Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transport and localization of waves in ladder-shaped lattices with
  locally $\mathcal{PT}$-symmetric potentials   We study numerically the transport and localization properties of waves in
ordered and disordered ladder-shaped lattices with local $\mathcal{PT}$
symmetry. Using a transfer matrix method, we calculate the transmittance and
the reflectance for the individual channels and the Lyapunov exponent for the
whole system. In the absence of disorder, we find that when the gain/loss
parameter $\rho$ is smaller than the interchain coupling parameter $t_{v}$, the
transmittance and the reflectance are periodic functions of the system size,
whereas when $\rho$ is larger than $t_{v}$, the transmittance is found to be an
exponentially-decaying function while the reflectance attains a saturation
value in the thermodynamic limit. For a fixed system size, there appear perfect
transmission resonances in each individual channel at several values of the
gain/loss strength smaller than $t_{v}$. A singular behavior of the
transmittance is also found to appear at various values of $\rho$ for a given
system size. When disorder is inserted into the on-site potentials, these
behaviors are changed substantially due to the interplay between disorder and
the gain/loss effect. When $\rho$ is smaller than $t_{v}$, we find that the
presence of locally $\mathcal{PT}$-symmetric potentials suppresses Anderson
localization, as compared to the localization in the corresponding Hermitian
system. When $\rho$ is larger than $t_{v}$, we find that localization becomes
more pronounced at higher gain/loss strengths. We also find that the phenomenon
of anomalous localization occurs in disordered locally $\mathcal{PT}$-symmetric
systems precisely at the spectral positions $E=0$ and
$E=\pm\sqrt{t_{v}^2-\rho^2}$. The anomaly at the band center manifests as a
sharp peak contrary to the conventional cases, whereas the anomalies at
$E=\pm\sqrt{t_{v}^2-\rho^2}$ manifest as sharp dips.

27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn