Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Markovian Stochastic Liouville equation and its Markovian
  representation. Extensions of the continuous time random walk approach   Some specific features and extensions of the continuous time random walk
(CTRW) approach are analyzed in detail within the Markovian representation (MR)
and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR
CTRW processes are represented by multidimensional Markovian ones. In this
representation the probability distribution function (PDF) W(t) of fluctuation
renewals is associated with that of reoccurrences in a certain jump state of
some Markovian controlling process. Within the MR the non-Markovian SLE, which
describes the effect of CTRW-like noise on relaxation of dynamic and stochastic
systems, is generalized to take into account the influence of relaxing systems
on statistical properties of noise. The generalized non-Markovian SLE is
applied to study two modifications of the CTRW approach. One of them considers
the cascaded CTRWs in which the controlling process is actually CTRW-like one
controlled by another CTRW process, controlled in turn by the third one, etc.
Within the MR simple expression for the PDF W(t) of total controlling process
is obtained in terms of Markovian variants of controlling PDFs in the cascade.
The expression is shown to be especially simple and instructive in the case of
anomalous processes determined by long time tailed W(t). The cascaded CTRWs can
model the effect of complexity of a system on relaxation kinetics (in glasses,
fractals, branching media, ultrametric structures, etc.). Another
CTRW-modification describes the kinetics of processes governed by fluctuating
W(t). Within the MR the problem is analyzed in a general form without
restrictive assumptions on correlations of PDFs of consecutive renewals. The
analysis shows that W(t) can strongly affect the kinetics of the process.
Possible manifestations of this effect are discussed.

37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph