Energy Cost to Make a Hole in the Fermi Sea

TL;DR

This paper establishes rigorous lower bounds on the energy change in an ideal Fermi gas due to local potential insertions or density modifications, linking quantum effects to semiclassical approximations.

Contribution

It provides the first rigorous bounds connecting quantum energy changes in Fermi gases to semiclassical estimates, enhancing theoretical understanding.

Findings

Energy changes are bounded below by a universal constant times semiclassical estimates.

The bounds apply to local potential insertions and density modifications in Fermi gases.

Results improve the theoretical foundation for energy calculations in condensed matter physics.

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.