Quantum Algorithm for Simulating Hamiltonian Dynamics with an Off-diagonal Series Expansion

We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its off-diagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current state-of-the-art. We provide an analysis of resource costs for several sample models.

Effect of Torsion Stress on the Offset and Sensitivity of Diagonal and Off-Diagonal GMI in Amorphous Wires

In this paper, the torsional stress effect on Giant Magneto-Impedance (GMI) was studied in Co-rich amorphous wires. The study, which was conducted in the context of the development of a current clamp based on GMI, considered torsion as a parameter of the influence of this sensor. Both diagonal, Z11, and off-diagonal, Z21, components of the impedance tensor were investigated. The samples were Co-rich wires with a 100 µ diameter. The wires were twisted positive and negative angles with respect to a reference position. For each component of the impedance, the intrinsic sensitivity and offset were measured as a function of the rotation angle. The results showed that the sensitivity of the diagonal component at a given working point slightly increased for angles between −90° to +90°, whereas the sensitivity was almost constant for the off-diagonal component at zero-field. The intrinsic offset in the diagonal configuration was almost unchanged for the rotation angles considered, whereas this offset increased in the off-diagonal configuration. Furthermore, the GMI ratio of Z11 was also measured as a function of the rotation angle for comparison purposes with known data. The maximum of this ratio was obtained for a rotation angle of about 50°.

Anisotropic wall permeability effects on turbulent channel flows

Streamwise–wall-normal ( $x$ – $y$ ) and streamwise–spanwise ( $x$ – $z$ ) plane measurements are carried out by planar particle image velocimetry for turbulent channel flows over anisotropic porous media at the bulk Reynolds number $Re_{b}=900{-}13\,600$ . Three kinds of anisotropic porous media are constructed to form the bottom wall of the channel. Their wall permeability tensor is designed to have a larger wall-normal diagonal component (wall-normal permeability) than the other components. Those porous media are constructed to have three mutually orthogonal principal axes and those principal axes are aligned with the Cartesian coordinate axes of the flow geometry. Correspondingly, the permeability tensor of each porous medium is diagonal. With the $x$ – $y$ plane data, it is found that the turbulence level well accords with the order of the streamwise diagonal component of the permeability tensor (streamwise permeability). This confirms that the turbulence strength depends on the streamwise permeability rather than the wall-normal permeability when the permeability tensor is diagonal and the wall-normal permeability is larger than the streamwise permeability. To generally characterize those phenomena including isotropic porous wall cases, modified permeability Reynolds numbers are discussed. From a quadrant analysis, it is found that the contribution from sweeps and ejections to the Reynolds shear stress near the porous media is influenced by the streamwise permeability. In the $x$ – $z$ plane data, although low- and high-speed streaks are also observed near the anisotropic porous walls, large-scale spanwise patterns appear at a larger Reynolds number. It is confirmed that they are due to the transverse waves induced by the Kelvin–Helmholtz instability. By the two-point correlation analyses of the fluctuating velocities, the spacing of the streaks and the wavelengths of the Kelvin–Helmholtz (K–H) waves are discussed. It is then confirmed that the transition point from the quasi-streak structure to the roll-cell-like structure is characterized by the wall-normal distance including the zero-plane displacement of the log-law velocity which can be characterized by the streamwise permeability. It is also confirmed that the normalized wavelengths of the K–H waves over porous media are in a similar range to that of the turbulent mixing layers irrespective of the anisotropy of the porous media.

Stressed-Strain State of Multi Layer Foil under One-Axis Tension

Multilayer protective materials and coatings attract attention last years because the possibility appears to obtain unique properties of materials due to combination of properties and sizes of layers. In his paper analytical solution is constructed for the problem on multilayer foil tension. It is assumed that stress and strain tensor components depend on one space coordinate in the axis direction perpendicular to layers and generalized plane stressed state is realized. Interesting effect is detected for two-layer material: thickness of the coating exists when one of diagonal stress tensor components is minimal, that ensure minimal break in the corresponding stresses in interface. This effect is observed previously experimentally by many authors. However, other diagonal component of stress tensor has maximal value for other value of coating thickness. The positions of the maximal and minimal values of stresses and breaks depend on combination of properties and thicknesses of layers.

Bianchi type-II cosmological model: some remarks

Within the framework of a Bianchi type-II (BII) cosmological model the behavior of matter distribution has been considered. It is shown that the non-zero off-diagonal component of the Einstein tensor implies some severe restrictions on the choice of matter distribution. In particular, for a locally rotationally symmetric Bianchi type-II (LRS BII) space-time, it is proved that the matter distribution should be strictly isotropic if the corresponding matter field possesses only non-zero diagonal components of the energy-momentum tensor.

ABSENCE OF TRANSPORT IN ANDERSON LOCALIZATION

We consider the charge transport in the tight-binding Anderson model. Under a mild condition on the Fermi projection, we show that it is zero almost surely. This result has wider applicability than our previous work [12], while the definition of charge transport is slightly different. It also applies to the computation of non-diagonal component of the conductivity tensor which recovers the famous result of quantization of Hall conductivity in quantum Hall systems.

Self-diffusion in granular shear flows

The collisionally induced random particle velocities in a rapid granular shear flow drive the diffusion of particles in manner directly analogous to the thermal diffusion of molecules or the eddy-induced diffusion in a turbulent flow. This paper reports measurements, via computer simulation, of the anisotropic diffusion tensor for a granular shear flow. The components are determined both by particle tracking and through velocity correlations, which are found to agree with reasonable accuracy. As might be expected from symmetry arguments, there are four non-zero components generated in a simple shear flow: the three diagonal components and one off-diagonal component.