Author： Lieb E.H. Yngvason J.
Publisher： Springer Publishing Company
ISSN： 0022-4715
Source： Journal of Statistical Physics, Vol.103, Iss.3-4, 2001-05, pp. : 509-526
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Abstract
The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E_0/N=(2πℏ^2ρ/m) |ln(ρa^2)|^−1, to leading order, with a relative error at most O(|ln(ρa^2)|^−1/5). Here N is the number of particles, ρ=N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E_0 is not simply N(N-1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger.
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