Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Particle production at a finite potential step: Transition from
  Euler-Heisenberg to Klein paradox   Spontaneous pair production for spin-$1/2$ and spin-$0$ particles is explored
in a quantitative manner for a static $\tanh$-Sauter potential step (SS),
evaluating the imaginary part of the effective action. We provide finite-valued
per unit-surface results, including the exact sharp-edge Klein paradox (KP)
limit, which is the upper bound to pair production. At the vacuum instability
threshold the spin-$0$ particle production can surpass that for the spin-$1/2$
rate. Presenting the effect of two opposite sign Sauter potential steps
creating a well we show that spin-$0$ pair production, contrary to the case of
spin-$1/2$, requires a smoothly sloped wall.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an