Penalized maximum likelihood and semiparametric second-order efficiency

We consider the problem of estimation of a shift parameter of an unknown symmetric function in Gaussian white noise. We introduce a notion of semiparametric second-order efficiency and propose estimators that are semiparametrically efficient and second-order efficient in our model. These estimators are of a penalized maximum likelihood type with an appropriately chosen penalty. We argue that second-order efficiency is crucial in semiparametric problems since only the second-order terms in asymptotic expansion for the risk account for the behavior of the ``nonparametric component'' of a semiparametric procedure, and they are not dramatically smaller than the first-order terms.Comment: Published at http://dx.doi.org/10.1214/009053605000000895 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Irreversibility on the Level of Single-Electron Tunneling

We present a low-temperature experimental test of the fluctuation theorem for electron transport through a double quantum dot. The rare entropy-consuming system trajectories are detected in the form of single charges flowing against the source-drain bias by using time-resolved charge detection with a quantum point contact. We find that these trajectories appear with a frequency that agrees with the theoretical predictions even under strong nonequilibrium conditions, when the finite bandwidth of the charge detection is taken into account

Absence of electron dephasing at zero temperature

Dephasing of electrons due to the electron-electron interaction has recently been the subject of a controversial debate, with different calculations yielding mutually incompatible results. In this paper we prove, by means of Ward identities, that neither a Coulomb interaction nor a short-ranged model interaction can lead to phase breaking at zero temperature in spatial dimensions d>2.Comment: 7 pp., LaTeX, no figs, final version as publishe

Low temperature properties of a quantum particle coupled to dissipative environments

We study the dynamics of a quantum particle coupled to dissipative (ohmic) environments, such as an electron liquid. For some choices of couplings, the properties of the particle can be described in terms of an effective mass. A particular case is the three dimensional dirty electron liquid. In other environments, like the one described by the Caldeira-Leggett model, the effective mass diverges at low temperatures, and quantum effects are strongly suppressed. For interactions within this class, arbitrarily weak potentials lead to localized solutions. Particles bound to external potentials, or moving in closed orbits, can show a first order transition, between strongly and weakly localized regimes.Comment: 10 page

Fixed-N Superconductivity: The Crossover from the Bulk to the Few-Electron Limit

We present a truly canonical theory of superconductivity in ultrasmall metallic grains by variationally optimizing fixed-N projected BCS wave-functions, which yields the first full description of the entire crossover from the bulk BCS regime (mean level spacing $d \ll$ bulk gap $\tilde\Delta$) to the ``fluctuation-dominated'' few-electron regime ($d\gg\tilde\Delta$). A wave-function analysis shows in detail how the BCS limit is recovered for $d\ll \tilde \Delta$, and how for $d \gg \tilde \Delta$ pairing correlations become delocalized in energy space. An earlier grand-canonical prediction for an observable parity effect in the spectral gaps is found to survive the fixed-N projection.Comment: 4 pages, 3 figures, RevTeX, V2: minor charges to mach final printed versio

Effect of Level Statistics on Superconductivity in Ultrasmall Metallic Grains

We examine the destruction of superconducting pairing in metallic grains as their size is decreased for both even and odd numbers of electrons. This occurs when the average level spacing d is of the same order as the BCS order parameter. The energy levels of these grains are randomly distributed according to random matrix theory, and we must work statistically. We find that the average value of the critical level spacing is larger than for the model of equally spaced levels for both parities, and derive numerically the probabilities $P_{o,e}(d)$ that a grain of mean level spacing d shows pairing.Comment: 12 pages, 2 PostScript files, RevTex format, submitted to PR

A small superconducting grain in the canonical ensemble

By means of the Lanczos method we analyze superconducting correlations in ultrasmall grains at fixed particle number. We compute the ground state properties and the excitation gap of the pairing Hamiltonian as a function of the level spacing $\delta$. Both quantities turn out to be parity dependent and universal functions of the ratio $\delta/\Delta$ ($\Delta$ is the BCS gap). We then characterize superconductivity in the canonical ensemble from the scaling behavior of correlation functions in energy space.Comment: 11 pages Revtex, 5 figures .ep

Bayesian recovery of the initial condition for the heat equation

We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distributions indexed by a parameter quantifying "smoothness" and show that the corresponding posterior distributions contract around the true parameter at a rate that depends on the smoothness of the true initial condition and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the optimal minimax rate. One type of priors leads to a rate-adaptive Bayesian procedure. The frequentist coverage of credible sets is shown to depend on the combination of the prior and true parameter as well, with smoother priors leading to zero coverage and rougher priors to (extremely) conservative results. In the latter case credible sets are much larger than frequentist confidence sets, in that the ratio of diameters diverges to infinity. The results are numerically illustrated by a simulated data example.Comment: 17 pages, 4 figures. Published in Comm. Statist. Theory Methods. This version differs from the original in pagination and typographic detail. arXiv admin note: text overlap with arXiv:1103.269