degree of freedom.

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.

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