"How much energy does it cost to make a hole in an ideal Fermi gas?"

The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities. In this talk I will explain that the well-known semiclassical approximation provides a lower bound to the correct quantum mechanical energy of the perturbed Fermi sea, up to a universal constant. This work generalizes a famous estimate of Lieb and Thirring, in the vacuum.

It is a collaboration with R. Frank, E.H. Lieb (Princeton, USA) and R. Seiringer (McGill, Montréal, Canada).

Ref: Energy Cost to Make a Hole in the Fermi Sea, Phys. Rev. Lett. 106 (2011), 150402 A positive density analogue of the Lieb-Thirring inequality, Duke Math. Journal, (2012), in press