Bogoliubov quasiparticle dispersion
= Bogoliubov quasiparticle dispersion
{c}
{title2=$E_k=\sqrt{\epsilon_k(\epsilon_k+2nV_k)}$}
= Bogoliubov spectrum
{c}
{synonym}
The stable quadratic spectrum is $E_k=\sqrt{\epsilon_k(\epsilon_k+2nV_k)}$. If $V_k\to V_0>0$, its low-momentum form is $\hbar|k|\sqrt{nV_0/m}$, a linear sound branch. For contact repulsion the <healing length> separates the <phonon> and particle regimes. General momentum-dependent interactions can change the higher-energy shape.