Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral projections of the complex cubic oscillator   We prove the spectral instability of the complex cubic oscillator
$-\frac{d^2}{dx^2}+ix^3+i\alpha x$ for non-negative values of the parameter
$\alpha$, by getting the exponential growth rate of $\|\Pi_n(\alpha)\|$, where
$\Pi_n(\alpha)$ is the spectral projection associated with the $n$-th
eigenvalue of the operator. More precisely, we show that for all non-negative
$\alpha$ \[
  \lim\limits_{n\to+\infty}\frac{1}{n}\log\|\Pi_n(\alpha)\| =
\frac{\pi}{\sqrt{3}}. \]

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The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
23
The categories of this paper are: solv-int