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Using a periodic train of Lorentzian voltage pulses, which generates soliton-like electronic excitations called Levitons, we investigate the charge density backscattered off a quantum point contact in the fractional quantum Hall regime. We find a regular pattern of peaks and valleys, reminiscent of analogous self-organization recently observed for optical solitons in non-linear environments. This crystallization phenomenon is confirmed by additional side dips in the Hong-Ou-Mandel noise, a feature that can be observed in nowadays electron quantum optics experiments., Comment: 9 pages, 4 figures

These lecture notes are based on a series of lectures given at the XIII Modave summer school in mathematical physics. We review the construction due to Hamilton, Kabat, Lifschytz and Lowe for reconstructing local bulk operators from CFT operators in the context of AdS/CFT and show how to recover bulk correlation functions from this definition. Building on the work of these authors, it has been noted that the bulk displays quantum error correcting properties. We will discuss tensor network toy models to exemplify these remarkable features. We will discuss the role of gauge invariance and of diffeomorphism symmetry in the reconstruction of bulk operators. Lastly, we provide another method of bulk reconstruction specified to AdS$_3$/CFT$_2$ in which bulk operators create cross-cap states in the CFT., Comment: 35 pages, 8 figures, lecture notes, v4: a few minor improvements upon the published proceedings version (version 3 of these lecture notes in arXiv) have been implemented

We give necessary and sufficient conditions for laws of large numbers to hold in $L^2$ for the empirical measure of a large class of branching Markov processes, including $\lambda$-positive systems but also some $\lambda$-transient ones, such as the branching Brownian motion with drift and absorption at $0$. This is a significant improvement over previous results on this matter, which had only dealt so far with $\lambda$-positive systems. Our approach is purely probabilistic and is based on spinal decompositions and many-to-few lemmas. In addition, we characterize when the limit in question is always strictly positive on the event of survival, and use this characterization to derive a simple method for simulating (quasi-)stationary distributions., Comment: 37 pages, 0 figures. This is a shortened version of the preprint arXiv:1701.07634 with a slightly different approach

We study theoretically the impact of an applied DC-current on a mesoscopic chiral $p$-wave superconductor. Performing quasiclassical calculations on a two-dimensional system, with an external magnetic flux to generate a DC current, we show that the current can trigger a transition to a state with a domain wall between regions of different chiralities. The system shows an hysteretic behavior, as different domain wall configurations are possible for a given current. This domain wall creation mechanism can give new insights on recent experiments observing anomalous current variations in Sr${}_2$RuO${}_4$ junctions., Comment: 7 pages, 3 figures

We study the photoassisted shot noise generated by a periodic voltage in the fractional quantum Hall regime. Fluctuations of the current are due to the presence of a quantum point contact operating in the weak backscattering regime. We show how to reconstruct the photoassisted absorption and emission probabilities by varying independently the dc and ac contributions to the voltage drive. This is made possible by the peculiar power-law behavior of the tunneling rates in the chiral Luttinger liquid theory, which allow to approximate the typical infinite sums of the photoassisted transport formalism in a simple and particularly convenient way., Comment: 6 pages, 2 figures, Proceedings of LT28 (Gothenburg, Sweden)

Selective transfer of information between spin-1/2 particles arranged in a ring is achieved by optimizing the transfer fidelity over a readout time window via shaping, externally applied, static bias fields. Such static control fields have properties that clash with the expectations of classical control theory. Previous work has shown that there are cases in which the logarithmic differential sensitivity of the transfer fidelity to uncertainty in coupling strength or spillage of the bias field to adjacent spins is minimized by controllers that produce the best fidelity. Here we expand upon these examples and examine cases of both classical and non-classical behavior of logarithmic sensitivity to parameter uncertainty and robustness as measured by the $\mu$ function for quantum systems. In particular we examine these properties in an 11-spin ring with a single uncertainty in coupling strength or a single bias spillage., Comment: 6 pages, 8 figures, 4 tables, accepted for 56th IEEE Conference on Decision and Control (CDC) 2017

