Justification of c-Number Substitutions in Bosonic Hamiltonians

Elliott H. Lieb, Robert Seiringer, and Jakob Yngvason
Phys. Rev. Lett. 94, 080401 – Published 2 March 2005

Abstract

The validity of substituting a c-number z for the k=0 mode operator a0 is established rigorously in full generality, thereby verifying one aspect of Bogoliubov's 1947 theory. This substitution not only yields the correct value of thermodynamic quantities such as the pressure or ground state energy, but also the value of |z|2 that maximizes the partition function equals the true amount of condensation in the presence of a gauge-symmetry-breaking term. This point had previously been elusive.

  • Received 16 December 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.080401

©2005 American Physical Society

Authors & Affiliations

Elliott H. Lieb and Robert Seiringer

  • Department of Physics, Jadwin Hall, Princeton University, P.O. Box 708, Princeton, New Jersey 08544, USA

Jakob Yngvason

  • Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, A-1090 Vienna, Austria

See Also

Equivalence of Bose-Einstein Condensation and Symmetry Breaking

András Sütő
Phys. Rev. Lett. 94, 080402 (2005)

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Issue

Vol. 94, Iss. 8 — 4 March 2005

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