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.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
- Bose gas
- Ground state energy
- Low density
- Scattering length