Quantum Spatial Search with Electric Potential: Long-Time Dynamics and Robustness to Noise

We present various results on the scheme introduced in a previous work, which is a quantum spatial-search algorithm on a two-dimensional (2D) square spatial grid, realized with a 2D Dirac discrete-time quantum walk (DQW) coupled to a Coulomb electric field centered on the the node to be found. In such a walk, the electric term acts as the oracle of the algorithm, and the free walk (i.e., without electric term) acts as the “diffusion” part, as it is called in Grover’s algorithm. The results are the following. First, we run long time simulations of this electric Dirac DQW, and observe that there is a second localization peak around the node marked by the oracle, reached in a time O(N), where N is the number of nodes of the 2D grid, with a localization probability scaling as O(1/lnN). This matches the state-of-the-art 2D-DQW search algorithms before amplitude amplification We then study the effect of adding noise on the Coulomb potential, and observe that the walk, especially the second localization peak, is highly robust to spatial noise, more modestly robust to spatiotemporal noise, and that the first localization peak is even highly robust to spatiotemporal noise.     

Efficient Time Propagation Technique for MAS NMR Simulation: Application to Quadrupolar Nuclei

The quantum mechanical Floquet theory is investigated in order to derive an efficient way of performing numerical calculations of the dynamics of nuclear spin systems in MAS NMR experiments. Here, we take advantage of time domain integration of the quantum evolution over one period as proposed by Edenet al.(1). But a full investigation of the propagatorU(t,t₀), and especially its dependence with respect totandt₀within a formalized approach, leads to further simplifications and to a substantial reduction in computation time when performing powder averaging for any complex sequence. Such an approximation is suitable for quadrupolar nuclei (I> 1/2) and can be applied to the simulation of the RIACT (rotational induced adiabatic coherence transfer) phenomenon that occurs under special experimental conditions in spin locking experiments (2–4). The present method is also compared to the usual infinite dimensional Floquet space approach (5, 6), which is shown to be rather inefficient. As far as we know, it has never been reported for quadrupolar nuclei withI≥ 3/2 in spin locking experiments. The method can also be easily extended to other areas of spectroscopy.     

Beta-delayed two-neutron emission from 30,31,32Na

Beta-delayed two-neutron emission from mass-separated samples of short-lived sodium isotopes has been detected both by n-n time correlations with a 4π neutron counter and by γ-spectroscopic identification of daughter products with mass A ? 2. The observed cases (intensities per beta decay) are ${}^{30}\text{Na}\text{(1.2 ± 0.2\%),}{}^{31}\text{Na}\text{(0.70 ± 0.25\%)}\text{and}{}^{32}\text{Na}\text{(5.1 ± 1.8\%)}$. The results are in good agreement with a simple model of beta-particle emission.     

Multipolarity of the continuum γ-rays in 152Dy and 160Er via linear polarisation measurements

The multipolarity of the continuum transitions in ¹⁵²Dy and ¹⁶⁰Er has been deduced from γ-ray linear polarisation and angular distribution measurements. The yrast part for ¹⁶⁰Er agrees with the predicted stretched E2 cascade. The statistical parts for both ¹⁵²Dy and ¹⁶⁰Er consist of a mixture of dipolar stretched and non-stretched transitions, predominantly of electrical character. Below 1.5 MeV, the data of ¹⁵²Dy exhibit a different structure, and reveal a stretched M1 component in the low-energy region.     

Integrated microfluidic devices with enhanced separation performance: application to phosphoproteome analyses of differentiated cell model systems

This work reports on the application of a microfluidic device integrating nanoscale LC to nanoelectrospray MS (nano-LC-chip-MS) for the analysis of complex protein digests. Peak profile analyses of more than 700 peptide ions, reproducibly detected across replicate nano-LC-chip-MS runs (n = 5), indicated that the system provided RSD values of 0.24% on retention time, +/- 30 ppm on m/z measurement and +/- 30% variation on intensity over three orders of magnitude. RP adsorbant media with different alkyl chains and particle size packed in both trapping and separation channels were investigated to improve the chromatographic performance of this system. A two-fold improvement in chromatographic peak capacity was achieved using microfluidic devices comprising a 5 mircrom C3 trap with 2.5 microm C18 trap separation channel compared to the traditional 5 microm C18 stationary phase. Enhanced sample selectivity for the identification of phosphopeptides was obtained by combining immobilized metal affinity media prior to peptide separation on the RP microfluidic device. This system was evaluated in the context of differential phosphoproteome analyses to identify changes in signaling events and protein expression of human monocytes following the administration of phorbol ester.     

On proto-differentiability and strict proto-differentiability of multifunctions of feasible points in perturbed optimization problems

This paper is concerned with the study of the proto-differentiability of the multifunction associated with the feasible points of optimization problems. It is proved under some natural conditions that the proto-differentiability of the data multifunctions ensure that of the resulting multifunctions of feasible points.     

Constructive Tensor Field Theory: the {T^4_3} Model

In a basic framework of a complex Hilbert space equipped with a complex conjugation and an involution, linear operators can be real, quaternionic, symmetric or anti-symmetric, and orthogonal projections can furthermore be Lagrangian. This paper investigates index pairings of projections and unitaries submitted to such symmetries. Various scenarios emerge: Noether indices can take either arbitrary integer values or only even integer values or they can vanish and then possibly have secondary \({{\mathbb {Z}_{2}}}\)-invariants. These general results are applied to prove index theorems for the strong invariants of disordered topological insulators. The symmetries come from the Fermi projection (K-theoretic part of the pairing) and the Dirac operator (K-homological part of the pairing depending on the dimension of physical space).