Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Negative modes and decay-rate transition   We investigate a relationship between the number of the negative modes around
periodic instanton solution and the type of the decay-rate transition. It is
shown that for the case of first-order decay-rate transition the lowest
positive mode at low energy periodic instanton becomes additional negative mode
at high energy regime, while in the second-order case there is only one
negative mode in the full range of energy. This kind of analysis on the
negative modes makes it possible to derive the criterion for the first-order
transition.

35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas