Moving frames for cotangent bundles

Cartan's moving frames method is a standard tool in riemannian geometry. We set up the machinery for applying moving frames to cotangent bundles and its sub-bundles defined by non-holonomic constraints.Comment: 13 pages, to appear in Rep. Math. Phy

Disentangling the exchange coupling of entangled donors in the Si quantum computer architecture

We develop a theory for micro-Raman scattering by single and coupled two-donor states in silicon. We find the Raman spectra to have significant dependence on the donor exchange splitting and the relative spatial positions of the two donor sites. In particular, we establish a strong correlation between the temperature dependence of the Raman peak intensity and the interdonor exchange coupling. Micro-Raman scattering can therefore potentially become a powerful tool to measure interqubit coupling in the development of a Si quantum computer architecture.Comment: Title changed. Other minor change

Silicon-based spin and charge quantum computation

Silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals due to the relatively long spin coherence times. For these spin qubits, donor electron charge manipulation by external gates is a key ingredient for control and read-out of single-qubit operations, while shallow donor exchange gates are frequently invoked to perform two-qubit operations. More recently, charge qubits based on tunnel coupling in P$_2^+$ substitutional molecular ions in Si have also been proposed. We discuss the feasibility of the building blocks involved in shallow donor quantum computation in silicon, taking into account the peculiarities of silicon electronic structure, in particular the six degenerate states at the conduction band edge. We show that quantum interference among these states does not significantly affect operations involving a single donor, but leads to fast oscillations in electron exchange coupling and on tunnel-coupling strength when the donor pair relative position is changed on a lattice-parameter scale. These studies illustrate the considerable potential as well as the tremendous challenges posed by donor spin and charge as candidates for qubits in silicon.Comment: Review paper (invited) - to appear in Annals of the Brazilian Academy of Science

Exchange in silicon-based quantum computer architecture

The silicon-based quantum computer proposal has been one of the intensely pursued ideas during the past three years. Here we calculate the donor electron exchange in silicon and germanium, and demonstrate an atomic-scale challenge for quantum computing in Si (and Ge), as the six (four) conduction band minima in Si (Ge) lead to inter-valley electronic interferences, generating strong oscillations in the exchange splitting of two-donor two-electron states. Donor positioning with atomic scale precision within the unit cell thus becomes a decisive factor in determining the strength of the exchange coupling--a fundamental ingredient for two-qubit operations in a silicon-based quantum computer.Comment: 5 pages, 2 figure

Domain size effects in Barkhausen noise

The possible existence of self-organized criticality in Barkhausen noise is investigated theoretically through a single interface model, and experimentally from measurements in amorphous magnetostrictive ribbon Metglas 2605TCA under stress. Contrary to previous interpretations in the literature, both simulation and experiment indicate that the presence of a cutoff in the avalanche size distribution may be attributed to finite size effects.Comment: 5 pages, 3 figures, submitted so Physical Review

Electron Exchange Coupling for Single Donor Solid-State Qubits

Inter-valley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighbouring phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wavefunctions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys. Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighbouring donors that have been implanted into the silicon substrate using an 15keV ion beam in the so-called 'top down' fabrication scheme for a Kane solid-state quantum computer. In addition we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wavefunctions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighbouring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller.Comment: 10 Pages, 8 Figures. To appear in Physical Review

Depinning transition and thermal fluctuations in the random-field Ising model

We analyze the depinning transition of a driven interface in the 3d random-field Ising model (RFIM) with quenched disorder by means of Monte Carlo simulations. The interface initially built into the system is perpendicular to the [111]-direction of a simple cubic lattice. We introduce an algorithm which is capable of simulating such an interface independent of the considered dimension and time scale. This algorithm is applied to the 3d-RFIM to study both the depinning transition and the influence of thermal fluctuations on this transition. It turns out that in the RFIM characteristics of the depinning transition depend crucially on the existence of overhangs. Our analysis yields critical exponents of the interface velocity, the correlation length, and the thermal rounding of the transition. We find numerical evidence for a scaling relation for these exponents and the dimension d of the system.Comment: 6 pages, including 9 figures, submitted for publicatio

Swimming using surface acoustic waves

Microactuation of free standing objects in fluids is currently dominated by the rotary propeller, giving rise to a range of potential applications in the military, aeronautic and biomedical fields. Previously, surface acoustic waves (SAWs) have been shown to be of increasing interest in the field of microfluidics, where the refraction of a SAW into a drop of fluid creates a convective flow, a phenomenon generally known as SAW streaming. We now show how SAWs, generated at microelectronic devices, can be used as an efficient method of propulsion actuated by localised fluid streaming. The direction of the force arising from such streaming is optimal when the devices are maintained at the Rayleigh angle. The technique provides propulsion without any moving parts, and, due to the inherent design of the SAW transducer, enables simple control of the direction of travel

Driven interfaces in disordered media: determination of universality classes from experimental data

While there have been important theoretical advances in understanding the universality classes of interfaces moving in porous media, the developed tools cannot be directly applied to experiments. Here we introduce a method that can identify the universality class from snapshots of the interface profile. We test the method on discrete models whose universality class is well known, and use it to identify the universality class of interfaces obtained in experiments on fluid flow in porous media.Comment: 4 pages, 5 figure

Homoclinic chaos in the dynamics of a general Bianchi IX model

The dynamics of a general Bianchi IX model with three scale factors is examined. The matter content of the model is assumed to be comoving dust plus a positive cosmological constant. The model presents a critical point of saddle-center-center type in the finite region of phase space. This critical point engenders in the phase space dynamics the topology of stable and unstable four dimensional tubes $R \times S^3$, where $R$ is a saddle direction and $S^3$ is the manifold of unstable periodic orbits in the center-center sector. A general characteristic of the dynamical flow is an oscillatory mode about orbits of an invariant plane of the dynamics which contains the critical point and a Friedmann-Robertson-Walker (FRW) singularity. We show that a pair of tubes (one stable, one unstable) emerging from the neighborhood of the critical point towards the FRW singularity have homoclinic transversal crossings. The homoclinic intersection manifold has topology $R \times S^2$ and is constituted of homoclinic orbits which are bi-asymptotic to the $S^3$ center-center manifold. This is an invariant signature of chaos in the model, and produces chaotic sets in phase space. The model also presents an asymptotic DeSitter attractor at infinity and initial conditions sets are shown to have fractal basin boundaries connected to the escape into the DeSitter configuration (escape into inflation), characterizing the critical point as a chaotic scatterer.Comment: 11 pages, 6 ps figures. Accepted for publication in Phys. Rev.