Sub-quadratic time for Riemann-Roch spaces. The case of smooth divisors over nodal plane projective curves

International audienceWe revisit the seminal Brill-Noether algorithm in the rather generic situation of smooth divisors over a nodal plane projective curve. Our approach takes advantage of fast algorithms for polynomials and structured matrices. We reach sub-quadratic time for computing a basis of a Riemann-Roch space. This improves upon previously known complexity bounds

The ‘Blueprint’ framework for career management skills: a critical exploration

This article examines the Blueprint framework for career management skills as it has been revealed across sequential implementations in the USA, Canada and Australia. It is argued that despite its lack of an empirical basis, the framework forms a useful and innovative means through which career theory, practice and policy can be connected. The framework comprises both core elements (learning areas, learning model and levels) and contextual elements (resources, community of practice, service delivery approach and policy connection). Each of these elements is explored

Hacia una web social libre y federada: el caso de Lorea

This paper tackles the limitations of web 2.0, the keys to overcome them and the recent efforts towards a free and federated social web. Between these we will focus on the case of Lorea from our direct experience with it.Este artículo aborda las limitaciones de la web 2.0, las claves para superarlas y las recientes iniciativas de web social libre y federada. De entre ellas nos centraremos en el caso de Lorea desde nuestra experiencia directa con ella

Optically induced coherent intra-band dynamics in disordered semiconductors

On the basis of a tight-binding model for a strongly disordered semiconductor with correlated conduction- and valence band disorder a new coherent dynamical intra-band effect is analyzed. For systems that are excited by two, specially designed ultrashort light-pulse sequences delayed by tau relatively to each other echo-like phenomena are predicted to occur. In addition to the inter-band photon echo which shows up at exactly t=2*tau relative to the first pulse, the system responds with two spontaneous intra-band current pulses preceding and following the appearance of the photon echo. The temporal splitting depends on the electron-hole mass ratio. Calculating the population relaxation rate due to Coulomb scattering, it is concluded that the predicted new dynamical effect should be experimentally observable in an interacting and strongly disordered system, such as the Quantum-Coulomb-Glass.Comment: to be published in Physical Review B15 February 200

Directed current due to broken time-space symmetry

We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2\pi) under the influence of a time-periodic space-homogeneous external field E(t)=E(t+T). If E(t) is neither symmetric function of t nor antisymmetric under time shifts $E(t \pm T/2) \neq -E(t)$, an ensemble of trajectories with zero current at t=0 yields a nonzero finite current as $t\to \infty$. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.Comment: 2 figure

Theory of Fast Quantum Control of Exciton Dynamics in Semiconductor Quantum Dots

Optical techniques for the quantum control of the dynamics of multiexciton states in a semiconductor quantum dot are explored in theory. Composite bichromatic phase-locked pulses are shown to reduce the time of elementary quantum operations on excitons and biexcitons by an order of magnitude or more. Analytic and numerical methods of designing the pulse sequences are investigated. Fidelity of the operation is used to gauge its quality. A modified Quantum Fourier Transform algorithm is constructed with only Rabi rotations and is shown to reduce the number of operations. Application of the designed pulses to the algorithm is tested by a numerical simulation.Comment: 11 pages,5 figure

On Multi-Index Filtrations Associated to Weierstraß Semigroups

This paper is a survey on the main techniques involved in the computation of the Weierstraß semigroup at several points of curves defined over perfect fields, with special emphasis on the case of two points. Some hints about the usage of some packages of the computer algebra software Singular are also given; these are however only valid for curves defined over Fp with p a prime number

Coherent control using adaptive learning algorithms

We have constructed an automated learning apparatus to control quantum systems. By directing intense shaped ultrafast laser pulses into a variety of samples and using a measurement of the system as a feedback signal, we are able to reshape the laser pulses to direct the system into a desired state. The feedback signal is the input to an adaptive learning algorithm. This algorithm programs a computer-controlled, acousto-optic modulator pulse shaper. The learning algorithm generates new shaped laser pulses based on the success of previous pulses in achieving a predetermined goal.Comment: 19 pages (including 14 figures), REVTeX 3.1, updated conten

Identification of competing ultrafast all-optical switching mechanisms in Si woodpile photonic crystals

We present a systematic study of ultrafast all-optical switching of Si photonic band gap woodpile crystals using broadband tunable nondegenerate pump-probe spectroscopy. At pump-probe coincidence, we investigate the behavior the differential reflectivity at the blue edge of the stopband for a wide range of pump- and probe frequencies. Both dispersive and absorptive features are observed from the probe spectra at coincidence. As the pump frequency is tuned through half the electronic bandgap of Si, the magnitude of both these features increases. For the first time we unambiguously identify this dispersive effect with the electronic Kerr effect in photonic crystals, and attribute the the absorptive features to nondegenerate two photon absorption. The dispersive and absorptive nonlinear coefficients are extracted, and are found to agree well with literature. Finally, we propose a nondegenerate figure of merit (NFOM), which defines the quality of switching for all nondegenerate optical switching processes.Comment: Accepted by JOSA

Spintronics: Fundamentals and applications

Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. This article reviews the current status of this subject, including both recent advances and well-established results. The primary focus is on the basic physical principles underlying the generation of carrier spin polarization, spin dynamics, and spin-polarized transport in semiconductors and metals. Spin transport differs from charge transport in that spin is a nonconserved quantity in solids due to spin-orbit and hyperfine coupling. The authors discuss in detail spin decoherence mechanisms in metals and semiconductors. Various theories of spin injection and spin-polarized transport are applied to hybrid structures relevant to spin-based devices and fundamental studies of materials properties. Experimental work is reviewed with the emphasis on projected applications, in which external electric and magnetic fields and illumination by light will be used to control spin and charge dynamics to create new functionalities not feasible or ineffective with conventional electronics.Comment: invited review, 36 figures, 900+ references; minor stylistic changes from the published versio