Spin Hall effect of conserved current: Conditions for a nonzero spin Hall current

We study the spin Hall effect taking into account the impurity scattering effect as general as possible with the focus on the definition of the spin current. The conserved bulk spin current (Shi et al. [Phys. Rev. Lett. 96, 076604 (2006)]) satisfying the continuity equation of spin is considered in addition to the conventional one defined by the symmetric product of the spin and velocity operators. Conditions for non-zero spin Hall current are clarified. In particular, it is found that (i) the spin Hall current is non-zero in the Rashba model with a finite-range impurity potential, and (ii) the spin Hall current vanishes in the cubic Rashba model with a $\delta$-function impurity potential.Comment: 5 pages, minor change from the previous versio

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

Effective theoretical approach of Gauge-Higgs unification model and its phenomenological applications

We derive the low energy effective theory of Gauge-Higgs unification (GHU) models in the usual four dimensional framework. We find that the theories are described by only the zero-modes with a particular renormalization condition in which essential informations about GHU models are included. We call this condition ``Gauge-Higgs condition'' in this letter. In other wards, we can describe the low energy theory as the SM with this condition if GHU is a model as the UV completion of the Standard Model. This approach will be a powerful tool to construct realistic models for GHU and to investigate their low energy phenomena.Comment: 18 pages, 2 figures; Two paragraphs discussing the applicable scope of this approach are adde

PHLPP Regulates Hexokinase 2-Dependent Glucose Metabolism in Colon Cancer Cells

Increased glucose metabolism is considered as one of the most important metabolic alterations adapted by cancer cells in order to generate energy as well as high levels of glycolytic intermediates to support rapid proliferation. PH domain leucine-rich repeat protein phosphatase (PHLPP) belongs to a novel family of Ser/Thr protein phosphatases that function as tumor suppressors in various types of human cancer. Here we determined the role of PHLPP in regulating glucose metabolism in colon cancer cells. Knockdown of PHLPP increased the rate of glucose consumption and lactate production, whereas overexpression of PHLPP had the opposite effect. Bioenergetic analysis using Seahorse Extracelluar Flux Analyzer revealed that silencing PHLPP expression induced a glycolytic shift in colon cancer cells. Mechanistically, we found that PHLPP formed a complex with Akt and hexokinase 2 (HK2) in the mitochondrial fraction of colon cancer cells and knockdown of PHLPP enhanced Akt-mediated phosphorylation and mitochondrial localization of HK2. Depletion of HK2 expression or treating cells with Akt and HK2 inhibitors reversed PHLPP loss-induced increase in glycolysis. Furthermore, PHLPP knockdown cells became addicted to glucose as a major energy source in that glucose starvation significantly decreased cancer cell survival. As HK2 is the key enzyme that determines the direction and magnitude of glucose flux, our study identified PHLPP as a novel regulator of glucose metabolism by controlling HK2 activity in colon cancer cells

Immersion Anomaly of Dirac Operator on Surface in R^3

In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in $R^3$ by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using the Ward-Takahashi identity, I showed that the expectation value of the action of the Dirac field is expressed by the Willmore functional and area of the surface.Comment: AMS-Tex Us

On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3

Recently I quantized an elastica with Bernoulli-Euler functional in two-dimensional space using the modified KdV hierarchy. In this article, I will quantize a Willmore surface, or equivalently a surface with the Polyakov extrinsic curvature action, using the modified Novikov-Veselov (MNV) equation. In other words, I show that the density of state of the partition function for the quantized Willmore surface is expressed by volume of a subspace of the moduli of the MNV equation.Comment: AMS-Tex Us

Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions

Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator ${\bold{D}}$, identities of Pfaffians, symmetric functions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu} = -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu \sigma \sigma)/2\sigma^2$. The connection between his theory and the modern soliton theory was also discussed.Comment: AMS-Tex, 12 page

Two Cyclin-Dependent Kinase Pathways Are Essential for Polarized Trafficking of Presynaptic Components

SummaryPolarized trafficking of synaptic proteins to axons and dendrites is crucial to neuronal function. Through forward genetic analysis in C. elegans, we identified a cyclin (CYY-1) and a cyclin-dependent Pctaire kinase (PCT-1) necessary for targeting presynaptic components to the axon. Another cyclin-dependent kinase, CDK-5, and its activator p35, act in parallel to and partially redundantly with the CYY-1/PCT-1 pathway. Synaptic vesicles and active zone proteins mostly mislocalize to dendrites in animals defective for both PCT-1 and CDK-5 pathways. Unlike the kinesin-3 motor, unc-104/Kif1a mutant, cyy-1 cdk-5 double mutants have no reduction in anterogradely moving synaptic vesicle precursors (SVPs) as observed by dynamic imaging. Instead, the number of retrogradely moving SVPs is dramatically increased. Furthermore, this mislocalization defect is suppressed by disrupting the retrograde motor, the cytoplasmic dynein complex. Thus, PCT-1 and CDK-5 pathways direct polarized trafficking of presynaptic components by inhibiting dynein-mediated retrograde transport and setting the balance between anterograde and retrograde motors

Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlev\'e equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.Comment: AMS-Tex Us