2007/02/05 by A. M. Ettouhami, Ettouhami, A. M.
Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum Gases (cond-mat.quant-gas) #Quantum and electron transport phenomena #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.cond-mat/0702058
openalex publication_date 2007/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
As is well-known, in Bogoliubov's theory of an interacting Bose gas the ground state of the Hamiltonian H=∑\bf k≠ 0H\bf k is found by diagonalizing each of the Hamiltonians H\bf k corresponding to a given momentum mode \bf k independently of the Hamiltonians H\bf k'(≠ k) of the remaining modes. We argue that this way of diagonalizing H may not be adequate, since the Hilbert spaces where the single-mode Hamiltonians H\bf k are diagonalized are not disjoint, but have the \bf k=0 in common. A number-conserving generalization of Bogoliubov's method is presented where the total Hamiltonian H is diagonalized directly. When this is done, the spectrum of excitations changes from a gapless one, as predicted by Bogoliubov's method, to one which has a finite gap in the k→ 0 limit.