Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direction-Dependent Parity-Time Phase Transition and Non-Reciprocal
  Directional Amplification with Dynamic Gain-Loss Modulation   We show that a dynamic gain-loss modulation in an optical structure can lead
to a direction-dependent parity-time (PT) phase transition. The phase
transition can be made thresholdless in the forward direction, and yet remains
with a non-zero threshold in the backward direction. As a result,
non-reciprocal directional amplification can be realized.

21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph