Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Electronic States in One, Two, and Three Dimensional Highly Amorphous
  Materials: A Tight Binding Treatment   In a tight binding framework, we analyze the characteristics of electronic
states in strongly disordered materials (hopping sites are placed randomly with
no local order) with tunneling matrix elements decaying exponentially in the
atomic separation with various decay ranges l examined. We calculate the
density of states (DOS) and the Inverse Participation Ratio (IPR) for amorphous
atomic configurations in one, two, and three dimensions. With a finite size
scaling analysis of the IPR statistical distributions, it is shown that states
are either extended or localized for a particular energy, and phase portraits
for wave functions are obtained showing extended and localized behavior in the
thermodynamic limit. While we conclude that all states are localized in 1D, in
the 2D case there is a threshold for l above which some eigenstates appear to
be extended and below which wave functions are entirely localized. For 3D
geometries, there are two mobility boundaries flanking an intermediate range of
energies where states are extended with eigenstates localized for energies
above or below this range. While a zone of extended states persists even for
very short l, the width of the region tends to zero exponentially (i.e. scaling
as exp{-A/l}) for very small decay length scales.

22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph