Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic spectral analysis in semiconductor nanowire heterostructures   Mathematical settings in which heterogeneous structures affect electron
transport through a tube-shaped quantum waveguide are studied, highlighting the
interaction between heterogeneities and geometric parameters like curvature and
torsion. First, the macroscopic behavior of a nanowire made of composite fibers
with microscopic periodic texture is analyzed, which amounts to determining the
asymptotic behavior of the spectrum of an elliptic Dirichlet eigenvalue problem
with finely oscillating coefficients in a tube with shrinking cross section. A
suitable formal expansion suggests that the effective one-dimensional limit
problem is of Sturm-Liouville type and yields the explicit formula for the
underlying potential. In the torsion-free case, these findings are made
rigorous by performing homogenization and 3d-1d dimension reduction for the
two-scale problem in a variational framework by means of Gamma-convergence.
Second, waveguides with non-oscillating inhomogeneities in the cross section
are investigated. This leads to explicit criteria for propagation and
localization of eigenmodes.

1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn