Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fluctuations of random matrix products and 1D Dirac equation with random
  mass   We study the fluctuations of certain random matrix products $\Pi_N=M_N\cdots
M_2M_1$ of $\mathrm{SL}(2,\mathbb{R})$, describing localisation properties of
the one-dimensional Dirac equation with random mass. In the continuum limit,
i.e. when matrices $M_n$'s are close to the identity matrix, we obtain
convenient integral representations for the variance
$\Gamma_2=\lim_{N\to\infty}\mathrm{Var}(\ln||\Pi_N||)/N$. The case studied
exhibits a saturation of the variance at low energy $\varepsilon$ along with a
vanishing Lyapunov exponent $\Gamma_1=\lim_{N\to\infty}\ln||\Pi_N||/N$, leading
to the behaviour $\Gamma_2/\Gamma_1\sim\ln(1/|\varepsilon|)\to\infty$ as
$\varepsilon\to0$. Our continuum description sheds new light on the
Kappus-Wegner (band center) anomaly.

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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: math
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: physics