Control laws for selective transfer of information encoded in excitations of a quantum network, based on shaping the energy landscape using time-invariant, spatially-varying bias fields, can be successfully designed using numerical optimization. Such control laws, already departing from classicality by replacing closed-loop asymptotic stability with alternative notions of localization, have the intriguing property that for all practical purposes they achieve the upper bound on the fidelity, yet the (logarithmic) sensitivity of the fidelity to such structured perturbation as spin coupling errors and bias field leakages is nearly vanishing. Here, these differential sensitivity results are extended to large structured variations using $\mu$-design tools to reveal a crossover region in the space of controllers where objectives usually thought to be conflicting are actually concordant., Comment: 7 pages, 6 figures

We compute four-point functions of two heavy and two "perturbatively heavy" operators in the semiclassical limit of Liouville theory on the sphere. We obtain these "Heavy-Heavy-Light-Light" (HHLL) correlators to leading order in the conformal weights of the light insertions in two ways: (a) via a path integral approach, combining different methods to evaluate correlation functions from complex solutions for the Liouville field, and (b) via the conformal block expansion. This latter approach identifies an integral over the continuum of normalizable states and a sum over an infinite tower of lighter discrete states, whose contribution we extract by analytically continuing standard results to our HHLL setting. The sum over this tower reproduces the sum over those complex saddlepoints of the path integral that contribute to the correlator. Our path integral computations reveal that when the two light operators are inserted at equal time in radial quantization, the leading-order HHLL correlator is independent of their separation, and more generally that at this order there is no short-distance singularity as the two light operators approach each other. The conformal block expansion likewise shows that in the discrete sum short-distance singularities are indeed absent for all intermediate states that contribute. In particular, the Virasoro vacuum block, which would have been singular at short distances, is not exchanged. The separation-independence of equal-time correlators is due to cancelations between the discrete contributions. These features lead to a Lorentzian singularity that, in conformal theories with anti-de Sitter (AdS) duals, would be associated to locality below the AdS scale., Comment: 40 pages, 1 figure; v2: clarifications added, minor typos corrected, published version

Parallaxes for 331 classical Cepheids, 31 Type II Cepheids and 364 RR Lyrae stars in common between Gaia and the Hipparcos and Tycho-2 catalogues are published in Gaia Data Release 1 (DR1) as part of the Tycho-Gaia Astrometric Solution (TGAS). In order to test these first parallax measurements of the primary standard candles of the cosmological distance ladder, that involve astrometry collected by Gaia during the initial 14 months of science operation, we compared them with literature estimates and derived new period-luminosity ($PL$), period-Wesenheit ($PW$) relations for classical and Type II Cepheids and infrared $PL$, $PL$-metallicity ($PLZ$) and optical luminosity-metallicity ($M_V$-[Fe/H]) relations for the RR Lyrae stars, with zero points based on TGAS. The new relations were computed using multi-band ($V,I,J,K_{\mathrm{s}},W_{1}$) photometry and spectroscopic metal abundances available in the literature, and applying three alternative approaches: (i) by linear least squares fitting the absolute magnitudes inferred from direct transformation of the TGAS parallaxes, (ii) by adopting astrometric-based luminosities, and (iii) using a Bayesian fitting approach. TGAS parallaxes bring a significant added value to the previous Hipparcos estimates. The relations presented in this paper represent first Gaia-calibrated relations and form a "work-in-progress" milestone report in the wait for Gaia-only parallaxes of which a first solution will become available with Gaia's Data Release 2 (DR2) in 2018., Comment: 29 pages, 25 figures. Accepted for publication by A&A

