APS » PROLA » Phys. Rev. Lett. » Volume 88 » Issue 1

Phys. Rev. Lett. 88, 010402 (2001) [4 pages]

Rigorous Approach to the Problem of Ultraviolet Divergencies in Dilute Bose Gases
Download: PDF (102 kB) or Buy this Article (Use Article Pack) Export: BibTeX or EndNote (RIS)

Maxim Olshanii1 * and Ludovic Pricoupenko2 †
1Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484
2Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, URA 765 of CNRS, case 121, 4 place Jussieu 75252 Paris Cedex, 05 France

Received 17 January 2001; published 17 December 2001

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.


©2002 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v88/e010402
DOI: 10.1103/PhysRevLett.88.010402
PACS: 05.30.Jp, 03.75.Fi

* Email address: olshanii@physics.usc.edu
† Email address: pricoupenko@lptl.jussieu.fr

[ Abstract  |  Previous article  |  Next article  |  Issue 1 ]