2000/02/06 by Elliott H. Lieb, Lieb, Elliott H., Jakob Yngvason +1
Mathematics · Physics and Astronomy · #35Q55 #46N50 #81V70 #Advanced Thermodynamics and Statistical Mechanics #Cold Atom Physics and Bose-Einstein Condensates #Condensed Matter (cond-mat) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum, superfluid, helium dynamics #cond-mat #math-ph #math.MP #msc:35Q55 #msc:46N50 #msc:81V70
paper · pdf · doi:10.48550/arxiv.math-ph/0002014
arxiv created 2000/02/06 · openalex publication_date 2000/02/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 = (2πℏ2ρ/m)|ln (ρa2)|-1, to leading order, with a relative error at most \rm O (|ln (ρa2)|-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, 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.