Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Burgers' Flows as Markovian Diffusion Processes   We analyze the unforced and deterministically forced Burgers equation in the
framework of the (diffusive) interpolating dynamics that solves the so-called
Schr\"{o}dinger boundary data problem for the random matter transport. This
entails an exploration of the consistency conditions that allow to interpret
dispersion of passive contaminants in the Burgers flow as a Markovian diffusion
process. In general, the usage of a continuity equation $\partial_t\rho
=-\nabla (\vec{v}\rho)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the
Burgers field and $\rho $ is the density of transported matter, is at variance
with the explicit diffusion scenario. Under these circumstances, we give a
complete characterisation of the diffusive transport that is governed by
Burgers velocity fields. The result extends both to the approximate description
of the transport driven by an incompressible fluid and to motions in an
infinitely compressible medium. Also, in conjunction with the Born statistical
postulate in quantum theory, it pertains to the probabilistic (diffusive)
counterpart of the Schr\"{o}dinger picture quantum dynamics.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex