Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: L\'{e}vy flights in inhomogeneous environments   We study the long time asymptotics of probability density functions (pdfs) of
L\'{e}vy flights in different confining potentials. For that we use two models:
Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics.
It turns out that the semigroup modeling provides much stronger confining
properties than the standard Langevin one. Since contractive semigroups set a
link between L\'{e}vy flights and fractional (pseudo-differential) Hamiltonian
systems, we can use the latter to control the long - time asymptotics of the
pertinent pdfs. To do so, we need to impose suitable restrictions upon the
Hamiltonian and its potential. That provides verifiable criteria for an
invariant pdf to be actually an asymptotic pdf of the semigroup-driven
jump-type process. For computational and visualization purposes our
observations are exemplified for the Cauchy driver and its response to external
polynomial potentials (referring to L\'{e}vy oscillators), with respect to both
dynamical mechanisms.

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The categories of this paper are: econ
3
The categories of this paper are: physics
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: stat