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

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.