Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-ergodicity, fluctuations, and criticality in heterogeneous diffusion
  processes   We study the stochastic behavior of heterogeneous diffusion processes with
the power-law dependence $D(x)\sim|x|^{\alpha}$ of the generalized diffusion
coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on
statistical measures such as the amplitude scatter of the time averaged mean
squared displacement of individual realizations, the ergodicity breaking and
non-Gaussianity parameters, as well as the probability density function
$P(x,t)$ we analyze the weakly non-ergodic character of the heterogeneous
diffusion process and, particularly, the degree of irreproducibility of
individual realization. As we show, the fluctuations between individual
realizations increase with growing modulus $|\alpha|$ of the scaling exponent.
The fluctuations appear to diverge when the critical value $\alpha=2$ is
approached, while for even larger $\alpha$ the fluctuations decrease, again. At
criticality, the power-law behavior of the mean squared displacement changes to
an exponentially fast growth, and the fluctuations of the time averaged mean
squared displacement do not seem to converge for increasing number of
realizations. From a systematic comparison we observe some striking
similarities of the heterogeneous diffusion process with the familiar
subdiffusive continuous time random walk process with power-law waiting time
distribution and diverging characteristic waiting time.

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The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
1
The categories of this paper are: cs