Molecular orbital calculations of two-electron states for P-donor solid-state spin qubits

We theoretically study the Hilbert space structure of two neighboring P-donor electrons in silicon-based quantum computer architectures. To use electron spins as qubits, a crucial condition is the isolation of the electron spins from their environment, including the electronic orbital degrees of freedom. We provide detailed electronic structure calculations of both the single donor electron wave function and the two-electron pair wave function. We adopted a molecular orbital method for the two-electron problem, forming a basis with the calculated single donor electron orbitals. Our two-electron basis contains many singlet and triplet orbital excited states, in addition to the two simple ground state singlet and triplet orbitals usually used in the Heitler-London approximation to describe the two-electron donor pair wave function. We determined the excitation spectrum of the two-donor system, and study its dependence on strain, lattice position, and interdonor separation. This allows us to determine how isolated the ground state singlet and triplet orbitals are from the rest of the excited state Hilbert space. In addition to calculating the energy spectrum, we are also able to evaluate the exchange coupling between the two donor electrons, and the double occupancy probability that both electrons will reside on the same P donor. These two quantities are very important for logical operations in solid-state quantum computing devices, as a large exchange coupling achieves faster gating times, while the magnitude of the double occupancy probability can affect the error rate.

Algebraic Bethe ansatz for the anisotropic supersymmetric U model

We present an algebraic Bethe ansatz for the anisotropic supersymmetric U model for correlated electrons on the unrestricted 4(L)-dimensional electronic Hilbert space x(n=l)(L)C(4)(where L is the lattice length). The supersymmetry algebra of the local Hamiltonian is the quantum superalgebra U-q[gl(2\1)] and the model contains two symmetry-preserving free real parameters; the quantization parameter q and the Hubbard interaction parameter U. The parameter U arises from the one-parameter family of inequivalent typical four-dimensional irreps of U-q[gl(2\1)]. Eigenstates of the model are determined by the algebraic Bethe ansatz on a one-dimensional periodic lattice.

Calculating current densities and fields produced by shielded magnetic resonance imaging probes

A method is presented for computing the fields produced by radio frequency probes of the type used in magnetic resonance imaging. The effects of surrounding the probe with a shielding coil, intended to eliminate stray fields produced outside the probe, are included. An essential feature of these devices is the fact that the conducting rungs of the probe are of finite width relative to the coil radius, and it is therefore necessary to find the distribution of current within the conductors as part of the solution process. This is done here using a numerical method based on the inverse finite Hilbert transform, applied iteratively to the entire structure including its shielding coils. It is observed that the fields are influenced substantially by the width of the conducting rungs of the probe, since induced eddy currents within the rungs become more pronounced as their width is increased. The shield is also shown to have a significant effect on both the primary current density and the resultant fields. Quality factors are computed for these probes and compared with values measured experimentally.

Integrable extended hubbard models with boundary Kondo impurities

Three kinds of integrable Kondo impurity additions to one-dimensional q-deformed extended Hubbard models are studied by means of the boundary Z(2)-graded quantum inverse scattering method. The boundary K matrices depending on the local magnetic moments of the impurities are presented as nontrivial realisations of the reflection equation algebras in an impurity Hilbert space. The models are solved by using the algebraic Bethe ansatz method, and the Bethe ansatz equations are obtained.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

Qudit quantum-state tomography

Recently quantum tomography has been proposed as a fundamental tool for prototyping a few qubit quantum device. It allows the complete reconstruction of the state produced from a given input into the device. From this reconstructed density matrix, relevant quantum information quantities such as the degree of entanglement and entropy can be calculated. Generally, orthogonal measurements have been discussed for this tomographic reconstruction. In this paper, we extend the tomographic reconstruction technique to two new regimes. First, we show how nonorthogonal measurements allow the reconstruction of the state of the system provided the measurements span the Hilbert space. We then detail how quantum-state tomography can be performed for multiqudits with a specific example illustrating how to achieve this in one- and two-qutrit systems.

Compadre, será que o teu hotel tem mais quartos e janelas do que o meu?

[...] viagem ao hotel infinito de Hilbert. Sei que na atual crise económica não é prudente qualquer devaneio turístico, mas como o prometido é devido, eis-me a tentar explicar um desafio que ficou em banho-maria desde dezembro e que consistia em resolver o seguinte enigma: se um hotel tiver um número infinito de quartos e cada quarto possuir um número infinito de janelas, será que existem mais quartos do que janelas? [...].

Comparative analysis of time-frequency methods estimating the time-varying microstructure of sleep EEG spindles

Proceedings of the Information Technology Applications in Biomedicine, Ioannina - Epirus, Greece, October 26-28, 2006

Characterization of earth-based mortars for rammed earth repair

All over the world, many earth buildings are deteriorating due to lack of maintenance and repair. Repairs on rammed earth walls are mainly done with mortars, by rendering application; however, often the repair is inadequate, resorting to the use of incompatible materials, including cement-based mortars. It has been observed that such interventions, in walls that until that day only had presented natural ageing issues, created new problems, much more dangerous for the building than the previous ones, causing serious deficiencies in this type of construction. One of the problems is that the detachment of the new cement-based mortar rendering only occurs after some time but, until that occurrence, degradations develop in the wall itself. When the render detaches, instead of needing only a new render, the surface has to be repaired in depth, with a repair mortar. Consequently, it has been stablished that the renders, and particularly repair mortars, should have physical, mechanical and chemical properties similar to those of the rammed earth walls. This article intends to contribute to a better knowledge of earth-based mortars used to repair the surface of rammed earth walls. The studied mortars are based on four types of earth: three of them were collected from non-deteriorated parts of walls of unstabilized rammed earth buildings located in Alentejo region, south of Portugal; the fourth is a commercial earth, consisting mainly of clay. Other components were also used, particularly: sand to control shrinkage; binders stabilizers such as dry hydrated air-lime, natural hydraulic lime, Portland cement and natural cement; as well as natural vegetal fibers (hemp fibers). The experimental analysis of the mortars in the fresh state consisted in determining the consistency by flow table and the bulk density. In the hardened state, the tests made it possible to evaluate the following properties: linear and volumetric shrinkage; capillary water absorption; drying capacity; dynamic modulus of elasticity; flexural and compressive strength.

Procesos físicos en relatividad general

Para 1997 se propone realizar las siguientes tareas: Teoría de Superficies Nulas en Relatividad General. * Estudiar la formación de cáusticas y singularidades de las superficies nulas en forma cinemática y dinámica. * Analizar la dinámica de superficies características hasta segundo orden en un esquema perturbativo. * Formalizar la teoría de Superficies Nulas usando espacios fibrados. Cuantificación asintótica del campo gravitatorio. Continuar el estudio del espacio de Hilbert asintótico para el campo gravitatorio. Es conveniente recordar que la cuantifiación de este campo es uno de los problemas teóricos más importantes sin resolver. Cuantificación de Superficies Nulas. Continuar con el estudio de la cuantización del campo gravitatorio usando el formalismo de superficies nulas. Hasta el momento el principal resultado obtenido fue probar que no sólo el campo gravitatorio sino también los puntos del espacio-tiempo se vuelven operadores con relaciones de conmutación. Esto demuestra de manera concreta la especulación de Wheeler que en la gravedad cuántica los puntos del espacio tiempo no están bien definidos. Simulación de un detector de rayos Gamma. (...) Para este año se prevé cumplir las siguientes etapas: * Se estudiarán los efectos de la polarización del fotón incidente en la sección eficaz y su posible método de detección. * Se implementarán las subrutinas correspondientes en las simulaciones Monte Carlo para incorporar secciones eficaces polarizadas en el Código GEANT. Asimismo, se piensa comenzar con el diseño de un nuevo detector de rayos Gamma en un rango de energías (0.1 / 1 MeV) muy inferior al anterior para ser usado como cámara Gamma ultra sensible.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

Asymptotics of orthogonal polynomials via the Koosis theorem

The main aim of this short paper is to advertize the Koosis theorem in the mathematical community, especially among those who study orthogonal polynomials. We (try to) do this by proving a new theorem about asymptotics of orthogonal polynomi- als for which the Koosis theorem seems to be the most natural tool. Namely, we consider the case when a SzegÄo measure on the unit circumference is perturbed by an arbitrary measure inside the unit disk and an arbitrary Blaschke sequence of point masses outside the unit disk.

Shelah's singular compactness theorem

We present Shelah’s famous theorem in a version for modules, together with a self-contained proof and some examples. This exposition is based on lectures given at CRM in October 2006.