Glimpses of the Octonions and Quaternions History and Todays Applications in Quantum Physics

Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to nonassociativity. Our reflections keep wandering back to the $Brahmagupta$ $Fibonacc$ two square identity and then via the $Euler$ four square identity up to the $Degen$ $Ggraves$ $Cayley$ eight square identity. These glimpses of history incline and invite us to retell the story on how about one month after quaternions have been carved on the $Broughamian$ bridge octonions were discovered by $John$ $Thomas$ $Ggraves$, jurist and mathematician, a friend of $William$ $Rowan$ $Hamilton$. As for today we just mention en passant quaternionic and octonionic quantum mechanics, generalization of $Cauchy$ $Riemann$ equations for octonions and triality principle and $G_2$ group in spinor language in a descriptive way in order not to daunt non specialists. Relation to finite geometries is recalled and the links to the 7stones of seven sphere, seven imaginary octonions units in out of the $Plato$ cave reality applications are appointed . This way we are welcomed back to primary ideas of $Heisenberg$, $Wheeler$ and other distinguished fathers of quantum mechanics and quantum gravity foundations.Comment: 26 pages, 7 figure

Role of Surface Morphology in Wafer Bonding

The strain patterns detected by x-ray topography in wafers bonded for silicon-on-insulator (SOI) technology were found related to the flatness nonuniformity of the original wafers. Local stresses due to the bonding process are estimated to be about 1×108 dynes/cm2. The stress is reduced about 100 times for the thin (0.5 μm) SOI films. Most of the wafer deformation occurs during room temperature mating of the wafers. The deformation is purely elastic even at 1200 °C. The magnitude of the stress appears insignificant for complimentary metal-oxide-semiconductor devices performance

Andreev bound states in ferromagnet-superconductor nanostructures

We discuss the properties of a ferromagnet - superconductor heterostructure on the basis of a Hubbard model featuring exchange splitting in the ferromagnet and electron - electron attraction in the superconductor. We have solved the spin - polarized Hartree - Fock - Gorkov equations together with the Maxwell's equation (Ampere's law) fully self-consistently. We have found that a Proximity Effect - Fulde - Ferrell - Larkin - Ovchinnikov state is realized in such a heterostructure. It manifests itself in an oscillatory behavior of the pairing amplitude in the ferromagnet and spontaneously generated spin polarized current in the ground state. We argue that it is built up from the Andreev bound states, whose energy can be tuned by the exchange splitting and hence can coincide with the Fermi energy giving rise to a current carrying $\pi$-state. We also suggest experiments to verify these predictions.Comment: 12 pages, 5 figures included; to be published in Physica

Magnetotransport Mechanisms in Strongly Underdoped YBa_2Cu_3O_x Single Crystals

We report magnetoresistivity measurements on strongly underdoped YBa_2Cu_3O_x (x=6.25, 6.36) single crystals in applied magnetic fields H || c-axis. We identify two different contributions to both in-plane and out-of-plane magnetoresistivities. The first contribution has the same sign as the temperature coefficient of the resistivity \partial ln(\rho_i)/\partial T (i={c,ab}). This contribution reflects the incoherent nature of the out-of-plane transport. The second contribution is positive, quadratic in field, with an onset temperature that correlates to the antiferromagnetic ordering.Comment: 4 pages, 3 figure

Compressibility of a two-dimensional hole gas in tilted magnetic field

We have measured compressibility of a two-dimensional hole gas in p-GaAs/AlGaAs heterostructure, grown on a (100) surface, in the presence of a tilted magnetic field. It turns out that the parallel component of magnetic field affects neither the spin splitting nor the density of states. We conclude that: (a) g-factor in the parallel magnetic field is nearly zero in this system; and (b) the level of the disorder potential is not sensitive to the parallel component of the magnetic field

Low-temperature electrical transport in bilayer manganite La1.2_{1.2}Sr1.8_{1.8}Mn2_{2}O7_{7}

