First-order quantum correction to the ground-state energy density of two-dimensional hard-sphere Bose atoms

Details First-order quantum correction to the ground-state energy density of two-dimensional hard-sphere Bose atoms First-order quantum correction to the ground-state energy density of two-dimensional hard-sphere Bose atoms

2008-08-25

arxiv.org/abs/0808.3288v1

Physics

Condensed Matter

Statistical Mechanics

9 pages, 3 figures,

Scientific paper

Divergence exponents of the first-order quantum correction of a two-dimensional hard-sphere Bose atoms are obtained by an effective field theory method. The first-order correction to the ground-state energy density with respect to the zeroth-order is given by $\cale_1/\cale_0 \sim |D-2|^{-\al}|\ln\gamma|^{-\al'}$, where $D$ is the spatial dimension, and $\gamma$ is the gas parameter ($\gamma=n a^D$). As $D \to 2$, $\al =\al'=1$. We show that the first-order quantum correction of the energy density is not perturbative in low dimensions of $D < 2.2$ regardless of any gas parameter which is much less that 1.

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