The two faces of quantum sound

Understand

Fluctuations around a Bose-Einstein condensate can be described by means of Bogolubov theory leading to the notion of quasiparticle and antiquasiparticle familiar to non-relativistic condensed matter practitioners.

• On the other hand, we already know that these perturbations evolve according to a relativistic Klein-Gordon equation in the long wavelength approximation.
• For shorter wavelengths, we show that this equation acquires nontrivial corrections which modify the Klein-Gordon product.
• In this approach, quasiparticles can also be defined (up to the standard ambiguities due to observer-dependence).