Ground-state energy of the interacting Bose gas in two dimensions: An explicit construction
- Department of Physics, University of New Hampshire, Durham, New Hampshire 03824-3568 (United States)
The isotropic scattering phase shift is calculated for nonrelativistic bosons interacting at low energies via an arbitrary finite-range potential in d space-time dimensions. Scattering on a (d-1)-dimensional torus is then considered, and the eigenvalue equation relating the energy levels on the torus to the scattering phase shift is derived. With this technology in hand, and focusing on the case of two spatial dimensions, a perturbative expansion is developed for the ground-state energy of N identical bosons which interact via an arbitrary finite-range potential in a finite area. The leading nonuniversal effects due to range corrections and three-body forces are included. It is then shown that the thermodynamic limit of the ground-state energy in a finite area can be taken in closed form to obtain the energy per particle in the low-density expansion by explicitly summing the parts of the finite-area energy that diverge with powers of N. The leading and subleading finite-size corrections to the thermodynamic limit equation of state are also computed. Closed-form results--some well known, others perhaps not--for two-dimensional lattice sums are included in an Appendix.
- OSTI ID:
- 21528933
- Journal Information:
- Physical Review. A, Vol. 82, Issue 6; Other Information: DOI: 10.1103/PhysRevA.82.063610; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
BOSE-EINSTEIN GAS
BOSONS
CORRECTIONS
DENSITY
EIGENVALUES
ENERGY LEVELS
EQUATIONS OF STATE
ONE-DIMENSIONAL CALCULATIONS
PHASE SHIFT
POTENTIALS
SCATTERING
SPACE-TIME
THREE-BODY PROBLEM
TWO-DIMENSIONAL CALCULATIONS
EQUATIONS
MANY-BODY PROBLEM
PHYSICAL PROPERTIES