Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariants of the single impurity Anderson model and implications for
  conductance functionals   An exact relation between the conductance maximum $G_0$ at zero temperature
and a ratio of lead densities is derived within the framework of the single
impurity Anderson model: $G_0={\mathfrak R}[n] \frac{2e^2}{h}$, where
${\mathfrak R}[n]=4\Delta N_{{\cal L},x} \Delta N_{{\cal R},x}/(\Delta N_{{\cal
L},x}+\Delta N_{{\cal R},x})^2$ and $\Delta N_{{\cal L},x}$, $\Delta N_{{\cal
R},x}$ denote the excess density in the left/right lead at distance $x$ due to
the presence of the impurity at the origin, $x=0$. The relation constitutes a
parameter-free expression of the conductance of the model in terms of the
ground state density that generalizes an earlier result to the generic case of
asymmetric lead couplings. It turns out that the specific density ratio,
${\mathfrak R}[n]$, is independent of the distance to the impurity $x$, the
(magnetic) band-structure and filling fraction of the contacting wires, the
strength of the onsite interaction, the gate voltage and the temperature.
Disorder induced backscattering in the contacting wires has an impact on
${\mathfrak R}$ that we discuss. Our result suggests that it should be
possible, in principle, to determine experimentally the peak conductance of the
Anderson impurity by performing a combination of measurements of ground-state
densities.

32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc