The analysis of large bosonic systems has been an active area of research in mathematical physics over the past few decades. In this talk we will address a question closely related to Bose-Einstein Condensation, namely, the characterization of macroscopic observables.
The talk will begin with a gentle introduction to the problem, leading up to one of the key results in the field: the rigorous derivation of the Lee-Huang-Yang (LHY) formula. This formula is an asymptotic expansion of the ground state energy in the thermodynamic limit originally predicted in 1957 using tools from Bogoliubov's theory. We will review the mathematical results and discuss the heuristics behind existing proofs.
The second part of the talk will focus on contributions obtained by the speaker and collaborators. Among these, the existence of trial states whose energy (almost) captures the LHY asymptotics for non-integrable interaction potentials has offered a novel perspective on the problem.