Rigorous Approach to the Problem of Ultraviolet Divergencies in Dilute Bose Gases

Maxim Olshanii and Ludovic Pricoupenko
Phys. Rev. Lett. 88, 010402 – Published 17 December 2001
PDFExport Citation

Abstract

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.

  • Received 17 January 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.010402

©2001 American Physical Society

Authors & Affiliations

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

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

References (Subscription Required)

Click to Expand
Issue

Vol. 88, Iss. 1 — 7 January 2002

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×