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The analysis of data stored in multiple sites has become more popular, raising new concerns about the security of data storage and communication. Federated learning, which does not require centralizing data, is a common approach to preventing heavy data transportation, securing valued data, and protecting personal information protection. Therefore, determining how to aggregate the information obtained from the analysis of data in separate local sites has become an important statistical issue. The commonly used averaging methods may not be suitable due to data nonhomogeneity and incomparable results among individual sites, and applying them may result in the loss of information obtained from the individual analyses. Using a sequential method in federated learning with distributed computing can facilitate the integration and accelerate the analysis process. We develop a data-driven method for efficiently and effectively aggregating valued information by analyzing local data without encountering potential issues such as information security and heavy transportation due to data communication. In addition, the proposed method can preserve the properties of classical sequential adaptive design, such as data-driven sample size and estimation precision when applied to generalized linear models. We use numerical studies of simulated data and an application to COVID-19 data collected from 32 hospitals in Mexico, to illustrate the proposed method., Comment: 22 pages

We make use of the time-dependent density functional theory to derive a new formally exact expression for the dc resistivity of metals with impurities. This expression takes fully into account the dynamics of electron-electron interactions. Correction to the conventional $T$-matrix (phase-shifts) theory is treated within hydrodynamics of inhomogeneous viscous electron liquid. As a first application, we present calculations of the residual resistivity of aluminum as a function of the atomic number of the impurities. We show that the inclusion of many-body corrections considerably improves the agreement between theory and experiment., Comment: 4 pages, 1 figure

We have theoretically studied the thermoelectric properties of serially coupled quantum dots (SCQD) embedded in an insulator matrix connected to metallic electrodes. In the framework of Keldysh Green's function technique, the Landauer formula of transmission factor is obtained by using the equation of motion method. Based on such analytical expressions of charge and heat currents, we calculate the electrical conductance, Seebeck coefficient, electron thermal conductance and figure of merit (ZT) of SCQD in the linear response regime. The effects of electron Coulomb interactions on the reduction and enhancement of ZT are analyzed. We demonstrate that ZT is not a monotonic increasing function of interdot electron hopping strength ($t_c$). We also show that in the absence of phonon thermal conductance, SCQD can reach the Carnot efficiency as $t_c$ approaches zero., Comment: corrected some argumenets

A transfer-matrix algorithm is presented herein as a beginning to study the transmission characteristics of coherent light through three-dimensional periodic microstructures, in which the structures are treated as two-dimensional-layer stacks and multiple reflections are considered negligible. The spatial-correlated noise is further introduced layer by layer to realize the actual decoherence of the light and allows for statistical investigation of the partial spatially coherent optics in transparent mediums. Numerical analyses show comparable results to the Gaussian Schell model in free-space cases, indicating the validity of the algorithms., Comment: 15 pages, 7 figures

The scalar $f_{xc}$ and tensor $\hat{f}_{xc}$ exchange-correlation (xc) kernels are key ingredients of the time-dependent density functional theory and the time-dependent current density functional theory, respectively. We derive a comparatively simple relation between these two kernels under the assumption that the dynamic xc can be considered "weak". We expect our formula to serve as a convenient bridge between the scalar $f_{xc}$ which directly enters many applications and the tensor $\hat{f}_{xc}$ which, due to its locality in space, is much easier to approximate., Comment: 8 pages, Submitted to Journal of Chemical Physics

The dynamical exchange-correlation kernel $f_{xc}$ of a non-uniform electron gas is an essential input for the time-dependent density functional theory of electronic systems. The long-wavelength behavior of this kernel is known to be of the form $f_{xc}= \alpha/q^2$ where $q$ is the wave vector and $\alpha$ is a frequency-dependent coefficient. We show that in the limit of weak non-uniformity the coefficient $\alpha$ has a simple and exact expression in terms of the ground-state density and the frequency-dependent kernel of a {\it uniform} electron gas at the average density. We present an approximate evaluation of this expression for Si and discuss its implications for the theory of excitonic effects., Comment: 5 pages, 2 figures

Due to the strongly nonlocal nature of $f_{xc}({\bf r},{\bf r}',\omega)$ the {\em scalar} exchange and correlation (xc) kernel of the time-dependent density-functional theory (TDDFT), the formula for Q the friction coefficient of an interacting electron gas (EG) for ions tends to give a too large value of Q for heavy ions in the medium- and low-density EG, if we adopt the local-density approximation (LDA) to $f_{xc}({\bf r},{\bf r}',\omega)$, even though the formula itself is formally exact. We have rectified this unfavorable feature by reformulating the formula for Q in terms of the {\em tensorial} xc kernel of the time dependent current-density functional theory, to which the LDA can be applied without intrinsic difficulty. Our numerical results find themselves in a considerably better agreement with the experimental stopping power of Al and Au for slow ions than those previously obtained within the LDA to the TDDFT., Comment: 26 pages, 3 figures

We resolve the existing controversy concerning the selection of the sign of the normal-to-the-interface component of the wave-vector $k_z$ of an electromagnetic wave in an active (gain) medium. Our method exploits the fact that no ambiguity exists in the case of a {\em film} of the active medium since its coefficient of reflectance is invariant under the inversion of the sign of $k_z$. Then we show that the limit of the infinite film thickness determines a unique and physically consistent choice of the wave-vector and the refractive index. Practically important implications of the theory are identified and discussed., Comment: 6 pages, 4 figures