We investigate minimal excitation states for heat transport into a fractional quantum Hall system driven out of equilibrium by means of time-periodic voltage pulses. A quantum point contact allows for tunneling of fractional quasi-particles between opposite edge states, thus acting as a beam splitter in the framework of the electron quantum optics. Excitations are then studied through heat and mixed noise generated by the random partitioning at the barrier. It is shown that levitons, the single-particle excitations of a filled Fermi sea recently observed in experiments, represent the cleanest states for heat transport, since excess heat and mixed shot noise both vanish only when Lorentzian voltage pulses carrying integer electric charge are applied to the conductor. This happens in the integer quantum Hall regime and for Laughlin fractional states as well, with no influence of fractional physics on the conditions for clean energy pulses. In addition, we demonstrate the robustness of such excitations to the overlap of Lorentzian wavepackets. Even though mixed and heat noise have nonlinear dependence on the voltage bias, and despite the non-integer power-law behavior arising from the fractional quantum Hall physics, an arbitrary superposition of levitons always generates minimal excitation states., Comment: 15 pages, 7 figures

The {\pi}-{\pi} interactions between organic molecules are among the most important parameters for optimizing the transport and optical properties of organic transistors, light-emitting diodes, and (bio-) molecular devices. Despite substantial theoretical progress, direct experimental measurement of the {\pi}-{\pi} electronic coupling energy parameter t has remained an old challenge due to molecular structural variability and the large number of parameters that affect the charge transport. Here, we propose a study of {\pi}-{\pi} interactions from electrochemical and current measurements on a large array of ferrocene-thiolated gold nanocrystals. We confirm the theoretical prediction that t can be assessed from a statistical analysis of current histograms. The extracted value of t ca. 35 meV is in the expected range based on our density functional theory analysis. Furthermore, the t distribution is not necessarily Gaussian and could be used as an ultrasensitive technique to assess intermolecular distance fluctuation at the subangstr\"om level. The present work establishes a direct bridge between quantum chemistry, electrochemistry, organic electronics, and mesoscopic physics, all of which were used to discuss results and perspectives in a quantitative manner., Comment: Nano Lett (2017), full text and supporting information

Context. The first Gaia Data Release contains the Tycho-Gaia Astrometric Solution (TGAS). This is a subset of about 2 million stars for which, besides the position and photometry, the proper motion and parallax are calculated using Hipparcos and Tycho-2 positions in 1991.25 as prior information. Aims. We investigate the scientific potential and limitations of the TGAS component by means of the astrometric data for open clusters. Methods. Mean cluster parallax and proper motion values are derived taking into account the error correlations within the astrometric solutions for individual stars, an estimate of the internal velocity dispersion in the cluster, and, where relevant, the effects of the depth of the cluster along the line of sight. Internal consistency of the TGAS data is assessed. Results. Values given for standard uncertainties are still inaccurate and may lead to unrealistic unit-weight standard deviations of least squares solutions for cluster parameters. Reconstructed mean cluster parallax and proper motion values are generally in very good agreement with earlier Hipparcos-based determination, although the Gaia mean parallax for the Pleiades is a significant exception. We have no current explanation for that discrepancy. Most clusters are observed to extend to nearly 15 pc from the cluster centre, and it will be up to future Gaia releases to establish whether those potential cluster-member stars are still dynamically bound to the clusters. Conclusions. The Gaia DR1 provides the means to examine open clusters far beyond their more easily visible cores, and can provide membership assessments based on proper motions and parallaxes. A combined HR diagram shows the same features as observed before using the Hipparcos data, with clearly increased luminosities for older A and F dwarfs., Comment: Accepted for publication by A&A. 21 pages main text plus 46 pages appendices. 34 figures main text, 38 figures appendices. 8 table in main text, 19 tables in appendices

We investigate the proximity effect in junctions between $N=3$ superconductors under commensurate voltage bias. The bias is chosen to highlight the role of transport processes that exchange multiple Cooper pairs coherently between more than two superconductors. Such non-local processes can be studied in the dc response, where local transport processes do not contribute. We focus on the proximity-induced normal density of states that we investigate in a wide parameter space. We reveal the presence of deep and highly tunable pseudogaps and other rich structures. These are due to a static proximity effect that is absent for $N=2$ and is sensitive to an emergent superconducting phase associated to non-local coherent transport. In comparison with results for $N=2$, we find similarities in the signature peaks of multiple Andreev reflections. We discuss the effect of electron-hole decoherence and of various types of junction asymmetries. Our predictions can be investigated experimentally using tunneling spectroscopy., Comment: 13 pages, 17 figures

