Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mean--field stability for the junction of quasi 1D systems with Coulomb
  interactions   Junctions appear naturally when one studies surface states or transport
properties of quasi one dimensional materials such as carbon nanotubes,
polymers and quantum wires. These materials can be seen as 1D systems embedded
in the 3D space. In this article, we first establish a mean--field description
of reduced Hartree--Fock type for a 1D periodic system in the 3D space (a quasi
1D system), the unit cell of which is unbounded. With mild summability
condition, we next show that a quasi 1D system in its ground state can be
described by a mean--field Hamiltonian. We also prove that the Fermi level of
this system is always negative. A junction system is described by two different
infinitely extended quasi 1D systems occupying separately half spaces in 3D,
where Coulombic electron-electron interactions are taken into account and
without any assumption on the commensurability of the periods. We prove the
existence of the ground state for a junction system, the ground state is a
spectral projector of a mean--field Hamiltonian, and the ground state density
is unique.

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The categories of this paper are: cs
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys