The quantum speed up as advanced knowledge of the solution

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple two line argument for this without having to describe the details of the search algorithm". The answer provided in this work is: "because any quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem". This empirical fact, unnoticed so far, holds for both quadratic and exponential speed ups and is theoretically justified in three steps: (i) once the physical representation is extended to the production of the problem on the part of the oracle and to the final measurement of the computer register, quantum computation is reduction on the solution of the problem under a relation representing problem-solution interdependence, (ii) the speed up is explained by a simple consideration of time symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution; this advanced knowledge of the solution reduces the size of the solution space to be explored by the algorithm, (iii) if I is the information acquired by measuring the content of the computer register at the end of the algorithm, the quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of I, which brings us to the initial statement.Comment: 23 pages, to be published in IJT

Electronic Structure of Transition-Metal Dicyanamides Me[N(CN)2_2]2_2 (Me = Mn, Fe, Co, Ni, Cu)

The electronic structure of Me[N(CN)$_2$]$_2$ (Me=Mn, Fe, Co, Ni, Cu) molecular magnets has been investigated using x-ray emission spectroscopy (XES) and x-ray photoelectron spectroscopy (XPS) as well as theoretical density-functional-based methods. Both theory and experiments show that the top of the valence band is dominated by Me 3d bands, while a strong hybridization between C 2p and N 2p states determines the valence band electronic structure away from the top. The 2p contributions from non-equivalent nitrogen sites have been identified using resonant inelastic x-ray scattering spectroscopy with the excitation energy tuned near the N 1s threshold. The binding energy of the Me 3d bands and the hybridization between N 2p and Me 3d states both increase in going across the row from Me = Mn to Me = Cu. Localization of the Cu 3d states also leads to weak screening of Cu 2p and 3s states, which accounts for shifts in the core 2p and 3s spectra of the transition metal atoms. Calculations indicate that the ground-state magnetic ordering, which varies across the series is largely dependent on the occupation of the metal 3d shell and that structural differences in the superexchange pathways for different compounds play a secondary role.Comment: 20 pages, 11 figures, 2 table

Fermionic SK-models with Hubbard interaction: Magnetism and electronic structure

Models with range-free frustrated Ising spin- and Hubbard interaction are treated exactly by means of the discrete time slicing method. Critical and tricritical points, correlations, and the fermion propagator, are derived as a function of temperature T, chemical potential \mu, Hubbard coupling U, and spin glass energy J. The phase diagram is obtained. Replica symmetry breaking (RSB)-effects are evaluated up to four-step order (4RSB). The use of exact relations together with the 4RSB-solutions allow to model exact solutions by interpolation. For T=0, our numerical results provide strong evidence that the exact density of states in the spin glass pseudogap regime obeys \rho(E)=const |E-E_F| for energies close to the Fermi level. Rapid convergence of \rho'(E_F) under increasing order of RSB is observed. The leading term resembles the Efros-Shklovskii Coulomb pseudogap of localized disordered fermionic systems in 2D. Beyond half filling we obtain a quadratic dependence of the fermion filling factor on the chemical potential. We find a half filling transition between a phase for U>\mu, where the Fermi level lies inside the Hubbard gap, into a phase where \mu(>U) is located at the center of the upper spin glass pseudogap (SG-gap). For \mu>U the Hubbard gap combines with the lower one of two SG-gaps (phase I), while for \mu<U it joins the sole SG-gap of the half-filling regime (phase II). We predict scaling behaviour at the continuous half filling transition. Implications of the half-filling transition between the deeper insulating phase II and phase I for delocalization due to hopping processes in itinerant model extensions are discussed and metal-insulator transition scenarios described.Comment: 29 pages, 26 Figures, 4 jpeg- and 3 gif-Fig-files include

Ultrafast Nonlinear Optical Response of Strongly Correlated Systems: Dynamics in the Quantum Hall Effect Regime

We present a theoretical formulation of the coherent ultrafast nonlinear optical response of a strongly correlated system and discuss an example where the Coulomb correlations dominate. We separate out the correlated contributions to the third-order nonlinear polarization, and identify non-Markovian dephasing effects coming from the non-instantaneous interactions and propagation in time of the collective excitations of the many-body system. We discuss the signatures, in the time and frequency dependence of the four-wave-mixing (FWM) spectrum, of the inter-Landau level magnetoplasmon (MP) excitations of the two-dimensional electron gas (2DEG) in a perpendicular magnetic field. We predict a resonant enhancement of the lowest Landau level (LL) FWM signal, a strong non-Markovian dephasing of the next LL magnetoexciton (X), a symmetric FWM temporal profile, and strong oscillations as function of time delay, of quantum kinetic origin. We show that the correlation effects can be controlled experimentally by tuning the central frequency of the optical excitation between the two lowest LLs.Comment: 21 pages, 10 figure

Studies of Hadronic Event Structure in e+e- Annihilation from 30 GeV to 209 GeV with the L3 Detector

In this Report, QCD results obtained from a study of hadronic event structure in high energy e^+e^- interactions with the L3 detector are presented. The operation of the LEP collider at many different collision energies from 91 GeV to 209 GeV offers a unique opportunity to test QCD by measuring the energy dependence of different observables. The main results concern the measurement of the strong coupling constant, \alpha_s, from hadronic event shapes and the study of effects of soft gluon coherence through charged particle multiplicity and momentum distributions.Comment: To appear in Physics Report

Predicting intensive care unit readmissions using probabilistic fuzzy systems

We propose the application of probabilistic fuzzy systems (PFS) to model the prediction of early readmission in intensive care unit patients and compare it with the gold-standard method - logistic regression based on the APACHE II score. PFS are characterized by the combination of the linguistic description of the system with the statistical properties of data. On one hand, results point that PFS models perform comparably to the gold-standard method, with AUC values of 0.66±0.03. On the other hand, results also show that PFS models use a significant lower number of variables which, from the clinical practice point of view, suggests improved gains in terms of simplicit

Mortality prediction of septic shock patients using probabilistic fuzzy systems

Mortality scores based on multiple regressions are common in critical care medicine for prognostic stratification of patients. However, to be used at the point of care, they need to be both accurate and easily interpretable. In this work, we propose the application of one existent type of rule base system using statistical information – probabilistic fuzzy systems (PFS) – to predict mortality of septic shock patients. To assess its accuracy and interpretability, these models are compared to methodologies previously proposed in this domain: Takagi-Sugeno fuzzy models and logistic regression models. The methods are tested using a retrospective cohort study including ICU patients with abdominal septic shock. Regarding accuracy, PFS models are comparable to fuzzy modeling and logistic regression. In terms of interpretability, results indicate that PFS models increase the transparency of the learned system (using fuzzy rules), but at the same time, provide additional means for validating the fuzzy classifier using expert knowledge (from physicians in this paper). By providing accurate and interpretable estimates for the mortality risk, results suggest the usefulness of PFS to develop scores for critical care medicine