Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodicity breaking, ageing, and confinement in generalised diffusion
  processes with position and time dependent diffusivity   We study generalised anomalous diffusion processes whose diffusion
coefficient $D(x,t)\sim D_0|x|^{\alpha}t^{\beta}$ depends on both the position
$x$ of the test particle and the process time $t$. This process thus combines
the features of scaled Brownian motion and heterogeneous diffusion parent
processes. We compute the ensemble and time averaged mean squared displacements
of this generalised diffusion process. The scaling exponent of the ensemble
averaged mean squared displacement is shown to be the product of the critical
exponents of the parent processes, and describes both subdiffusive and
superdiffusive systems. We quantify the amplitude fluctuations of the time
averaged mean squared displacement as function of the length of the time series
and the lag time. In particular, we observe a weak ergodicity breaking of this
generalised diffusion process: even in the long time limit the ensemble and
time averaged mean squared displacements are strictly disparate. When we start
to observe this process some time after its initiation we observe distinct
features of ageing. We derive a universal ageing factor for the time averaged
mean squared displacement containing all information on the ageing time and the
measurement time. External confinement is shown to alter the magnitudes and
statistics of the ensemble and time averaged mean squared displacements.

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The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con