scholarly journals Erratum: Saddle point anomaly of Landau levels in graphenelike structures [Phys. Rev. B 104 , 035419 (2021)]

2022 ◽  
Vol 105 (3) ◽  
Author(s):  
A. V. Nikolaev
Keyword(s):  
Saddle Point ◽  
Landau Levels

Chern-Simons theory for electrons in high Landau levels

1999 ◽  
Vol 09 (PR10) ◽  
pp. Pr10-223-Pr10-225
Author(s):  
S. Scheidl ◽  
B. Rosenow
Keyword(s):  
Landau Levels ◽  
Simons Theory ◽  
Chern Simons ◽  
Chern Simons Theory

MATHEMATICAL MODELING OF TEMPERATURE EFFECT ON THE FAN CHART OF MAGNETOABSORPTION SPECTRUM IN SEMICONDUCTORS

2019 ◽  
pp. 104-115
Author(s):  
G. Gulyamov ◽  
U. I. Erkaboev ◽  
A. G. Gulyamov
Keyword(s):  
Mathematical Modeling ◽  
Magnetic Field ◽  
Temperature Dependence ◽  
Density Of States ◽  
Landau Levels ◽  
Joint Density ◽  
Narrow Gap ◽  
Narrow Gap Semiconductors ◽  
Dispersion Law ◽  
The Magnetic Field

The article considers the oscillations of interband magneto-optical absorption in semiconductors with the Kane dispersion law. We have compared the changes in oscillations of the joint density of states with respect to the photon energy for different Landau levels in parabolic and non-parabolic zones. An analytical expression is obtained for the oscillation of the combined density of states in narrow-gap semiconductors. We have calculated the dependence of the maximum photon energy on the magnetic field at different temperatures. A theoretical study of the band structure showed that the magnetoabsorption oscillations decrease with an increase in temperature, and the photon energies nonlinearly depend on a strong magnetic field. The article proposes a simple method for calculating the oscillation of joint density of states in a quantizing magnetic field with the non-quadratic dispersion law. The temperature dependence of the oscillations joint density of states in semiconductors with non-parabolic dispersion law is obtained. Moreover, the article studies the temperature dependence of the band gap in a strong magnetic field with the non-quadratic dispersion law. The method is applied to the research of the magnetic absorption in narrow-gap semiconductors with nonparabolic dispersion law. It is shown that as the temperature increases, Landau levels are washed away due to thermal broadening and density of states turns into a density of states without a magnetic field. Using the mathematical model, the temperature dependence of the density distribution of energy states in strong magnetic fields is considered. It is shown that the continuous spectrum of the density of states, measured at the temperature of liquid nitrogen, at low temperatures turns into discrete Landau levels. Mathematical modeling of processes using experimental values of the continuous spectrum of the density of states makes it possible to calculate discrete Landau levels. We have created the three-dimensional fan chart of magneto optical oscillations of semiconductors with considering for the joint density of energy states. For a nonquadratic dispersion law, the maximum frequency of the absorbed light and the width of the forbidden band are shown to depend nonlinearly on the magnetic field. Modeling the temperature  dependence allowed us to determine the Landau levels in semiconductors in a wide temperature spectrum. Using the proposed model, the experimental results obtained for narrow-gap semiconductors are analyzed. The theoretical results are compared with experimental results.

Saddle point criteria in semi-infinite minimax fractional programming under (Φ,ρ)-invexity

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2557-2574 ◽  
Author(s):  
Tadeusz Antczak
Keyword(s):  
Saddle Point ◽  
Fractional Programming ◽  
Generalized Convexity ◽  
Equality Constraints ◽  
New Class ◽  
Minimax Fractional Programming

Semi-infinite minimax fractional programming problems with both inequality and equality constraints are considered. The sets of parametric saddle point conditions are established for a new class of nonconvex differentiable semi-infinite minimax fractional programming problems under(?,?)-invexity assumptions. With the reference to the said concept of generalized convexity, we extend some results of saddle point criteria for a larger class of nonconvex semi-infinite minimax fractional programming problems in comparison to those ones previously established in the literature.

Bimolecular Reactions, Transition-State Theory

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Transition State ◽  
Saddle Point ◽  
Transition State Theory ◽  
Classical Mechanics ◽  
Small Degree ◽  
State Theory ◽  
Reaction Coordinate ◽  
Partition Functions ◽  
Bimolecular Reactions ◽  
Activated Complex

This chapter discusses an approximate approach—transition-state theory—to the calculation of rate constants for bimolecular reactions. A reaction coordinate is identified from a normal-mode coordinate analysis of the activated complex, that is, the supermolecule on the saddle-point of the potential energy surface. Motion along this coordinate is treated by classical mechanics and recrossings of the saddle point from the product to the reactant side are neglected, leading to the result of conventional transition-state theory expressed in terms of relevant partition functions. Various alternative derivations are presented. Corrections that incorporate quantum mechanical tunnelling along the reaction coordinate are described. Tunnelling through an Eckart barrier is discussed and the approximate Wigner tunnelling correction factor is derived in the limit of a small degree of tunnelling. It concludes with applications of transition-state theory to, for example, the F + H2 reaction, and comparisons with results based on quasi-classical mechanics as well as exact quantum mechanics.

Quantum Hall effect in a saddle-point system

1998 ◽  
Vol 2 (1-4) ◽  
pp. 523-526
Author(s):  
M.V Budantsev ◽  
Z.D Kvon ◽  
A.G Pogosov ◽  
E.B Olshanetskii ◽  
D.K Maude ◽  
...  
Keyword(s):  
Saddle Point ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Point System ◽  
Saddle Point System

The Improvement of Newton Method and the Validation of Optimization Idea of Blind Walking Repeatedly

2011 ◽  
Vol 250-253 ◽  
pp. 4061-4064
Author(s):  
Chun Ling Zhang
Keyword(s):  
Saddle Point ◽  
Newton Method ◽  
Optimization Problem ◽  
Initial Point ◽  
Optimization Method ◽  
Maximum Point ◽  
Optimal Result ◽  
Feasible Domain ◽  
Parallel Arithmetic ◽  
Newton Direction

The existence of maximum point, oddity point and saddle point often leads to computation failure. The optimization idea is based on the reality that the optimum towards the local minimum related the initial point. After getting several optimal results with different initial point, the best result is taken as the final optimal result. The arithmetic improvement of multi-dimension Newton method is improved. The improvement is important for the optimization method with grads convergence rule or searching direction constructed by grads. A computational example with a saddle point, maximum point and oddity point is studied by multi-dimension Newton method, damped Newton method and Newton direction method. The importance of the idea of blind walking repeatedly is testified. Owing to the parallel arithmetic of modernistic optimization method, it does not need to study optimization problem with seriate feasible domain by modernistic optimization method.

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