QLunch: Marco Olivieri

Speaker: Marco Olivieri

Title: The thermodynamic energy of a mixture of dilute Bose gas: a second order expansion

Abstract: We consider a system of two species of bosons in three dimensions, interacting via pairwise, positive inter-species and intra-species potentials. In the dilute regime, we prove a second-order expansion for the thermodynamic energy density of the gas.

In the case of integrable potentials, we derive the correct second-order term of the expansion, whereas under the additional assumption of “softness” of the potentials, we also compute its precise coefficient. The obtained expression is consistent with the results in the physics literature. Moreover, by letting the density and interaction potential of one species tend to zero, we recover the well-known Lee–Huang–Yang formula for the second-order energy expansion of a single-species Bose gas.