= Bogoliubov theory
{c}
Expand an interacting Bose field about a macroscopically occupied condensate and retain terms quadratic in its fluctuations. A <Bogoliubov transformation> diagonalizes the stable quadratic Hamiltonian. For contact repulsion this gives the <Bogoliubov quasiparticle dispersion> $E_k=\sqrt{\epsilon_k(\epsilon_k+2g_Bn_0)}$, a linear sound mode at small <momentum> and particle-like behavior at large <momentum>. Mixing creation and <annihilation operators> also produces <quantum depletion of a Bose condensate>. The approximation requires controlled fluctuations; it does not give an exact strongly interacting liquid or the full fluctuation-dominated critical region.
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