Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balanced gain and loss in spatially extended
  non-$\mathcal{PT}$-symmetric multi-well potentials   The experimental realization of balanced gain and loss in a quantum system
has been a long standing goal in quantum mechanics since the introduction of
the concept of $\mathcal{PT}$ symmetry and has only recently been achieved. In
this paper we analyze balanced gain and loss in Gaussian multi-well potentials
with either only gain or loss in each well. By means of symmetrization via
matrix models we can construct asymmetric extended potentials with partially
real or complex conjugate spectra. This will be demonstrated explicitly for
double-well and triple-well systems. Such systems can be realized with
Bose-Einstein condensates in optical trapping potentials in the presence of
localized particle gain and loss. The usage of asymmetric potentials in the
process is more versatile and is considered beneficial in real experimental
implementations.

25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn