Quantum feedback with weak measurements

The problem of feedback control of quantum systems by means of weak measurements is investigated in detail. When weak measurements are made on a set of identical quantum systems, the single-system density matrix can be determined to a high degree of accuracy while affecting each system only slightly. If this information is fed back into the systems by coherent operations, the single-system density matrix can be made to undergo an arbitrary nonlinear dynamics, including for example a dynamics governed by a nonlinear Schr\"odinger equation. We investigate the implications of such nonlinear quantum dynamics for various problems in quantum control and quantum information theory, including quantum computation. The nonlinear dynamics induced by weak quantum feedback could be used to create a novel form of quantum chaos in which the time evolution of the single-system wave function depends sensitively on initial conditions.Comment: 11 pages, TeX, replaced to incorporate suggestions of Asher Pere

Multiscale Bone Remodelling with Spatial P Systems

Many biological phenomena are inherently multiscale, i.e. they are characterized by interactions involving different spatial and temporal scales simultaneously. Though several approaches have been proposed to provide "multilayer" models, only Complex Automata, derived from Cellular Automata, naturally embed spatial information and realize multiscaling with well-established inter-scale integration schemas. Spatial P systems, a variant of P systems in which a more geometric concept of space has been added, have several characteristics in common with Cellular Automata. We propose such a formalism as a basis to rephrase the Complex Automata multiscaling approach and, in this perspective, provide a 2-scale Spatial P system describing bone remodelling. The proposed model not only results to be highly faithful and expressive in a multiscale scenario, but also highlights the need of a deep and formal expressiveness study involving Complex Automata, Spatial P systems and other promising multiscale approaches, such as our shape-based one already resulted to be highly faithful.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005

Estimation of Piecewise-Deterministic Trajectories in a Quantum Optics Scenario

The manipulation of individual copies of quantum systems is one of the most groundbreaking experimental discoveries in the field of quantum physics. On both an experimental and a theoretical level, it has been shown that the dynamics of a single copy of an open quantum system is a trajectory of a piecewise-deterministic process. To the best of our knowledge, this application field has not been explored by the literature in applied mathematics, from both probabilistic and statistical perspectives. The objective of this chapter is to provide a self-contained presentation of this kind of model, as well as its specificities in terms of observations scheme of the system, and a first attempt to deal with a statistical issue that arises in the quantum world

Sustained safety and performance of the second-generation drug-eluting absorbable metal scaffold in patients with de novo coronary lesions: 12-month clinical results and angiographic findings of the BIOSOLVE-II first-in-man trial.

Metal absorbable scaffolds constitute a conceptually attractive alternative to polymeric scaffolds. Promising 6-month outcomes of a second-generation drug-eluting absorbable metal scaffold (DREAMS 2G), consisting of an absorbable magnesium scaffold backbone, have been reported. We assessed the 12-month safety and performance of this novel device. The prospective, international, multi-centre, first-in-man BIOSOLVE-II trial enrolled 123 patients with up to two de novo lesions with a reference diameter between 2.2 and 3.7 mm. All patients were scheduled for angiographic follow-up at 6 months, and-if subjects consented-at 12 months. Dual antiplatelet therapy was recommended for 6 months. Quantitative coronary angiography (QCA) parameters remained stable from 6 to 12 months [paired data of 42 patients: in-segment late lumen loss 0.20 ± 0.21 mm vs. 0.25 ± 0.22 mm, P = 0.117, Δ 0.05 ± 0.21 mm (95% CI: -0.01;0.12); in-scaffold late lumen loss 0.37 ± 0.25 mm vs. 0.39 ± 0.27 mm, P = 0.446, Δ 0.03 ± 0.22 (95% CI: -0.04;0.10), respectively]. Intravascular ultrasound and optical coherence tomography findings corroborated the QCA results. Target lesion failure occurred in four patients (3.4%), consisting of one death of unknown cause, one target-vessel myocardial infarction, and two clinically driven target lesion revascularization. No additional event occurred beyond the 6-month follow-up. During the entire follow-up of 12 months, none of the patients experienced a definite or probable scaffold thrombosis. The novel drug-eluting metal absorbable scaffold DREAMS 2G showed a continuous favourable safety profile up to 12 months and stable angiographic parameters between 6 and 12 months. NCT01960504

Compaction of Rods: Relaxation and Ordering in Vibrated, Anisotropic Granular Material

We report on experiments to measure the temporal and spatial evolution of packing arrangements of anisotropic, cylindrical granular material, using high-resolution capacitive monitoring. In these experiments, the particle configurations start from an initially disordered, low-packing-fraction state and under vertical vibrations evolve to a dense, highly ordered, nematic state in which the long particle axes align with the vertical tube walls. We find that the orientational ordering process is reflected in a characteristic, steep rise in the local packing fraction. At any given height inside the packing, the ordering is initiated at the container walls and proceeds inward. We explore the evolution of the local as well as the height-averaged packing fraction as a function of vibration parameters and compare our results to relaxation experiments conducted on spherically shaped granular materials.Comment: 9 pages incl. 7 figure

Selective quantum evolution of a qubit state due to continuous measurement

We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We discuss the Bayesian formalism for such ``selective'' evolution of an individual qubit and apply it to several solid-state setups. In particular, we show how to suppress the qubit decoherence using continuous measurement and the feedback loop.Comment: 15 pages (including 9 figures

A method for finding new sets of axioms for classes of semigroups

We introduce a general technique for finding sets of axioms for a given class of semigroups. To illustrate the technique, we provide new sets of defining axioms for groups of exponent n, bands, and semilattices

On consistency of the quantum-like representation algorithm

In this paper we continue to study so called ``inverse Born's rule problem'': to construct representation of probabilistic data of any origin by a complex probability amplitude which matches Born's rule. The corresponding algorithm -- quantum-like representation algorithm (QLRA) was recently proposed by A. Khrennikov [1]--[5]. Formally QLRA depends on the order of conditioning. For two observables $a$ and $b,$ $b| a$- and $a | b$ conditional probabilities produce two representations, say in Hilbert spaces $H^{b| a}$ and $H^{a| b}.$ In this paper we prove that under natural assumptions these two representations are unitary equivalent. This result proves consistency QLRA

Integrable systems on the sphere associated with genus three algebraic curves

New variables of separation for few integrable systems on the two-dimensional sphere with higher order integrals of motion are considered in detail. We explicitly describe canonical transformations of initial physical variables to the variables of separation and vice versa, calculate the corresponding quadratures and discuss some possible integrable deformations of initial systems.Comment: 19 pages, LaTeX with AMS font