Linear response of a one-dimensional conductor coupled to a dynamical impurity with a Fermi edge singularity

Abstract

I study the dynamical correlations that a quantum impurity induces in the Fermi sea to which it is coupled. I consider a quantum transport setup in which the impurity can be realized in a double quantum dot. The same Hamiltonian describes tunneling states in metallic glasses, and can be mapped onto the Ohmic spin-boson model. It exhibits a Fermi edge singularity, i.e., many fermion correlations result in an impurity decay rate with a nontrivial power-law energy dependence. I show that there is a simple relation between temporal impurity correlations on the one hand and the linear response of the Fermi sea to external perturbations on the other. This results in a power-law singularity in the space and time dependence of the nonlocal polarizability of the Fermi sea, which can be detected in transport experiments.

Spatiotemporal Spread of Fermi-edge Singularity as Time Delayed Interaction and Impact on Time-dependent RKKY Type Coupling

“…It is, however, notable that with few exceptions [56,57] the focus has been on global response functions, and that there is a major lack of investigation of the spatial buildup and spread of the FES. In this paper we show that considering the spatio-temporal spread offers a new perspective on FES physics, and we provide a systematic access.…”