Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Plane Wave Methods for Quantum Eigenvalue Problems of Incommensurate
  Systems   We propose a novel numerical algorithm for computing the electronic structure
related eigenvalue problem of incommensurate systems. Unlike the conventional
practice that approximates the system by a large commensurate supercell, our
algorithm directly discretizes the eigenvalue problem under the framework of a
plane wave method. The emerging ergodicity and the interpretation from higher
dimensions give rise to many unique features compared to what we have been
familiar with in the periodic system. The numerical results of 1D and 2D
quantum eigenvalue problems are presented to show the reliability and
efficiency of our scheme. Furthermore, the extension of our algorithm to full
Kohn-Sham density functional theory calculations are discussed.

15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
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
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th