Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlocal Josephson effect in Andreev molecules   We propose the "Andreev molecule", an artificial quantum system composed of
two closely spaced Josephson junctions. The coupling between Josephson
junctions in an Andreev molecule occurs through the overlap and hybridization
of the junction's "atomic" orbitals, Andreev Bound States. A striking
consequence is that the supercurrent flowing through one junction depends on
the superconducting phase difference across the other junction. Using the
Bogolubiov-de-Gennes formalism, we derive the energy spectrum and non-local
current-phase relation for arbitrary separation. We demonstrate the possibility
of creating a $\varphi$-junction and propose experiments to verify our
predictions. Andreev molecules may have potential applications in quantum
information, metrology, sensing, and molecular simulation.

36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
2
The categories of this paper are: math
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th