 0063 Elliott H. Lieb, Jakob Yngvason
 The Ground State Energy of a Dilute Twodimensional Bose Gas
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Feb 6, 00

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Abstract. The ground state energy per particle of a dilute,
homogeneous, twodimensional Bose gas, in the thermodynamic limit is
shown rigorously to be $E_0/N = (2\pi \hbar^2\rho /m){\ln
(\rho a^2)^{1}}$, to leading order, with a relative error at most
${\rm O} \left(\ln (\rho a^2)^{1/5}\right)$. Here
$N$ is the number of particles, $\rho =N/V$ is the particle density and
$a$ is the scattering length of the twobody potential. We assume that
the twobody potential is short range and nonnegative. The amusing
feature of this result is that, in contrast to the threedimensional
case, the energy, $E_0$ is not simply $N(N1)/2$ times the energy of two
particles in a large box of volume (area, really) $V$. It is much
larger.
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