It is not uncommon in physics that a simple, straightforward question requires the development of considerable theoretical machinery and intuition before an answer is approached. Such an elementary question is the following: In an infinitely extended, noninteracting ideal Fermi gas, how does the energy of the gas change if there is a localized perturbation in its otherwise constant density? Many approaches based on perturbation theory and semiclassical approximations exist to solve this problem, but their accuracy is not known a priori.
Now, in a paper published in Physical Review Letters, Rupert Frank and collaborators at Princeton, McGill University, Canada, and the University of Cergy-Pontoise, France, provide, for the first time, a rigorous answer. In particular, they show that for spatial dimensions greater than or equal to two, 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. Given that the noninteracting Fermi gas is one of the fundamental models in physics and it is used to understand systems in astrophysics, condensed matter, and cold atom physics, their result is expected to touch upon many different fields. –Alex Klironomos