Asymptotic Behavior of the Integrated Density of States at Spectral Boundaries in Multidimensional Problems

1992 ◽  
pp. 190-254
Author(s):  
Leonid Pastur ◽  
Alexander Figotin
Keyword(s):  
Asymptotic Behavior ◽  
Density Of States ◽  
Integrated Density Of States ◽  
Multidimensional Problems

scholarly journals Asymptotics of Negative Exponential Moments for Annealed Brownian Motion in a Renormalized Poisson Potential

2011 ◽  
Vol 2011 ◽  
pp. 1-43 ◽  
Author(s):  
Xia Chen ◽  
Alexey Kulik
Keyword(s):  
Asymptotic Behavior ◽  
Brownian Motion ◽  
Detailed Analysis ◽  
Density Of States ◽  
Random Schrödinger Operators ◽  
Integrated Density Of States ◽  
Random Potentials ◽  
Lifshitz Tails ◽  
Exponential Moments ◽  
Negative Exponential

In (Chen and Kulik, 2009), a method of renormalization was proposed for constructing some more physically realistic random potentials in a Poisson cloud. This paper is devoted to the detailed analysis of the asymptotic behavior of the annealed negative exponential moments for the Brownian motion in a renormalized Poisson potential. The main results of the paper are applied to studying the Lifshitz tails asymptotics of the integrated density of states for random Schrödinger operators with their potential terms represented by renormalized Poisson potentials.

scholarly journals The landscape law for the integrated density of states

2021 ◽  
Vol 390 ◽  
pp. 107946
Author(s):  
G. David ◽  
M. Filoche ◽  
S. Mayboroda
Keyword(s):  
Density Of States ◽  
Integrated Density Of States

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.

Sign in / Sign up

Export Citation Format

Share Document