Regularity of the Density of States for Stochastic Jacobi Matrices: A Review

1987 ◽  
pp. 245-266 ◽  
Author(s):  
Barry Simon
Keyword(s):  
Density Of States ◽  
Jacobi Matrices

A TRACE FORMULA FOR A FAMILY OF JACOBI OPERATORS

2009 ◽  
Vol 07 (02) ◽  
pp. 115-130 ◽  
Author(s):  
ALFONSO F. AGNEW ◽  
ALAIN BOURGET
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Density Of States ◽  
Trace Formula ◽  
Jacobi Matrices ◽  
Jacobi Operators ◽  
Leading Term

In this paper, we compute the leading term in the asymptotic expansion of the trace of a family of Jacobi matrices as their order gets arbitrarily large. We then apply this formula to compute the density of states of the zeros of a class of polynomials associated with the Heun differential equation.

DENSITY OF STATES EFFECTS IN ALLOYS OF SmS WITH YS AND SmAs

1976 ◽  
Vol 37 (C4) ◽  
pp. C4-241-C4-248 ◽  
Author(s):  
S. VON MOLNAR ◽  
T. PENNEY ◽  
F. HOLTZBERG
Keyword(s):  
Density Of States

DISORDER INDUCED DENSITY OF STATES WITHIN THE BAND GAP

1981 ◽  
Vol 42 (C4) ◽  
pp. C4-59-C4-62
Author(s):  
H. Leschke ◽  
B. Kramer
Keyword(s):  
Band Gap ◽  
Density Of States

Density of states near the localization threshold

1996 ◽  
Vol 166 (8) ◽  
pp. 907
Author(s):  
Igor' M. Suslov
Keyword(s):  
Density Of States ◽  
Localization Threshold

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.

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