We develop a scheme for building the scalar exchange-correlation (xc) kernel of time-dependent density functional theory (TDDFT) from the tensorial kernel of time-dependent {\em current} density functional theory (TDCDFT) and the Kohn-Sham current density response function. Resorting to the local approximation to the kernel of TDCDFT results in a nonlocal approximation to the kernel of TDDFT, which is free of the contradictions that plague the standard local density approximation (LDA) to TDDFT. As an application of this general scheme, we calculate the dynamical xc contribution to the stopping power of electron liquids for slow ions to find that our results are in considerably better agreement with experiment than those obtained using TDDFT in the conventional LDA., Comment: 6 pages, 3 figures, accepted to Phys. Rev. B

We have developed a method to systematically compute the form of Rashba- and Dresselhaus-like contributions to the spin Hamiltonian of heterostructures to an arbitrary order in the wavevector k. This is achieved by using the double group representations to construct general symmetry-allowed Hamiltonians with full spin-orbit effects within the tight-binding formalism. We have computed full-zone spin Hamiltonians for [001]-, [110]- and [111]-grown zinc blende heterostructures (D_{2d},C_{4v},C_{2v},C_{3v} point group symmetries), which are commonly used in spintronics. After an expansion of the Hamiltonian up to third order in k, we are able to obtain additional terms not found previously. The present method also provides the matrix elements for bulk zinc blendes (T_d) in the anion/cation and effective bond orbital model (EBOM) basis sets with full spin-orbit effects., Comment: v1: 11 pages, 3 figures, 8 tables

We apply the D'yakonov-Perel' (DP) formalism to [111]-grown zincblende quantum wells (QWs) to compute the spin lifetimes of electrons in the two-dimensional electron gas. We account for both bulk and structural inversion asymmetry (Rashba) effects. We see that, under certain conditions, the spin splitting vanishes to first order in k, which effectively suppresses the DP spin relaxation mechanism for all spin components. We predict extended spin lifetimes as a result, giving rise to the possibility of enhanced spin storage. We also study [110]-grown QWs, where the effect of structural inversion asymmetry is to augment the spin relaxation rate of the component perpendicular to the well. We derive analytical expressions for the spin lifetime tensor and its proper axes, and see that they are dependent on the relative magnitude of the BIA- and SIA-induced splittings., Comment: v1: 5 pages, 2 figures, submitted to PRL v2: added 1 figure and supporting content, PRB format

We show theoretically that a strongly spin-polarized current can be generated in semiconductors by taking advantage of the ferromagnetic phase of a quantum dot array (QDA). A Hubbard model with coupling to leads is used to study the tunneling current of the QDA system as a function of gate voltage. Due to the weak interdot coupling and strong Coulomb repulsion, it is found that a ferromagnetic phase exists in QDA within a window of gate voltage. Therefore QDA can be used as a spin filter to detect and control spin states in quantum information devices., Comment: 3 pages, 2 figures

The theoretical studies of optical properties of Ga$_{1-x}$In$_x$As self-assembled quantum-wires (QWR's) made of short-period superlattices with strain-induced lateral ordering are presented. Valence-band anisotropy, band mixing, and effects due to local strain distribution at the atomistic level are all taken into account. Using realistic material parameters which are experimentally feasible, we perform simulations of the absorption spectra for both inter-subband and inter-band transitions (including the excitonic effect) of this material.It is shown that the self-assembled QWR's have favorable optical properties for application in infra-red detection with normal incidence. The wavelength of detection ranges from 10 $\mu m$ to 20 $\mu m$ with the length of QWR period varying from 140\AA to 300\AA., Comment: 16 pages, 15 figures

Band Structures and optical matrix elements of quantum wires(QWR's) made of short-period superlattices(SPS) with strain-induced lateral ordering(SILO) are investigated theoretically via an effective bond-orbital model(EBOM) combined with a valence-force field(VFF) model. Valence-band anistropy, band mixing, and effects due to local strain distribution at the atomistic level are all taken into account. In particular, Ga(1-x)In(x)As QWR's grown by SILO process are considered. A VFF model is used to find the equilibrium atomic positions in the SILO QWR structure by minimizing the lattice energy. The strain tensor at each atomic(In or GA) site is then obtained and included in the calculations of electronic states and optical peroperties. It is found that different local arrangement of atoms leads to very different strain distribution, which in term alters the optical properties. In particular, we found that the optical anisotropy can be reversed due to the change in shear strain caused by the inter-change of atomic positions. Good agreement with the existing experimental data on band gap and optical anisotropy can be obtained when a 2D alloy structure with lateral composition modulation in the InAs/GaAs interface planes of the SPS is used. Our studies revealed the possibility of "shear-strain engineering" in SILO QWR light-emitting devices to achieve desired optical anisotropy., Comment: 15 pages and 25 figures, some figures are relabed

We investigate the role played by nonequilibrium dynamical screening in the thermalization of carriers in a simplified two-component two-band model of a semiconductor. The main feature of our approach is the theoretically sound treatment of collisions. We abandon Fermi's Golden rule in favor of a nonequilibrium field theoretic formalism as the former is applicable only in the long-time regime. We also introduce the concept of nonequilibrium dynamical screening. The dephasing of excitonic quantum beats as a result of carrier-carrier scattering is brought out. At low densities it is found that the dephasing times due to carrier-carrier scattering is in picoseconds and not femtoseconds, in agreement with experiments. The polarization dephasing rates are computed as a function of the excited carrier density and it is found that the dephasing rate for carrier-carrier scattering is proportional to the carrier density at ultralow densities. The scaling relation is sublinear at higher densities, which enables a comparison with experiment., Comment: Revised version with additional refs. 12 pages, figs. available upon request; Submitted to Phys. Rev. B