Junctions appear naturally when one studies surface states or transport properties of
quasi-1-dimensional materials such as carbon nanotubes, polymers and quantum
wires. These materials can be seen as 1-dimensional systems embedded in the
3-dimensional space. We first establish a mean-field description of reduced
Hartree–Fock-type for a 1-dimensional periodic system in the 3-dimensional space (a
quasi-1-dimensional system), the unit cell of which is unbounded. With mild
summability condition, we next show that a quasi-1-dimensional quantum 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-1-dimensional systems occupying separate
half-spaces in three dimensions, 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.
Keywords
mean field, junction, quasi-1-dimensional, quantum Coulomb
system
