The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

Abstract

Starting from the Larmor clock we introduce a hierarchy of density of states. At the bottom of this hierarchy are the partial densities of states which represent the contribution to the local density of states if both the incident and the outgoing scattering channel is prescribed. We discuss the role of the partial densities of states in a number of electrical conduction problems in phase coherent mesoscopic systems: The partial densities of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial densities of states determine the degree of dephasing generated by a weakly coupled voltage probe. We show that the partial densities of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. We introduce the off-diagonal elements of the partial density of states matrix to describe fluctuation processes. These examples demonstrate that the analysis of the Larmor clock has a wide range of applications.

Wigner time delay and related concepts: Application to transport in coherent conductors

“…For this reason "clock approaches" have been proposed in order to provide more satisfactory answers to the question "how much time needs a wave packet to travel in a given region ?". We refer to the review articles [109,126,38,125,44,67] 3 and Büttiker's contributions [46,37,47].…”

“…with initial condition Z(0) = 0 and provides the value of the Wigner time delay τ W = Z(L). The analysis of the symmetry point ε = 0 is easy : the phase remains locked at 0 or π/2 (corresponding to m(x) = ±∞ for x < 0), therefore one can integrate (44). On gets…”

Wigner–Smith time-delay matrix in chaotic cavities with non-ideal contacts

“…Although there is a connection between those three time delay sets [21], they generally characterise different aspects of the problem [20]. Other characteristic times can also be introduced using certain derivatives of the S-matrix elements, see reviews [18][19][20][22][23][24][25] for relevant studies.…”