The ESA Gaia mission provides a unique time-domain survey for more than one billion sources brighter than G=20.7 mag. Gaia offers the unprecedented opportunity to study variability phenomena in the Universe thanks to multi-epoch G-magnitude photometry in addition to astrometry, blue and red spectro-photometry, and spectroscopy. Within the Gaia Consortium, Coordination Unit 7 has the responsibility to detect variable objects, classify them, derive characteristic parameters for specific variability classes, and provide global descriptions of variable phenomena. We describe the variability processing and analysis that we plan to apply to the successive data releases, and we present its application to the G-band photometry results of the first 14 months of Gaia operations that comprises 28 days of Ecliptic Pole Scanning Law and 13 months of Nominal Scanning Law. Out of the 694 million, all-sky, sources that have calibrated G-band photometry in this first stage of the mission, about 2.3 million sources that have at least 20 observations are located within 38 degrees from the South Ecliptic Pole. We detect about 14% of them as variable candidates, among which the automated classification identified 9347 Cepheid and RR Lyrae candidates. Additional visual inspections and selection criteria led to the publication of 3194 Cepheid and RR Lyrae stars, described in Clementini et al. (2016). Under the restrictive conditions for DR1, the completenesses of Cepheids and RR Lyrae stars are estimated at 67% and 58%, respectively, numbers that will significantly increase with subsequent Gaia data releases. Data processing within the Gaia Consortium is iterative, the quality of the data and the results being improved at each iteration. The results presented in this article show a glimpse of the exceptional harvest that is to be expected from the Gaia mission for variability phenomena. [abridged], Comment: 40 pages, 46 figures. Submitted to A&A

The Fermilab Tevatron collider's data-taking run ended in September 2011, yielding a dataset with rich scientific potential. The CDF and D0 experiments each have approximately 9 PB of collider and simulated data stored on tape. A large computing infrastructure consisting of tape storage, disk cache, and distributed grid computing for physics analysis with the Tevatron data is present at Fermilab. The Fermilab Run II data preservation project intends to keep this analysis capability sustained through the year 2020 and beyond. To achieve this goal, we have implemented a system that utilizes virtualization, automated validation, and migration to new standards in both software and data storage technology and leverages resources available from currently-running experiments at Fermilab. These efforts have also provided useful lessons in ensuring long-term data access for numerous experiments, and enable high-quality scientific output for years to come.

We study supercritical branching processes in which all particles evolve according to some general Markovian motion (which may possess absorbing states) and branch independently at a fixed constant rate. Under fairly natural assumptions on the asymptotic distribution of the underlying motion, we first show using only probablistic tools that there is convergence in $L^2$ of the empirical measure (normalized by the mean number of particles) if and only if an associated additive martingale is bounded in $L^2$. This is a significant improvement over previous results, which were mainly restricted to $\lambda$-positive motions. We then investigate under which conditions this limit is strictly positive on the event of non-extinction and show that this occurs whenever, on the latter event, particles do not accumulate on the boundary of the state space. In particular, this property also yields the convergence of the real empirical measure (normalized by the number of particles). Moreover, building on previous results we prove that if the motion is $\lambda$-positive then these limits hold also almost surely whenever the Doob's $h$-transform of this motion admits a suitable Lyapunov functional. Finally, we illustrate our results for a variety of different motions: ergodic motions without absorption, $\lambda$-positive systems either transient or with absorption, and also certain non $\lambda$-positive systems such as the Brownian motion with negative drift killed at $0$. A strong law of large numbers for the empirical measure in this last example was announced by Kesten in the late seventies, although a proof of it has remained undisclosed so far. Our results allow us to give a partial proof to Kesten's claim., Comment: 55 pages, 0 figures. New version offers a substantially simplified exposition, additional examples and some missing acknowledgements

