Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Green's functions for solving differential equations, in non-boundary
  value problems in near-field optics and in quantum transport through point
  contacts   This introduction to Green's functions is based on their role as kernels of
differential equations. The procedures to construct solutions to a differential
equation with an external source or with an inhomogeneity term are put together
to derive the Dyson equation for the Green's function of the inhomogeneous
system. Very different areas of physics such as, for example, electrodynamics
and quantum transport, can profit from this Green's function formalism. The
fundamental homogeneous-medium Green's tensor of electrodynamics is deduced
from the field of a dipole. Based upon that a numerical procedure is presented
to solve the wave-equation for the near-field in a scattering setup for
arbitrary material distributions. The full inhomogeneous system's Green's
function is not explicitly needed to get the fields, although it can be
obtained by a very similar calculation and in optics can be interpreted as a
density of states. It is demonstrated how the transport problem for two open
free-electron gas reservoirs with arbitrary coupling can be solved by finding
the system's Green's function. In this sense the article is an introduction on
Green's functions for treating interaction. A very detailed discussion of the
current formula is given on an elementary basis.

24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg