title: Energy cost to make a hole in the Fermi sea.
abstract: 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 condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.
authors.affiliation: Department of Mathematics, Princeton University, Washington Road, Princeton, New Jersey 08544, USA.
authors.forename: Rupert L
authors.initials: RL
authors.lastname: Frank
authors.forename: Mathieu
authors.initials: M
authors.lastname: Lewin
authors.forename: Elliott H
authors.initials: EH
authors.lastname: Lieb
authors.forename: Robert
authors.initials: R
authors.lastname: Seiringer