In this talk, I will describe ongoing work on the self-interactions of asymmetric dark matter.
At high number density, for example in the inner-most regions of dark matter haloes or in the core of neutron star in the case of dark matter capture, collective quantum effects can become important: Dark matter−dark matter interactions in the vicinity of the Fermi surface can lead to the formation of various condensates and even to phase transitions of the medium, therefore modifying drastically the behaviour of the dark matter, in contrast to the usual free gas picture.
I will discuss the phenomenon of Cooper pairing and superfluidity within the new formalism we developed, which goes beyond the usual contact-operator limit. Motivated by the usual dark matter scenario, I will then focus on non-relativistic systems and study the BCS, BEC, and cross-over phases in light of the effective-range formalism. I will also discuss the effects arising from the appearance of the so-called scalar density condensate and its thermodynamics.