Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Adiabatic quantum dynamics of a random Ising chain across its quantum
  critical point   We present here our study of the adiabatic quantum dynamics of a random Ising
chain across its quantum critical point. The model investigated is an Ising
chain in a transverse field with disorder present both in the exchange coupling
and in the transverse field. The transverse field term is proportional to a
function $\Gamma(t)$ which, as in the Kibble-Zurek mechanism, is linearly
reduced to zero in time with a rate $\tau^{-1}$, $\Gamma(t)=-t/\tau$, starting
at $t=-\infty$ from the quantum disordered phase ($\Gamma=\infty$) and ending
at $t=0$ in the classical ferromagnetic phase ($\Gamma=0$). We first analyze
the distribution of the gaps -- occurring at the critical point $\Gamma_c=1$ --
which are relevant for breaking the adiabaticity of the dynamics. We then
present extensive numerical simulations for the residual energy $E_{\rm res}$
and density of defects $\rho_k$ at the end of the annealing, as a function of
the annealing inverse rate $\tau$. %for different lenghts of the chain. Both
the average $E_{\rm res}(\tau)$ and $\rho_k(\tau)$ are found to behave
logarithmically for large $\tau$, but with different exponents, $[E_{\rm
res}(\tau)/L]_{\rm av}\sim 1/\ln^{\zeta}(\tau)$ with $\zeta\approx 3.4$, and
$[\rho_k(\tau)]_{\rm av}\sim 1/\ln^{2}(\tau)$. We propose a mechanism for
$1/\ln^2{\tau}$-behavior of $[\rho_k]_{\rm av}$ based on the Landau-Zener
tunneling theory and on a Fisher's type real-space renormalization group
analysis of the relevant gaps. The model proposed shows therefore a
paradigmatic example of how an adiabatic quantum computation can become very
slow when disorder is at play, even in absence of any source of frustration.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol