Perturbations of time optimal control problems for a class of abstract parabolic systems

In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application to PDEs systems concerns the behavior of optimal time and of the associated optimal controls for parabolic equations with highly oscillating coefficients, as we encounter in homogenization theory. Our main results assert that, provided that the target is a closed ball centered at the origin and of positive radius, the solutions of the time optimal control problems for the systems with oscillating coefficients converge, in the usual norms, to the solution of the corresponding problem for the homogenized system. In order to prove our main theorem, we provide several new results, which could be of a broader interest, on time and norm optimal control problems

A Comparative Study on Spin-Orbit Torque Efficiencies from W/ferromagnetic and W/ferrimagnetic Heterostructures

It has been shown that W in its resistive form possesses the largest spin-Hall ratio among all heavy transition metals, which makes it a good candidate for generating efficient dampinglike spin-orbit torque (DL-SOT) acting upon adjacent ferromagnetic or ferrimagnetic (FM) layer. Here we provide a systematic study on the spin transport properties of W/FM magnetic heterostructures with the FM layer being ferromagnetic Co$_{20}$Fe$_{60}$B$_{20}$ or ferrimagnetic Co$_{63}$Tb$_{37}$ with perpendicular magnetic anisotropy. The DL-SOT efficiency $|\xi_{DL}|$, which is characterized by a current-induced hysteresis loop shift method, is found to be correlated to the microstructure of W buffer layer in both W/Co$_{20}$Fe$_{60}$B$_{20}$ and W/Co$_{63}$Tb$_{37}$ systems. Maximum values of $|\xi_{DL}|\approx 0.144$ and $|\xi_{DL}|\approx 0.116$ are achieved when the W layer is partially amorphous in the W/Co$_{20}$Fe$_{60}$B$_{20}$ and W/Co$_{63}$Tb$_{37}$ heterostructures, respectively. Our results suggest that the spin Hall effect from resistive phase of W can be utilized to effectively control both ferromagnetic and ferrimagnetic layers through a DL-SOT mechanism

New class of 3D topological insulator in double perovskite

We predict a new class of three-dimensional topological insulators (TIs) in which the spin-orbit coupling (SOC) can more effectively generate a large band gap at $\Gamma$ point. The band gap of conventional TI such as Bi$_2$Se$_3$ is mainly limited by two factors, the strength of SOC and, from electronic structure perspective, the band gap when SOC is absent. While the former is an atomic property, we find that the latter can be minimized in a generic rock-salt lattice model in which a stable crossing of bands {\it at} the Fermi level along with band character inversion occurs for a range of parameters in the absence of SOC. Thus, large-gap TI's or TI's comprised of lighter elements can be expected. In fact, we find by performing first-principle calculations that the model applies to a class of double perovskites A$_2$BiXO$_6$ (A = Ca, Sr, Ba; X = Br, I) and the band gap is predicted up to 0.55 eV. Besides, more detailed calculations considering realistic surface structure indicate that the Dirac cones are robust against the presence of dangling bond at the boundary with a specific termination.Comment: submitted; title changed and new references added; see DOI for published versio

Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure

Modeling Noise Coupling Between Package and PCB Power/Ground Planes with an Efficient 2-D FDTD/Lumped Element Method

An efficient numerical approach based on the 2-D finite-difference time-domain (FDTD) method is proposed to model the power/ground plane noise or simultaneously switching noise (SSN), including the interconnect effect between the package and the print circuit board (PCB). The space between the power and ground planes on the package and PCB are meshed with 2-D cells. The equivalent R-L-C circuits of the via and the solder balls connecting the package and PCB can be incorporated into a 2-D Yee cell based on a novel integral formulation in the time domain. An efficient recursive updating algorithm is proposed to fit the lumped networks into the Yee equations. A test sample of a ball grid array (BGA) package mounted on a PCB was fabricated. The power/ground noise coupling behavior was measured and compared with the simulation. The proposed method significantly reduces the computing time compared with other full-wave numerical approaches

Landau level crossing in a spin-orbit coupled two-dimensional electron gas

We have studied experimentally theﾠLandau levelﾠ(LL) spectrum of a two-dimensionalﾠelectron gasﾠ(2DEG)ﾠin an In0.53Ga0.47As/InPﾠquantum wellﾠstructure by means of low-temperature magneto-transport coincidence measurement in vectorﾠmagnetic fields.ﾠIt is well known that LL crossing occurs in tiltedﾠmagnetic fieldsﾠdue to a competition between cyclotron energy andﾠZeeman effect.ﾠRemarkably, here we observe an additional type of level-crossing resulting from a competition between Rashba andﾠZeeman splittingﾠin a smallﾠmagnetic field,ﾠconsistent with theﾠtheoreticalﾠprediction for strongly spin-orbit coupledﾠ2DEG