Rigorous approach to the problem of ultraviolet divergencies in dilute Bose gases.
In this Letter we consider a system of N pairwise finite-range interacting atoms and prove rigorously that in the zero-range interaction limit all the eigenstates and eigenenergies of the Hamiltonian converge to those corresponding to N atoms interacting via the Fermi-Huang regularized pseudopotential. Next, we show that the latter eigensystem (if treated exactly) is invariant under a nontrivial transformation of the interaction potential. Finally, we realize that most of the approximate schemes of many-body physics do not exhibit this invariance: We use this property to resolve all inconsistencies of the Hartree-Fock-Bogoliubov variational formalism known thus far.
Olshanii
Maxim
M
Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA. olshanii@physics.usc.edu
Pricoupenko
Ludovic
L