Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas

Details Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas

2010-11-09

arxiv.org/abs/1011.1993v2

Phys. Rev. Lett. 106, 166804 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1103/PhysRevLett.106.166804

A smooth spatial disturbance of the Fermi surface in a Fermi gas inevitably becomes sharp. This phenomenon, called {\it the gradient catastrophe}, causes the breakdown of a Fermi sea to disconnected parts with multiple Fermi points. We study how the gradient catastrophe effects probing the Fermi system via a Fermi edge singularity measurement. We show that the gradient catastrophe transforms the single-peaked Fermi-edge singularity of the tunneling (or absorption) spectrum to a set of multiple asymmetric singular resonances. Also we gave a mathematical formulation of FES as a matrix Riemann-Hilbert problem.

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