Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Representations of Coherent and Squeezed States in an Extended
  Two-parameters Fock Space   Recently a $f$-deformed Fock space which is spanned by $|n>_{\lambda}$ has
been introduced. These bases are indeed the eigen-states of a deformed
non-Hermitian Hamiltonian. In this contribution, we will use a rather new
non-orthogonal basis vectors for the construction of coherent and squeezed
states, which in special case lead to the earlier known states. For this
purpose, we first generalize the previously introduced Fock space spanned by
$|n>_{\lambda}$ bases, to a new one, spanned by an extended two-parameters
bases $|n>_{\lambda_{1},\lambda_{2}}$. These bases are now the eigen-states of
a non-Hermitian Hamiltonian
$H_{\lambda_{1},\lambda_{2}}=a^{\dagger}_{\lambda_{1},\lambda_{2}}a+1/2$, where
$a^{\dagger}_{\lambda_{1},\lambda_{2}}=a^{\dagger}+\lambda_{1}a + \lambda_{2}$
and $a$ are respectively, the deformed creation and ordinary bosonic
annihilation operators. The bases $|n>_{\lambda_{1},\lambda_{2}}$ are
non-orthogonal (squeezed states), but normalizable. Then, we deduce the new
representations of coherent and squeezed states, in our two-parameters Fock
space. Finally, we discuss the quantum statistical properties, as well as the
non-classical properties of the obtained states, numerically.

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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol