Numerical simulations of a ballistic spin interferometer with the Rashba spin-orbital interaction

We numerically investigate the transport behavior of a quasi one-dimension (1D) square loop device containing the Rashba spin-orbital interaction in the presence of a magnetic flux. The conductance versus the magnetic field shows the Al'tshuler-Aronov-Spivak (AAS) and Aharonov-Bohm (AB) oscillations. We focus on the oscillatory amplitudes, and find that both of them are strongly dependent on the spin precession angle (i.e. the strength of the spin-orbit interaction) and exhibit no-periodic oscillations, which are well in agreement with a recent experiment by Koga et al. [cond-mat/0504743(unpublished)]. However, our numerical results for the ideal 1D square loop device for the node positions of the amplitudes of the AB and AAS oscillations are found to be of some discrepancies comparing with quasi-1D square loop with a finite width. In the presence of disorder and taking the disorder ensemble average, the AB oscillation in the conductance will disappear, while the time-reversal symmetric AAS oscillation still remains. Furthermore, the node positions of the AAS oscillatory amplitude remains the same.Comment: 6 pages, 7 figure

Residue theorem and summing over Kaluza-Klein excitations

Applying the equations of motion together with corresponding boundary conditions of bulk profiles at infrared and ultraviolet branes, we verify some lemmas on the eigenvalues of Kaluze-Klein modes in framework of warped extra dimension with the custodial symmetry $SU(3)_c\times SU(2)_L\times SU(2)_R\times U(1)_X\times P_{LR}$. Using the lemmas and performing properly analytic extensions of bulk profiles, we present the sufficient condition for a convergent series of Kaluze-Klein excitations and sum over the series through the residue theorem. The method can also be applied to sum over the infinite series of Kaluze-Klein excitations in unified extra dimension. Additional, we analyze the possible connection between the propagators in five dimensional full theory and the product of bulk profiles with corresponding propagators of exciting Kaluze-Klein modes in four dimensional effective theory, and recover some relations presented in literature for warped and unified extra dimensions respectively. As an example, we demonstrate that the corrections from neutral Higgs to the Wilson coefficients of relevant operators for $B\rightarrow X_s\gamma$ contain the suppression factor $m_b^3m_s/m_{_{\rm w}}^4$ comparing with that from other sectors, thus can be neglected safely.Comment: 44 pages, no figur

Applications of BGP-reflection functors: isomorphisms of cluster algebras

Given a symmetrizable generalized Cartan matrix $A$, for any index $k$, one can define an automorphism associated with $A,$ of the field $\mathbf{Q}(u_1, >..., u_n)$ of rational functions of $n$ independent indeterminates $u_1,..., u_n.$ It is an isomorphism between two cluster algebras associated to the matrix $A$ (see section 4 for precise meaning). When $A$ is of finite type, these isomorphisms behave nicely, they are compatible with the BGP-reflection functors of cluster categories defined in [Z1, Z2] if we identify the indecomposable objects in the categories with cluster variables of the corresponding cluster algebras, and they are also compatible with the "truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of preprojective or preinjective modules of hereditary algebras by Dlab-Ringel [DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we construct infinitely many cluster variables for cluster algebras of infinite type and all cluster variables for finite types.Comment: revised versio

Efficient Comb Elliptic Curve Multiplication Methods Resistant to Power Analysis

Elliptic Curve Cryptography (ECC) has found wide applications in smart cards and embedded systems. Point multiplication plays a critical role in ECC. Many efficient point multiplication methods have been proposed. One of them is the comb method which is much more efficient than other methods if precomputation points are calculated in advance or elsewhere. Unfortunately, Many efficient point multiplication methods including the comb method are vulnerable to power-analysis attacks. Various algorithms to make elliptic curve point multiplication secure to power-analysis attacks have been proposed recently, such as the double-and-add-always method, Möller\u27s window method, Okeya et al.\u27s odd-only window method, and Hedabou et al.\u27s comb method. In this paper, we first present a novel comb recoding algorithm which converts an integer to a sequence of signed, odd-only comb bit-columns. Using this recoding algorithm, we then present several comb methods, both Simple Power Analysis (SPA)-nonresistant and SPA-resistant, for point multiplication. These comb methods are more efficient than the original SPA-nonresistant comb method and Hedabou et al.\u27s SPA-resistant comb method. Our comb methods inherit the advantage of a comb method, running much faster than Möller\u27s window method and Okeya et al.\u27s odd-only window method, as well as other window methods such as the efficient signed $m$-ary window method, if only the evaluation phase is taken into account. Combined with randomization projective coordinates or other randomization techniques and certain precautions in selecting elliptic curves and parameters, our SPA-resistant comb methods are resistant to all power-analysis attacks

Numerical simulation of the massive scalar field evolution in the Reissner-Nordstr\"{o}m black hole background

We studied the massive scalar wave propagation in the background of Reissner-Nordstr\"{o}m black hole by using numerical simulations. We learned that the value $Mm$ plays an important role in determining the properties of the relaxation of the perturbation. For $Mm << 1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $Mm >> 1$, the dependence of the relaxation on the black hole parameters appears. The bigger mass of the black hole, the faster the perturbation decays. The difference of the relaxation process caused by the black hole charge $Q$ has also been exhibited.Comment: Accepted for publication in Phys. Rev.