Gradient Catastrophe and Fermi Edge Resonances in Fermi Gas

Abstract

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.

References in corpus (8)

• Minimal excitation states of electrons in one-dimensional wires
• Dynamic response of one-dimensional interacting fermions
• Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
• Magnetic-field-induced singularities in spin dependent tunneling through InAs quantum dots
• Tunable Fermi-Edge Resonance in an Open Quantum Dot
• Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
• Finite-temperature Fermi-edge singularity in tunneling studied using random telegraph signals
• Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas

Cited by in corpus (5)

• Fermi distribution of semicalssical non-eqilibrium Fermi states
• Fermi Edge Resonances in Non-equilibrium States of Fermi Gases
• Phase space holography with no strings attached
• Fermi edge singularity and finite frequency spectral features in a semi-infinite 1D wire
• Electron-electron correlations in a dynamical impurity system with a Fermi edge singularity