Two-electron entanglement in elliptically deformed quantum dots

Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.     

Fractional electrical model for modified bismuth oxide

Modified bismuth oxide (Bi₂O₃) is of great importance to fuel cells and oxide varistors. The electrical parameters of Bi₂O₃ vary with its modifying components as well as with its aging temperature. This paper presents an analysis of impedance test results carried out to find an equivalent electric model and the relationship between the model's elements to various additives used to modify Bi₂O₃ and to changes in aging temperature. The proposed model was tested via computer simulation and the model parameters correlated to individual modifiers.     

Growth, thermal stability and structure of ultrathin Zn-layers on Pd(1 1 1)

Low-energy ion scattering with monolayer sensitivity was applied to investigate ultrathin films of zinc on Pd(1?1?1). Uptake curves taken at 150?K indicate the simultaneous growth of multilayers with negligible interlayer transport. Annealing experiments for two-monolayer films reveal a rapid decrease in the zinc content on the surface layer at temperatures above 300?K, forming a metastable state with a Pd:Zn surface ratio of approx. 1:1 in the temperature region between 400 and 550?K. This state is most easily explained as a slightly buckled p(2?×?1)-PdZn surface alloy, with Zn atoms located approx. 0.25?? above their Pd counterparts.     

An $$H^1$$-Galerkin mixed finite element method for time fractional reaction–diffusion equation

In this article, an \(H^1\)-Galerkin mixed finite element (MFE) method for solving time fractional reaction–diffusion equation is presented. The optimal time convergence order \(O(\varDelta t^{2-\alpha })\) and the optimal spatial rate of convergence in \(H^1\) and \(L^2\)-norms for variable \(u\) and its gradient \(\sigma \) are derived. Moreover, some numerical results are shown to support our theoretical analysis.     

Ockham’s Calculus of Strict Implication

In his main work Summa Logicae written around 1323, William of Ockham developed a system of propositional modal logic which contains almost all theorems of a modern calculus of strict implication. This calculus is formally reconstructed here with the help of modern symbols for the operators of conjunction, disjunction, implication, negation, possibility, and necessity.     

Landauer–Büttiker and Thouless Conductance

In the independent electron approximation, the average (energy/charge/entropy) current flowing through a finite sample \({\mathcal{S}}\) connected to two electronic reservoirs can be computed by scattering theoretic arguments which lead to the famous Landauer–Büttiker formula. Another well known formula has been proposed by Thouless on the basis of a scaling argument. The Thouless formula relates the conductance of the sample to the width of the spectral bands of the infinite crystal obtained by periodic juxtaposition of \({\mathcal{S}}\). In this spirit, we define Landauer–Büttiker crystalline currents by extending the Landauer–Büttiker formula to a setup where the sample \({\mathcal{S}}\) is replaced by a periodic structure whose unit cell is \({\mathcal{S}}\). We argue that these crystalline currents are closely related to the Thouless currents. For example, the crystalline heat current is bounded above by the Thouless heat current, and this bound saturates iff the coupling between the reservoirs and the sample is reflectionless. Our analysis leads to a rigorous derivation of the Thouless formula from the first principles of quantum statistical mechanics.     

<Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript>-Classification of Gapped Parent Hamiltonians of Quantum Spin Chains

We consider the C ¹-classification of gapped Hamiltonians introduced in Fannes et al. (Commun Math Phys 144:443–490, 1992) and Nachtergaele (Commun Math Phys 175:565–606, 1996) as parent Hamiltonians of translation invariant finitely correlated states. Within this family, we show that the number of edge modes, which is equal at the left and right edge, is the complete invariant. The construction proves that translation invariance of the ‘bulk’ ground state does not need to be broken to establish C ¹-equivalence, namely that the spin chain does not need to be blocked.     

Distribution function estimates by Wasserstein metric and Bernstein approximation for C-1 functions

The aim of the paper is to estimate the density functions or distribution functions measured by Wasserstein metric, a typical kind of statistical distances, which is usually required in the statistical learningBased on the classical Bernstein approximation, a scheme is presented.To get the error estimates of the scheme, the problem turns to estimating the L1 norm of the Bernstein approximation for monotone C-1functions, which was rarely discussed in the classical approximation theoryFinally, we get a probability estimate by the statistical distance.     

Symplectic invariants for curves and integrable systems in similarity symplectic geometry

In this paper, similarity symplectic geometry for curves is proposed and studied. Explicit expressions of the symplectic invariants, Frenet frame and Frenet formulae for curves in similarity symplectic geometry are obtained by using the equivariant moving frame method. The relationships between the Euclidean symplectic invariants, Frenet frame, Frenet formulae and the similarity symplectic invariants, Frenet frame, Frenet formulae for curves are established. Invariant curve flows in four-dimensional similarity symplectic geometry are also studied. It is shown that certain intrinsic invariant curve flows in four-dimensional similarity symplectic geometry are related to the integrable Burgers and matrix Burgers equations.