Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bound states in Andreev billiards with soft walls   The energy spectrum and the eigenstates of a rectangular quantum dot
containing soft potential walls in contact with a superconductor are calculated
by solving the Bogoliubov-de Gennes (BdG) equation. We compare the quantum
mechanical solutions with a semiclassical analysis using a Bohr--Sommerfeld
(BS) quantization of periodic orbits. We propose a simple extension of the BS
approximation which is well suited to describe Andreev billiards with parabolic
potential walls. The underlying classical periodic electron-hole orbits are
directly identified in terms of ``scar'' like features engraved in the quantum
wavefunctions of Andreev states determined here for the first time.

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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas