Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BCS and Attractive Hubbard Model Comparative Study   We extend previous studies of the BCS canonical approach for the attractive
Hubbard model. A derivation of the BCS formulation is presented for both the
Hubbard and a simpler reduced Hamiltonian. Using direct diagonalization, exact
one and two dimensional solutions for both Hamiltonians are compared to BCS
variational calculations. Approximate and exact ground state energies and
energy gaps are computed for different electron number systems as well as
correlation observables not previously predicted. Reproducing published one
dimensional findings, the BCS is an excellent approximation for the Hubbard
ground state energy but not energy gap, a finding that remains true in two
dimensions. Propagators and correlators are found more sensitive to
wavefunctions and appreciable differences are computed with the Hubbard model
exhibiting a weaker degree of superconductivity than the BCS. However for the
reduced Hamiltonian model the BCS is an excellent approximation for all
observables in both one and two dimensions.

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The categories of this paper are: econ
2
The categories of this paper are: math
6
The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: cs