scholarly journals A generalised Gauss circle problem and integrated density of states

2016 ◽  
Vol 6 (4) ◽  
pp. 859-879 ◽  
Author(s):  
Jean Lagacé ◽  
Leonid Parnovski
Keyword(s):  
Density Of States ◽  
Integrated Density Of States ◽  
Circle Problem ◽  
Gauss Circle Problem

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.

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