The ground state energy of a dilute two-dimensional bose gas

Elliott H. Lieb, Jakob Yngvason

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The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E0/N = (2πh2p/m) |1n(pa2)| -1, to leading order, with a relative error at most O(|1n(pa2)|-1/5). Here N is the number of particles, p = 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, E0 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.

Original languageEnglish (US)
Pages (from-to)509-526
Number of pages18
JournalJournal of Statistical Physics
Issue number3-4
StatePublished - May 2001

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Bose gas
  • Ground state energy
  • Low density
  • Scattering length
  • Two-dimensions


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