Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamical Localization for the Random Dimer Model   We study the one-dimensional random dimer model, with Hamiltonian
$H_\omega=\Delta + V_\omega$, where for all $x\in\Z,
V_\omega(2x)=V_\omega(2x+1)$ and where the $V_\omega(2x)$ are i.i.d. Bernoulli
random variables taking the values $\pm V, V>0$. We show that, for all values
of $V$ and with probability one in $\omega$, the spectrum of $H$ is pure point.
If $V\leq1$ and $V\neq 1/\sqrt{2}$, the Lyapounov exponent vanishes only at the
two critical energies given by $E=\pm V$. For the particular value
$V=1/\sqrt{2}$, respectively $V=\sqrt{2}$, we show the existence of additional
critical energies at $E=\pm 3/\sqrt{2}$, resp. E=0. On any compact interval $I$
not containing the critical energies, the eigenfunctions are then shown to be
semi-uniformly exponentially localized, and this implies dynamical
localization: for all $q>0$ and for all $\psi\in\ell^2(\Z)$ with sufficiently
rapid decrease:
  $$ \sup_t r^{(q)}_{\psi,I}(t) \equiv \sup_t < P_I(H_\omega)\psi_t, |X|^q
P_I(H_\omega)\psi_t > <\infty. $$
  Here $\psi_t=e^{-iH_\omega t} \psi$, and $P_I(H_\omega)$ is the spectral
projector of $H_\omega$ onto the interval $I$. In particular if $V>1$ and
$V\neq \sqrt{2}$, these results hold on the entire spectrum (so that one can
take $I=\sigma(H_\omega)$).

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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph