Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonanalytic quantum oscillator image of complete replica symmetry
  breaking   We describe the effect of replica symmetry breaking in the field distribution
function P(h) of the T=0 SK-model as the difference between a split Gaussian
and the first excited state $\psi_1$ of a weakly anharmonic oscillator with
nonanalytic shift by means of the analogy $P(h)<->|\psi_1(x)|$. New numerical
calculations of the leading 100 orders of replica symmetry breaking (RSB) were
performed in order to obtain P(h), employing the exact mapping between density
of states $\rho(E)$ of the fermionic SK-model and P(h) of the standard model,
as derived by Perez-Castillo and Sherrington. Fast convergence towards a fixed
point function $\rho(E)$ for infinite steps of RSB is observed. A surprisingly
small number of harmonic oscillator wave-functions suffices to represent this
fixed point function. This allows to determine an anharmonic potential V(x)
with nonanalytic shift, whose first excited state represents $\rho(E)$ and
hence P(h). The harmonic potential with unconventional shift $V_2(x)\sim
(|x|-x_0)^2=(x-x_0\,sign(x))^2$ yields already a very good approximation, since
anharmonic couplings of $V(x)-V_2(x)\sim |x|^{m}, m>2,$ decay rapidly with
increasing m. We compare the pseudogap-forming effect of replica symmetry
breaking, hosted by the fermionic SK-model, with the analogous effect in the
Coulomb glass as designed by Davies-Lee-Rice and described by M\"uller-Pankov.

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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex