Generalized LFT-Based Representation of Parametric Uncertain Models

In this paper, we introduce a general descriptor-type linear fractional transformation (LFT) representation of rational parametric matrices. This is a generalized representation of arbitrary rationally dependent multivariate functions in LFT-form. As applications, we develop explicit LFT-realizations of the transfer-function matrix of a linear descriptor system whose state-space matrices depend rationally on a set of uncertain parameters. The resulting descriptor LFT-based uncertainty models generally have smaller orders than those obtained by using the standard LFT-based modelling approach. An example of an uncertain vehicle model illustrates the capability of the method

Reply to the Comment of den Hartog and van Wees on "Conductance Fluctuations in Mesoscopic Normal-Metal/Superconductor Samples"

In their comment cond-mat/9710285 [Phys. Rev. Lett. 80, 5024 (1998)] den Hartog and van Wees (HW) raise objections against our analysis of the experimental data presented in cond-mat/9708162 [Phys. Rev. Lett. 79, 1547 (1997)]. According to HW, we did not account for the quantum phase incoherence introduced by the Niobium compounds of the investigated Nb/Au hybrid samples. Here we show that and why this criticism is not justified. Some difficulties associated with a precise determination of the coherence lengths are discussed. It is discussed why these uncertainties do not have a qualitative impact on the results reported in our paper.Comment: Reply to the comment cond-mat/9710285 by den Hartog and van Wees; 1 page REVTE

Short-distance breakdown of the Higgs mechanism and the robustness of the BCS theory for charged superconductors

Through the Higgs mechanism, the long-range Coulomb interaction eliminates the low-energy Goldstone phase mode in superconductors and transfers spectral weight all the way up to the plasma frequency. Here we show that the Higgs mechanism breaks down for length scales shorter than the superconducting coherence length while it stays intact, even at high energies, in the long-wavelength limit. This effect is a consequence of the composite nature of the Higgs field of superconductivity and the broken Lorentz invariance in a solid. Most importantly, the breakdown of the Higgs mechanism inside the superconducting coherence volume is crucial to ensure the stability of the BCS mean-field theory in the weak-coupling limit. We also show that changes in the gap equation due to plasmon-induced fluctuations can lead to significant corrections to the mean-field theory and reveal that changes in the density-fluctuation spectrum of a superconductor are not limited to the vicinity of the gap.Comment: 10 pages, 4 figure