The temperature $T$ and magnetic field $H$ dependence of anisotropic in-plane $\rho_{ab}$ and out-of-plane $\rho_{c}$ resistivities have been investigated in single crystals of the bilayer manganite La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$. Below the Curie transition temperature $T_c=$ 125 K, $\rho_{ab}$ and $\rho_{c}$ display almost the same temperature dependence with an up-turn around 50 K. In the metallic regime (50 K $\leq T \leq$ 110 K), both $\rho_{ab}(T)$ and $\rho_{c}(T)$ follow a $T^{9/2}$ dependence, consistent with the two-magnon scattering. We found that the value of the proportionality coefficient $B_{ab}^{fit}$ and the ratio of the exchange interaction $J_{ab}/J_c$ obtained by fitting the data are in excellent agreement with the calculated $B_{ab}$ based on the two-magnon model and $J_{ab}/J_c$ deduced from neutron scattering, respectively. This provides further support for this scattering mechanism. At even lower $T$, in the non-metallic regime ($T<$ 50 K), {\it both} the in-plane $\sigma_{ab}$ and out-of-plane $\sigma_{c}$ conductivities obey a $T^{1/2}$ dependence, consistent with weak localization effects. Hence, this demonstrates the three-dimensional metallic nature of the bilayer manganite La$_{1.2}$Sr$_{1.8}$Mn$_{2}$O$_{7}$ at $T<T_c$.Comment: 7 pages and 5 figures, accepted for publication in Phys. Rev.

Adaptive Robust Fault-Tolerant Control for Linear MIMO Systems with Unmatched Uncertainties

In this paper, two novel fault-tolerant control design approaches are proposed for linear MIMO systems with actuator additive faults, multiplicative faults and unmatched uncertainties. For time-varying multiplicative and additive faults, new adaptive laws and additive compensation functions are proposed. A set of conditions is developed such that the unmatched uncertainties are compensated by actuators in control. On the other hand, for unmatched uncertainties with their projection in unmatched space being not zero, based on a (vector) relative degree condition, additive functions are designed to compensate for the uncertainties from output channels in presence of actuator faults. The developed fault-tolerant control schemes are applied to two aircraft systems to demonstrate the efficiency of the proposed approaches

Hard Photodisintegration of a Proton Pair

We present a study of high energy photodisintegration of proton-pairs through the gamma + 3He -> p+p+n channel. Photon energies from 0.8 to 4.7 GeV were used in kinematics corresponding to a proton pair with high relative momentum and a neutron nearly at rest. The s-11 scaling of the cross section, as predicted by the constituent counting rule for two nucleon photodisintegration, was observed for the first time. The onset of the scaling is at a higher energy and the cross section is significantly lower than for deuteron (pn pair) photodisintegration. For photon energies below the scaling region, the scaled cross section was found to present a strong energy-dependent structure not observed in deuteron photodisintegration.Comment: 7 pages, 3 figures, for submission to Phys. Lett.

Hidden degree of freedom and critical states in a two-dimensional electron gas in the presence of a random magnetic field

We establish the existence of a hidden degree of freedom and the critical states of a spinless electron system in a spatially-correlated random magnetic field with vanishing mean. Whereas the critical states are carried by the zero-field contours of the field landscape, the hidden degree of freedom is recognized as being associated with the formation of vortices in these special contours. It is argued that, as opposed to the coherent backscattering mechanism of weak localization, a new type of scattering processes in the contours controls the underlying physics of localization in the random magnetic field system. In addition, we investigate the role of vortices in governing the metal-insulator transition and propose a renormalization-group diagram for the system under study.Comment: 17 pages, 16 figures; Figs. 1, 7, 9, and 10 have been reduced in quality for e-submissio

Formation of Nanopits in Si Capping Layers on SiGe Quantum Dots

In-situ annealing at a high temperature of 640°C was performed for a low temperature grown Si capping layer, which was grown at 300°C on SiGe self-assembled quantum dots with a thickness of 50 nm. Square nanopits, with a depth of about 8 nm and boundaries along 〈110〉, are formed in the Si capping layer after annealing. Cross-sectional transmission electron microscopy observation shows that each nanopit is located right over one dot with one to one correspondence. The detailed migration of Si atoms for the nanopit formation is revealed by in-situ annealing at a low temperature of 540°C. The final well-defined profiles of the nanopits indicate that both strain energy and surface energy play roles during the nanopit formation, and the nanopits are stable at 640°C. A subsequent growth of Ge on the nanopit-patterned surface results in the formation of SiGe quantum dot molecules around the nanopits