SU(4) Fermi liquid state and spin filtering in a double quantum dot system

We study a symmetrical double quantum dot (DD) system with strong capacitive interdot coupling using renormalization group methods. The dots are attached to separate leads, and there can be a weak tunneling between them. In the regime where there is a single electron on the DD the low-energy behavior is characterized by an SU(4)-symmetric Fermi liquid theory with entangled spin and charge Kondo correlations and a phase shift pi/4. Application of an external magnetic field gives rise to a large magnetoconductance and a crossover to a purely charge Kondo state in the charge sector with SU(2) symmetry. In a four-lead setup we find perfectly spin-polarized transmission.     

Resonance splitting in gyrotropic ring resonators

We present the theoretical concept of an optical isolator based on resonance splitting in a silicon ring resonator covered with a magneto-optical polymer cladding. For this task, a perturbation method is derived for the modes in the cylindrical coordinate system. A polymer magneto-optical cladding causing a 0.01 amplitude of the off-diagonal element of the dielectric tensor is assumed. It is shown that the derived resonance splitting of the clockwise and counterclockwise modes increases for smaller ring radii. For the ring with a radius of approximately 1.5μm, a 29GHz splitting is demonstrated. An integrated optical isolator with a 10μm geometrical footprint is proposed based on a critically coupled ring resonator.     

Bounding the distance among longest paths in a connected graph

It is easy to see that in a connected graph any $2$ longest paths have a vertex in common. For $k\ge 7$, Skupień in 1966 obtained a connected graph in which some $k$ longest paths have no common vertex, but every $k?1$ longest paths have a common vertex. It is not known whether every $3$ longest paths in a connected graph have a common vertex and similarly for 4, 5, and $6$ longest path. Fujita et al. in 2015 give an upper bound on distance among $3$ longest paths in a connected graph. In this paper we give a similar upper bound on distance between $4$ longest paths and also for $k$ longest paths, in general.     

Two-Sample T 3 Plot: A Graphical Comparison of Two Distributions

Abstract

Consider two independent random variables x and y with means and standard deviations μ _x ,μ _y ,σ _x , and σ _y , respectively. Let F _x (t) = P[(x - μ, _x )/σ _x ≤ t] and F _y (t) = P[(y - μ _y )/σ _y ≤ t]. In this article we address the problem of testing the null hypothesis H ₀ : F _x ≡ F _y , against the alternative H ₁ : F _x ≡ F _y . A graphical tool called T ₃ plot for checking normality of independently and identically distributed univariate data was proposed in an earlier article by Ghosh. In the present article we develop a two-sample T ₃ plot where the basic statistic is the normalized difference between the T ₃ functions for the two samples. Significant departure of this difference function from the horizontal zero line is indicative of evidence against the null hypothesis. In contrast to the one-sample problem, the common distribution function under the null hypothesis is not specified in the two-sample case. Bootstrap is used to construct the acceptance region under H ₀, for the two-sample T ₃ plot.     

Numerical solution of the two-dimensional Poincaré equation

This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers. Inspired by the hyperbolicity of the equation we propose a discretisation particularly suited for this problem, which results in matrices whose size varies linearly with the number of grid points along the coordinate axes. Exact solutions are obtained, defined on a perturbed boundary. Furthermore, the problem is seen to be ill-posed and there is need for a regularisation scheme, which we base on a minimal-energy approach.     

Reduced order fully coupled structural–acoustic analysis via implicit moment matching

A reduced order model is developed for low frequency, undamped, fully coupled structural–acoustic analysis of interior cavities backed by flexible structural systems. The reduced order model is obtained by applying a projection of the coupled system matrices, from a higher dimensional to a lower dimensional subspace, whilst preserving essential properties of the coupled system. The basis vectors for projection are computed efficiently using the Arnoldi algorithm, which generates an orthogonal basis for the Krylov Subspace containing moments of the original system. The key idea of constructing a reduced order model via Krylov Subspaces is to remove the uncontrollable, unobservable and weakly controllable, observable parts without affecting the transfer function of the coupled system. Three computational test cases are analyzed, and the computational gains and the accuracy compared with the direct inversion method in ANSYS.     

Noisy scale-free networks

The impact of observational noise on the analysis of scale-free networks is studied. Various noise sources are modeled as random link removal, random link exchange and random link addition. Emphasis is on the resulting modifications for the node-degree distribution and for a functional ranking based on betweenness centrality. The implications for estimated gene-expressed networks for childhood acute lymphoblastic leukemia are discussed.     

Spin-adapted wave functions of the serber type and time reversal

A procedure is proposed for generating Serber-type spin eigenfunctions withM _s = 0. The procedure uses the time-reversal invariance of these functions to increase the efficiency and to reduce the storage requirements. Simplifications in calculating the matrix elements of an observable operator which follow from the use of the time-reversal symmetry are briefly discussed.     

Ring Opening of Pymisyl‐Protected Aziridines with Organocuprates

The pyrimidine‐2‐sulfonyl (pymisyl) group is introduced as a new protecting group that can be used to activate aziridines towards ring opening. It is readily introduced and removed under mild conditions. Regioselective ring opening of pymisyl‐protected 2‐methyl‐aziridine with organocuprates gives the corresponding sulfonamides in high yields, and the pymisyl group can subsequently be removed upon treatment with a thiolate. The versatility of this new nitrogen protecting group is illustrated with a new synthesis of Selegiline, a monoamine oxidase‐B inhibitor marketed for the treatment of Parkinson’s disease.