Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-scale homogenization with bounded ratios and Anomalous Slow
  Diffusion   We show that the effective diffusivity matrix $D(V^n)$ for the heat operator
$\partial_t-(\Delta/2-\nabla V^n \nabla)$ in a periodic potential
$V^n=\sum_{k=0}^n U_k(x/R_k)$ obtained as a superposition of Holder-continuous
periodic potentials $U_k$ (of period $\T^d:=\R^d/\Z^d$, $d\in \N^*$,
$U_k(0)=0$) decays exponentially fast with the number of scales when the
scale-ratios $R_{k+1}/R_k$ are bounded above and below. From this we deduce the
anomalous slow behavior for a Brownian Motion in a potential obtained as a
superposition of an infinite number of scales: $dy_t=d\omega_t -\nabla
V^\infty(y_t) dt$

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The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
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The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th