Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third Bose Fugacity Coefficient in One Dimension, as a Function of
  Asymptotic Quantities   In one of the very few exact quantum mechanical calculations of fugacity
coefficients, Dodd and Gibbs (\textit{J. Math.Phys}.,\textbf{15}, 41 (1974))
obtained $b_{2}$ and $b_{3}$ for a one dimensional Bose gas, subject to
repulsive delta-function interactions, by direct integration of the wave
functions. For $b_{2}$, we have shown (\textit{Mol. Phys}.,\textbf{103}, 1301
(2005)) that Dodd and Gibbs' result can be obtained from a phase shift
formalism, if one also includes the contribution of oscillating terms, usually
contributing only in 1 dimension. Now, we develop an exact expression for
$b_{3}-b_{3}^{0}$ (where $b_{3}^{0}$ is the free particle fugacity coefficient)
in terms of sums and differences of 3-body eigenphase shifts. Further, we show
that if we obtain these eigenphase shifts in a distorted-Born approximation,
then, to first order, we reproduce the leading low temperature behaviour,
obtained from an expansion of the two-fold integral of Dodd and Gibbs. The
contributions of the oscillating terms cancel. The formalism that we propose is
not limited to one dimension, but seeks to provide a general method to obtain
virial coefficients, fugacity coefficients, in terms of asymptotic quantities.
The exact one dimensional results allow us to confirm the validity of our
approach in this domain.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: econ
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The categories of this paper are: chao-dyn