Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Numerical solutions of the Dicke Hamiltonian   We study the numerical solutions of the Dicke Hamiltonian, which describes a
system of many two level atoms interacting with a monochromatic radiation field
into a cavity. The Dicke model is an example of a quantum collective behavior
which shows superradiant quantum phase transitions in the thermodynamic limit.
Results obtained employing two different bases are compared. Both of them use
the pseudospin basis to describe the atomic states. For the photon states we
use in one case Fock states, while in the other case we use a basis built over
a particular coherent state, associated to each atomic state.
  It is shown that, when the number of atoms increases, the description of the
ground state of the system in the superradiant phase requires an equivalent
number of photons to be included. This imposes a strong limit to the states
that can be calculated using Fock states, while the dimensionality needed to
obtain convergent results in the other basis decreases when the atomic number
increases, allowing calculations that are very difficult in the Fock basis.
Naturally, it reduces also the computing time, economizing computing resources.
We show results for the energy, the photon number and the number of excited
atoms, for the ground and the first excited state.

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The categories of this paper are: math
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-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: supr-con