Larmor precession time, Wigner delay time and the local density of states in a quantum wire

TL;DR

This paper examines the relationship between Larmor precession time, Wigner delay time, and local density of states in quantum wires, revealing limitations of existing theories when evanescent modes are considered and clarifying the interpretation of superluminal times at resonances.

Contribution

It demonstrates that the BTP approach to local density of states is not exact when evanescent modes are included and confirms the validity of Wigner delay time at Fano resonances despite stationary phase limitations.

Findings

Evanescent modes affect the exactness of LDOS definitions.

Wigner delay time correctly indicates superluminal times at Fano resonances.

Stationary phase approximation fails at Fano resonances, yet Wigner delay time remains valid.

Abstract

Buttiker-Thomas-Pretre (BTP) [Z. Phys B {\bf 94}, 133 (1994)] proposed that the concepts behind the Larmor clock tell us that it is possible to define exactly the local density of states (LDOS) in terms of the scattering matrix. However, we take into account evanescent modes and show that for an impurity in a quantum wire, this is in principle not exactly true. We also prove that the Wigner delay time gives correct superluminal times at the Fano resonances, in spite of the fact that the stationary phase approximation is not valid there.