Under the supervision of Prof. Sören Petrat, we are working jointly to (perturbatively) analyze the behaviour of quasiparticles in a B.E. condensate. To leading order, the spectral and dynamical properties can be modeled with Hartree Theory, while the next-to leading order is modeled by Bougoliubov Theory --- which already exhibits interaction-free quasi-particles. We work to the next order, beyond Bougoliubov Theory, where the interactions of the quasiparticles arise. 

We have performed symbolic computations, numerical simulations, and mathematical analysis to understand the behavior of different quasiparticles (mostly Rotons). It is still a contended topic whether these quasiparticle exhibit an attractive or repulsive behavior, and thus there is a direct gap in the literature we aim to address.