"How much energy does it cost to make a hole in an ideal Fermi gas?"
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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,
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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.
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It is a collaboration with R. Frank, E.H. Lieb (Princeton, USA) and R. Seiringer
(McGill, Montréal, Canada).

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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