Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low rank approximation for the numerical simulation of high dimensional
  Lindblad and Riccati equations   A systematic numerical approach to approximate high dimensional Lindblad
equations is described. It is based on a deterministic rank m approximation of
the density operator, the rank m being the only parameter to adjust. From a
known initial value, this rank m approximation gives at each time-step an
estimate of the largest m eigen-values with their eigen-vectors of the density
operator. A numerical scheme is proposed. Its numerical efficiency in the case
of a rank 12 approximation is demonstrated for oscillation revivals of 50 atoms
interacting resonantly with a slightly damped coherent quantized field of 200
photons. The approach may be employed for other similar equations. We in
particularly show how to adapt such low-rank approximation for Riccati
differential equations appearing in Kalman filtering.

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The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: math
24
The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an