Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Free-energy functional of the electronic potential for
  Schr\"{o}dinger-Poisson theory   In the study of model electronic device systems where electrons are typically
under confinement, a key obstacle is the need to iteratively solve the coupled
Schr\"{o}dinger-Poisson (SP) equation. It is possible to bypass this obstacle
by adopting a variational approach and obtaining the solution of the SP
equation by minimizing a functional. Further, using molecular dynamics methods
that treat the electronic potential as a dynamical variable, the functional can
be minimized on the fly in conjunction with the update of other dynamical
degrees of freedom leading to considerable reduction in computational costs.
But such approaches require access to a true free-energy functional, one that
evaluates to the equilibrium free energy at its minimum. In this paper, we
present a variational formulation of the Schr\"{o}dinger-Poisson (SP) theory
with the needed free-energy functional of the electronic potential. We apply
our formulation to semiconducting nanostructures and provide the expression of
the free-energy functional for narrow channel quantum wells where the local
density approximation yields accurate physics and for the case of wider
channels where Thomas-Fermi approximation is valid.

12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc