Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of a nonlinear quantum oscillator under non-Markovian pumping   We consider dynamics of a quantum nonlinear oscillator subjected to
non-Markovian pumping. Models of this kind can describe formation of
exciton-polariton Bose-Einstein condensates in course of stimulated scattering
and relaxation of reservoir excitons. Using the Markovian embedding techniques,
we obtain stochastic differential equations of motion with an additional degree
of freedom corresponding to dynamical memory. It is shown that the oscillator
asymptotically tends to the intrinsically non-Markovian stable fixed point
corresponding to constant product of oscillator amplitude and modulo of the
memory variable. The state corresponding to this point exhibits unlimited
growth of population, with the growth rate that decreases with time. Our
results show that the Markovian behavior could be observed only within some
limited early stage of oscillator evolution provided that decay of dynamical
memory is sufficiently fast. Transition from the Markovian regime to
non-Markovian one with increasing time is linked to phase shift of the pumping
term. Coherence properties of the oscillator are studied. It was found that
interaction between particles delimits growth of condensate population, thereby
impeding formation of Bose-Einstein condensate.

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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
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The categories of this paper are: math
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: alg-geom