MCS-MP Seminar: Alessandro Olgiati

Speaker: Alessandro Olgiati (Politecnico di Milano)

Title: The Lee-Huang-Yang formula for a hard-core dilute Bose gas: an upper bound

Abstract: The Lee-Huang-Yang formula captures the ground state energy of a dilute Bose gas in the thermodynamic limit. First derived heuristically in 1957, it predicts that, to second order in the dilute limit, the energy depends on the repulsive interaction only through the s-wave scattering length, independently of local integrability of the potential. This prediction has been largely confirmed by mathematical results over the past decades. Yet, while energy lower bounds are now known in considerable generality, all upper bounds known so far rely on local integrability assumptions. We construct a trial state for hard-core bosons whose energy matches the Lee-Huang-Yang asymptotics, thereby establishing the upper bound without requiring local integrability.
Based on joint work with Giulia Basti (Sapienza University of Rome), Morris Brooks (University of Zurich), Serena Cenatiempo (GSSI L'Aquila), and Benjamin Schlein (University of Zurich).