Energy Cost to Make a Hole in the Fermi Sea

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Energy Cost to Make a Hole in the Fermi Sea

Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, and Robert Seiringer

Phys. Rev. Lett. 106, 150402 – Published 12 April 2011

See Synopsis: Making a hole in a 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.

Received 7 February 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.150402

Synopsis

Making a hole in a Fermi sea

Published 12 April 2011

A semiclassical approximation gives an accurate answer to a simply stated, but difficult to solve, quantum mechanical problem.

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Authors & Affiliations

Rupert L. Frank¹, Mathieu Lewin², Elliott H. Lieb^1,3, and Robert Seiringer⁴

¹Department of Mathematics, Princeton University, Washington Road, Princeton, New Jersey 08544, USA
²CNRS and Department of Mathematics (UMR CNRS 8088), University of Cergy-Pontoise, F-95 000 Cergy-Pontoise, France
³Department of Physics, Princeton University, P.O. Box 708, Princeton, New Jersey 08542, USA
⁴Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montréal, Québec, H3A 2K6, Canada