DC-transport in superconducting point contacts: a full counting statistics view

We present a comprehensive theoretical analysis of the dc transport properties of superconducting point contacts. We determine the full counting statistics for these junctions, which allows us to calculate not only the current or the noise, but all the cumulants of the current distribution. We show how the knowledge of the statistics of charge transfer provides an unprecedented level of understanding of the different transport properties for a great variety of situations. We illustrate our results with the analysis of junctions between BCS superconductors, contacts between superconductors with pair-breaking mechanisms and short diffusive bridges. We also discuss the temperature dependence of the different cumulants and show the differences with normal contacts.Comment: revtex4, 20 pages, 15 figure

Quasiparticles and phonon satellites in spectral functions of semiconductors and insulators: Cumulants applied to full first principles theory and Fr\"ohlich polaron

The electron-phonon interaction causes thermal and zero-point motion shifts of electron quasiparticle (QP) energies $\epsilon_k(T)$. Other consequences of interactions, visible in angle-resolved photoemission spectroscopy (ARPES) experiments, are broadening of QP peaks and appearance of sidebands, contained in the electron spectral function $A(k,\omega)=-{\Im m}G_R(k,\omega) /\pi$, where $G_R$ is the retarded Green's function. Electronic structure codes (e.g. using density-functional theory) are now available that compute the shifts and start to address broadening and sidebands. Here we consider MgO and LiF, and determine their nonadiabatic Migdal self energy. The spectral function obtained from the Dyson equation makes errors in the weight and energy of the QP peak and the position and weight of the phonon-induced sidebands. Only one phonon satellite appears, with an unphysically large energy difference (larger than the highest phonon energy) with respect to the QP peak. By contrast, the spectral function from a cumulant treatment of the same self energy is physically better, giving a quite accurate QP energy and several satellites approximately spaced by the LO phonon energy. In particular, the positions of the QP peak and first satellite agree closely with those found for the Fr\"ohlich Hamiltonian by Mishchenko $\textit{et al.}$ (2000) using diagrammatic Monte Carlo. We provide a detailed comparison between the first-principles MgO and LiF results and those of the Fr\"ohlich Hamiltonian. Such an analysis applies widely to materials with infra-red active phonons. We also compare the retarded and time-ordered cumulant treatments: they are equivalent for the Fr\"ohlich Hamiltonian, and only slightly differ in first-principles electron-phonon results for wide-band gap materials.Comment: 21 pages, 19 figure

Propagation of Memory Parameter from Durations to Counts

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,1/2)$ to ensure that the corresponding counting process $N(t)$ satisfies $\textmd{Var} N(t) \sim C t^{2d+1}$ ($C>0$) as $t \to \infty$, with the same memory parameter $d \in [0,1/2)$ that was assumed for the durations. Thus, these conditions ensure that the memory in durations propagates to the same memory parameter in counts and therefore in realized volatility. We then show that any utoregressive Conditional Duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, while any Long Memory Stochastic Duration model with $d>0$ and all finite moments yields long memory in counts, with the same $d$

Effect of dipolar interactions on optical nonlinearity of two-dimensional nanocomposites

In this work, we calculate the contribution of dipole-dipole interactions to the optical nonlinearity of the two-dimensional random ensemble of nanoparticles that possess a set of exciton levels, for example, quantum dots. The analytical expressions for the contributions in the cases of TM and TE-polarized light waves propagating along the plane are obtained. It is shown that the optical nonlinearity, caused by the dipole-dipole interactions in the planar ensemble of the nanoparticles, is several times smaller than the similar nonlinearity of the bulk nanocomposite. This type of optical nonlinearity is expected to be observed at timescales much larger than the quantum dot exciton rise time. The proposed method may be applied to various types of the nanocomposite shapes.Comment: 8 page