Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bloch-like waves in random-walk potentials based on supersymmetry   Bloch's theorem was a major milestone that established the principle of
bandgaps in crystals. Although it was once believed that bandgaps could form
only under conditions of periodicity and long-range correlations for Bloch's
theorem, this restriction was disproven by the discoveries of amorphous media
and quasicrystals. While network and liquid models have been suggested for the
interpretation of Bloch-like waves in disordered media, these approaches based
on searching for random networks with bandgaps have failed in the deterministic
creation of bandgaps. Here, we reveal a deterministic pathway to bandgaps in
random-walk potentials by applying the notion of supersymmetry to the wave
equation. Inspired by isospectrality, we follow a methodology in contrast to
previous methods: we transform order into disorder while preserving bandgaps.
Our approach enables the formation of bandgaps in extremely-disordered
potentials analogous to Brownian motion, and also allows the tuning of
correlations while maintaining identical bandgaps, thereby creating a family of
potentials with 'Bloch-like eigenstates'.

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The categories of this paper are: cmp-lg
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The categories of this paper are: dg-ga
2
The categories of this paper are: math
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th