Non-Abelian spin-orbit gauge: Persistent spin helix and quantum square ring

We re-express the Rashba and Dresselhaus interactions as non-Abelian spin-orbit gauges and provide a new perspective in understanding the persistent spin helix [Phys. Rev. Lett. 97, 236601 (2006)]. A spin-orbit interacting system can be transformed into a free electron gas in the equal-strength Rashba-Dresselhaus [001] linear model, the Dresselhaus [110] linear model, and a one-dimensional system. A general tight-binding Hamiltonian for non-uniform spin-orbit interactions and hoppings along arbitrary directions, within the framework of finite difference method, is obtained. As an application based on this Hamiltonian, a quantum square ring in contact with two ideal leads is found to exhibit four states, insulating, spin-filtering, spin-flipping, and spin-keeping states.Comment: 7 pages, 3 figure

Quantum World-line Monte Carlo Method with Non-binary Loops and Its Application

A quantum world-line Monte Carlo method for high-symmetrical quantum models is proposed. Firstly, based on a representation of a partition function using the Matsubara formula, the principle of quantum world-line Monte Carlo methods is briefly outlined and a new algorithm using non-binary loops is given for quantum models with high symmetry as SU(N). The algorithm is called non-binary loop algorithm because of non-binary loop updatings. Secondary, one example of our numerical studies using the non-binary loop updating is shown. It is the problem of the ground state of two-dimensional SU(N) anti-ferromagnets. Our numerical study confirms that the ground state in the small N <= 4 case is a magnetic ordered Neel state, but the one in the large N >= 5 case has no magnetic order, and it becomes a dimer state.Comment: 14 pages, 5 figures, Invited talk at the 18th Annual Workshop on Recent Developments of Computer Simulation Studies in Condensed Matter Physics, Athens, 7-11 March, 200

Standardized maximim D-optimal designs for enzyme kineticinhibition models

Locally optimal designs for nonlinear models require a single set of nominal values for the unknown parameters.An alternative is the maximin approach that allows the user to specify a range of values for each parameter ofinterest. However, the maximin approach is difficult because we first have to determine the locally optimal designfor each set of nominal values before maximin types of optimal designs can be found via a nested optimizationprocess. We show that particle swarm optimization (PSO) techniques can solve such complex optimizationproblems effectively. We demonstrate numerical results from PSO can help find, for the first time, formulae forstandardized maximin D-optimal designs for nonlinear model with 3 or 4 parameters on the compact andnonnegative design space. Additionally, we show locally and standardized maximin D-optimal designs for inhibitionmodels are not necessarily supported at a minimum number of points. To facilitate use of such designs, wecreate a web-based tool for practitioners to find tailor-made locally and standardized maximin optimal designs

Rashba Spin Interferometer

A spin interferometer utilizing the Rashba effect is proposed. The novel design is composed of a one-dimensional (1D) straight wire and a 1D half-ring. By calculating the norm of the superposed wave function, we derive analytical expressions to describe the spin interference spectrum as a function of the Rashba coupling strength. Presented spin interference results are identified to include (i) the quantum-mechanical 4pi rotation effect, (ii) geometric effect, and (iii) Shubnikov-de Haas-like beating effect.Comment: 3 pages, 3 figures, appears in the proceedings of the 10th Joint MMM/Intermag Conferenc

TVICA - Time Varying Independent Component Analysis and Its Application to Financial Data

Source extraction and dimensionality reduction are important in analyzing high dimensional and complex financial time series that are neither Gaussian distributed nor stationary. Independent component analysis (ICA) method can be used to factorize the data into a linear combination of independent compo- nents, so that the high dimensional problem is converted to a set of univariate ones. However conventional ICA methods implicitly assume stationarity or stochastic homogeneity of the analyzed time series, which leads to a low accu- racy of estimation in case of a changing stochastic structure. A time varying ICA (TVICA) is proposed here. The key idea is to allow the ICA filter to change over time, and to estimate it in so-called local homogeneous intervals. The question of how to identify these intervals is solved by the LCP (local change point) method. Compared to a static ICA, the dynamic TVICA pro- vides good performance both in simulation and real data analysis. The data example is concerned with independent signal processing and deals with a portfolio of highly traded stocks.Adaptive Sequential Testing, Independent Component Analysis, Local Homogeneity, Signal Processing, Realized Volatility.

Broken spin-Hall accumulation symmetry by magnetic field and coexisted Rashba and Dresselhaus interactions

The spin-Hall effect in the two-dimensional electron gas (2DEG) generates symmetric out-of-plane spin Sz accumulation about the current axis in the absence of external magnetic field. Here we employ the real space Landauer-Keldysh formalism [B. K. Nikolic et al., Phys. Rev. Lett. 95, 046601 (2005); Phys. Rev. B 73, 075303 (2006)] by considering a four-terminal setup to investigate the circumstances in which this symmetry is broken. For the absence of Dresselhaus interaction, starting from the applied out-of-plane B corresponding to Zeeman splitting energy 0 - 0.5 times the Rashba hopping energy tR, the breaking process is clearly seen. The influence of the Rashba interaction on the magnetization of the 2DEG is studied herein. For coexisted Rashba tR and Dresselhaus tD spin-orbit couplings in the absence of B, interchanging tR and tD reverses the entire accumulation pattern.Comment: 3 pages, 2 figures, appears in the proceedings of 10th MMM/INTERMAG conferenc