A scattering view of the Bogoliubov-de Gennes equations

Abstract

We advocate the use of the T -matrix of the pair potential to study the properties of ultracold Fermi gases in the mean-field approximation. Our approach does not require renormalization procedures even in the limit of contact interaction, and it provides a rigorous definition of the range of the potential. We also rewrite the Bogoliubov-de Gennes equation for the pairing function as a function of the T-matrix, and use it to investigate finite-range effects on the main thermodynamic observables in a gas of 6Li atoms at unitarity, calculating the pair potential with ab initio quantum chemical methods

A Bird’s Eye View on the Concept of Multichannel Scattering with Applications to Materials Science, Condensed Matter, and Nuclear Astrophysics

“…The first is the calculation of the scattering length describing the interaction strength between alkali atoms. Secondly, we demonstrated (Simonucci et al, 2011(Simonucci et al, , 2012Garberoglio et al, 2013) that the BdG equations used to describe this system (and thus the pairing function ∆) can be naturally written in term of the T -matrix of the underlying potential. Many-body scattering techniques, as for the case of the Auger process, can thus be applied to the assessment of the UFG properties.…”

“…Hereby, after a description of the conceptual framework behind this approach we will prove its ability to span different research fields by interpreting a specific set of physical problems in the meV to MeV range. In particular, we will discuss the Auger effect in SiO 2 (Taioli et al, 2009b), the BEC-BCS crossover in ultracold Fermi gases (UFG) (Simonucci et al, 2011(Simonucci et al, , 2012Garberoglio et al, 2013), and finally the electron capture in stellar plasma .…”

“…Many-body scattering techniques, as for the case of the Auger process, can thus be applied to the assessment of the UFG properties. In particular, using this T -matrix based approach one can avoid issues related to the divergence of the interaction arising from the contact potential and, moreover, assess the effect of the actual finite range of the potential on the observables in and out the universality regime (Simonucci et al, 2011(Simonucci et al, , 2012Garberoglio et al, 2013). In Figure 1B we show the application of our approach to the calculation of the main observables in a 6 Li UFG as a function of the interaction effective range appearing in the second order expansion of the T -matrix (Simonucci et al, 2011).…”