We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its neighboring nodes become explored. Given an initial number of vertices $N$ growing to infinity, we study statistical properties of the proportion of explored nodes in time using scaling limits. We obtain exact limits for homogeneous graphs and prove an explicit central limit theorem for the final proportion of active nodes, known as the \emph{jamming constant}, through a diffusion approximation for the exploration process. We then focus on bounding the trajectories of such exploration processes on random geometric graphs, i.e. random sequential adsorption. As opposed to homogeneous random graphs, these do not allow for a reduction in dimensionality. Instead we build on a fundamental relationship between the number of explored nodes and the discovered volume in the spatial process, and obtain generic bounds: bounds that are independent of the dimension of space and the detailed shape of the volume associated to the discovered node. Lastly, we give two trajectorial interpretations of our bounds by constructing two coupled processes that have the same fluid limits., Comment: 25 pages, 3 figures

Selective information transfer in spin ring networks by energy landscape shaping control has the property that the error 1-prob, where prob is the transfer success probability, and the sensitivity of the error to spin coupling uncertainties are statistically increasing across a family of controllers of increasing error. The need for a statistical Hypothesis Testing of a concordant trend is made necessary by the noisy behavior of the sensitivity versus the error as a consequence of the optimization of the controllers in a challenging error landscape. Here, we examine the concordant trend between the error and another measure of performance - the logarithmic sensitivity - used in robust control to formulate a well known fundamental limitation. Contrary to error versus sensitivity, the error versus logarithmic sensitivity trend is less obvious, because of the amplification of the noise due to the logarithmic normalization. This results in the Kendall {\tau} test for rank correlation between the error and the log sensitivity to be somewhat pessimistic with marginal significance level. Here it is shown that the Jonckheere-Terpstra test, because it tests the Alternative Hypothesis of an ordering of the medians of some groups of log sensitivity data, alleviates this statistical problem. This identifies cases of concordant trend between the error and the logarithmic sensitivity, a highly anti-classical features that goes against the well know sensitivity versus complementary sensitivity limitation., Comment: 29 pages, 11 figures; accepted for Int J Robust and Nonlinear Control

We consider transport properties of a two dimensional topological insulator in a double quantum point contact geometry in presence of a time-dependent external field. In the proposed setup an external gate is placed above a single constriction and it couples only with electrons belonging to the top edge. This asymmetric configuration and the presence of an ac signal allow for a quantum pumping mechanism, which, in turn, can generate finite heat and charge currents in an unbiased device configuration. A microscopic model for the coupling with the external time-dependent gate potential is developed and the induced finite heat and charge currents are investigated. We demonstrate that in the non-interacting case, heat flow is associated with a single spin component, due to the helical nature of the edge states, and therefore a finite and polarized heat current is obtained in this configuration. The presence of e-e interchannel interactions strongly affects the current signal, lowering the degree of polarization of the system. Finally, we also show that separate heat and charge flows can be achieved, varying the amplitude of the external gate., Comment: 13 pages, 5 figures

We study Hanbury-Brown and Twiss current cross-correlations in a three-terminal junction where a central topological superconductor (TS) nanowire, bearing Majorana bound states at its ends, is connected to two normal leads. Relying on a non-perturbative Green function formalism, our calculations allow us to provide analytical expressions for the currents and their correlations at subgap voltages, while also giving exact numerical results valid for arbitrary external bias. We show that when the normal leads are biased at voltages $V_1$ and $V_2$ smaller than the gap, the sign of the current cross-correlations is given by $-\mbox{sgn}(V_1 \, V_2)$. In particular, this leads to positive cross-correlations for opposite voltages, a behavior in stark contrast with the one of a standard superconductor, which provides a direct evidence of the presence of the Majorana zero-mode at the edge of the TS. We further extend our results, varying the length of the TS (leading to an overlap of the Majorana bound states) as well as its chemical potential (driving it away from half-filling), generalizing the boundary TS Green function to those cases. In the case of opposite bias voltages, $\mbox{sgn}(V_1 \, V_2)=-1$, driving the TS wire through the topological transition leads to a sign change of the current cross-correlations, providing yet another signature of the physics of the Majorana bound state., Comment: 14 pages, 8 figures