Maximum intrinsic spin-Hall conductivity in two-dimensional systems with k-linear spin-orbit interaction

We analytically calculate the intrinsic spin-Hall conductivity (ISHC) ($\sigma^z_{xy}$ and $\sigma^z_{yx}$) in a clean, two-dimensional system with generic k-linear spin-orbit interaction. The coefficients of the product of the momentum and spin components form a spin-orbit matrix $\widetilde{\beta}$. We find that the determinant of the spin-orbit matrix \detbeta describes the effective coupling of the spin $s_z$ and orbital motion $L_z$. The decoupling of spin and orbital motion results in a sign change of the ISHC and the band-overlapping phenomenon. Furthermore, we show that the ISHC is in general unsymmetrical ($\sigma^z_{xy}\neq-\sigma^z_{yx}$), and it is governed by the asymmetric response function \Deltabeta, which is the difference in band-splitting along two directions: those of the applied electric field and the spin-Hall current. The obtained non-vanishing asymmetric response function also implies that the ISHC can be larger than $e/8\pi$, but has an upper bound value of $e/4\pi$. We will that the unsymmetrical properties of the ISHC can also be deduced from the manifestation of the Berry curvature at the nearly degenerate area. On the other hand, by investigating the equilibrium spin current, we find that \detbeta determines the field strength of the SU(2) non-Abelian gauge field.Comment: 13 pages, 6 figure

Conserved Spin and Orbital Angular Momentum Hall Current in a Two-Dimensional Electron System with Rashba and Dresselhaus Spin-orbit Coupling

We study theoretically the spin and orbital angular momentum (OAM) Hall effect in a high mobility two-dimensional electron system with Rashba and Dresselhuas spin-orbit coupling by introducing both the spin and OAM torque corrections, respectively, to the spin and OAM currents. We find that when both bands are occupied, the spin Hall conductivity is still a constant (i.e., independent of the carrier density) which, however, has an opposite sign to the previous value. The spin Hall conductivity in general would not be cancelled by the OAM Hall conductivity. The OAM Hall conductivity is also independent of the carrier density but depends on the strength ratio of the Rashba to Dresselhaus spin-orbit coupling, suggesting that one can manipulate the total Hall current through tuning the Rashba coupling by a gate voltage. We note that in a pure Rashba system, though the spin Hall conductivity is exactly cancelled by the OAM Hall conductivity due to the angular momentum conservation, the spin Hall effect could still manifest itself as nonzero magnetization Hall current and finite magnetization at the sample edges because the magnetic dipole moment associated with the spin of an electron is twice as large as that of the OAM. We also evaluate the electric field-induced OAM and discuss the origin of the OAM Hall current. Finally, we find that the spin and OAM Hall conductivities are closely related to the Berry vector (or gauge) potential.Comment: latest revised version; Accepted for publication in Physical Review

Geometry of Discrete Quantum Computing

Conventional quantum computing entails a geometry based on the description of an n-qubit state using 2^{n} infinite precision complex numbers denoting a vector in a Hilbert space. Such numbers are in general uncomputable using any real-world resources, and, if we have the idea of physical law as some kind of computational algorithm of the universe, we would be compelled to alter our descriptions of physics to be consistent with computable numbers. Our purpose here is to examine the geometric implications of using finite fields Fp and finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as the basis for computations in a theory of discrete quantum computing, which would therefore become a computable theory. Because the states of a discrete n-qubit system are in principle enumerable, we are able to determine the proportions of entangled and unentangled states. In particular, we extend the Hopf fibration that defines the irreducible state space of conventional continuous n-qubit theories (which is the complex projective space CP{2^{n}-1}) to an analogous discrete geometry in which the Hopf circle for any n is found to be a discrete set of p+1 points. The tally of unit-length n-qubit states is given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the discrete analog of the complex projective space, which has p^{2^{n}-1} (p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of entanglement, the purity, we explore the entanglement features of discrete quantum states and find that the n-qubit states based on the complexified field Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally entangled states with purity zero.Comment: 24 page

Andreev bound states and π\pi -junction transition in a superconductor / quantum-dot / superconductor system

We study Andreev bound states and $\pi$-junction transition in a superconductor / quantum-dot / superconductor (S-QD-S) system by Green function method. We derive an equation to describe the Andreev bound states in S-QD-S system, and provide a unified understanding of the $\pi$-junction transition caused by three different mechanisms: (1) {\it Zeeman splitting.} For QD with two spin levels $E_{\uparrow}$ and $E_{\downarrow}$, we find that the surface of the Josephson current $I(\phi =\frac \pi 2)$ vs the configuration of $(E_{\uparrow},E_{\downarrow})$ exhibits interesting profile: a sharp peak around $E_{\uparrow}=E_{\downarrow}=0$; a positive ridge in the region of $E_{\uparrow}\cdot E_{\downarrow}>0$; and a {\em % negative}, flat, shallow plain in the region of $E_{\uparrow}\cdot E_{\downarrow}<0$. (2){\it \ Intra-dot interaction.} We deal with the intra-dot Coulomb interaction by Hartree-Fock approximation, and find that the system behaves as a $\pi$-junction when QD becomes a magnetic dot due to the interaction. The conditions for $\pi$-junction transition are also discussed. (3) {\it \ Non-equilibrium distribution.} We replace the Fermi distribution $f(\omega)$ by a non-equilibrium one $\frac 12[ f(\omega -V_c)+f(\omega +V_c)]$, and allow Zeeman splitting in QD where $$ The curves of $I(\phi =\frac \pi 2)$ vs $$ show the novel effect of interplay of non-equilibrium distribution with magnetization in QD.Comment: 18 pages, 8 figures, Late

Analytic Study for the String Theory Landscapes via Matrix Models

We demonstrate a first-principle analysis of the string theory landscapes in the framework of non-critical string/matrix models. In particular, we discuss non-perturbative instability, decay rate and the true vacuum of perturbative string theories. As a simple example, we argue that the perturbative string vacuum of pure gravity is stable; but that of Yang-Lee edge singularity is inescapably a false vacuum. Surprisingly, most of perturbative minimal string vacua are unstable, and their true vacuum mostly does not suffer from non-perturbative ambiguity. Importantly, we observe that the instability of these tachyon-less closed string theories is caused by ghost D-instantons (or ghost ZZ-branes), the existence of which is determined only by non-perturbative completion of string theory.Comment: v1: 5 pages, 2 figures; v2: references and footnote added; v3: 7 pages, 4 figures, organization changed, explanations expanded, references added, reconstruction program from arbitrary spectral curves shown explicitl

Parametric modeling of cellular state transitions as measured with flow cytometry

<p>Abstract</p> <p>Background</p> <p>Gradual or sudden transitions among different states as exhibited by cell populations in a biological sample under particular conditions or stimuli can be detected and profiled by flow cytometric time course data. Often such temporal profiles contain features due to transient states that present unique modeling challenges. These could range from asymmetric non-Gaussian distributions to outliers and tail subpopulations, which need to be modeled with precision and rigor.</p> <p>Results</p> <p>To ensure precision and rigor, we propose a parametric modeling framework StateProfiler based on finite mixtures of skew <it>t</it>-Normal distributions that are robust against non-Gaussian features caused by asymmetry and outliers in data. Further, we present in StateProfiler a new greedy EM algorithm for fast and optimal model selection. The parsimonious approach of our greedy algorithm allows us to detect the genuine dynamic variation in the key features as and when they appear in time course data. We also present a procedure to construct a well-fitted profile by merging any redundant model components in a way that minimizes change in entropy of the resulting model. This allows precise profiling of unusually shaped distributions and less well-separated features that may appear due to cellular heterogeneity even within clonal populations.</p> <p>Conclusions</p> <p>By modeling flow cytometric data measured over time course and marker space with StateProfiler, specific parametric characteristics of cellular states can be identified. The parameters are then tested statistically for learning global and local patterns of spatio-temporal change. We applied StateProfiler to identify the temporal features of yeast cell cycle progression based on knockout of S-phase triggering cyclins Clb5 and Clb6, and then compared the S-phase delay phenotypes due to differential regulation of the two cyclins. We also used StateProfiler to construct the temporal profile of clonal divergence underlying lineage selection in mammalian hematopoietic progenitor cells.</p

A note on Zolotarev optimal rational approximation for the overlap Dirac operator

We discuss the salient features of Zolotarev optimal rational approximation for the inverse square root function, in particular, for its applications in lattice QCD with overlap Dirac quark. The theoretical error bound for the matrix-vector multiplication $H_w (H_w^2)^{-1/2}Y$ is derived. We check that the error bound is always satisfied amply, for any QCD gauge configurations we have tested. An empirical formula for the error bound is determined, together with its numerical values (by evaluating elliptic functions) listed in Table 2 as well as plotted in Figure 3. Our results suggest that with Zolotarev approximation to $(H_w^2)^{-1/2}$, one can practically preserve the exact chiral symmetry of the overlap Dirac operator to very high precision, for any gauge configurations on a finite lattice.Comment: 23 pages, 5 eps figures, v2:minor clarifications, and references added, to appear in Phys. Rev.