Energy-based Structure Prediction for d(Al70Co20Ni10)

We use energy minimization principles to predict the structure of a decagonal quasicrystal - d(AlCoNi) - in the Cobalt-rich phase. Monte Carlo methods are then used to explore configurations while relaxation and molecular dynamics are used to obtain a more realistic structure once a low energy configuration has been found. We find five-fold symmetric decagons 12.8 A in diameter as the characteristic formation of this composition, along with smaller pseudo-five-fold symmetric clusters filling the spaces between the decagons. We use our method to make comparisons with a recent experimental approximant structure model from Sugiyama et al (2002).Comment: 10pp, 2 figure

A practical, unitary simulator for non-Markovian complex processes

Stochastic processes are as ubiquitous throughout the quantitative sciences as they are notorious for being difficult to simulate and predict. In this letter we propose a unitary quantum simulator for discrete-time stochastic processes which requires less internal memory than any classical analogue throughout the simulation. The simulator's internal memory requirements equal those of the best previous quantum models. However, in contrast to previous models it only requires a (small) finite-dimensional Hilbert space. Moreover, since the simulator operates unitarily throughout, it avoids any unnecessary information loss. We provide a stepwise construction for simulators for a large class of stochastic processes hence directly opening the possibility for experimental implementations with current platforms for quantum computation. The results are illustrated for an example process.Comment: 12 pages, 5 figure

A new class of (2+1)(2+1)-d topological superconductor with Z8\mathbb{Z}_8 topological classification

The classification of topological states of matter depends on spatial dimension and symmetry class. For non-interacting topological insulators and superconductors the topological classification is obtained systematically and nontrivial topological insulators are classified by either integer or $Z_2$. The classification of interacting topological states of matter is much more complicated and only special cases are understood. In this paper we study a new class of topological superconductors in $(2+1)$ dimensions which has time-reversal symmetry and a $\mathbb{Z}_2$ spin conservation symmetry. We demonstrate that the superconductors in this class is classified by $\mathbb{Z}_8$ when electron interaction is considered, while the classification is $\mathbb{Z}$ without interaction.Comment: 5 pages main text and 3 pages appendix. 1 figur

Effective medium approximation and the complex optical properties of the inhomogeneous superconductor K_{0.8}Fe_{2-y}Se_2

The in-plane optical properties of the inhomogeneous iron-chalcogenide superconductor K_{0.8}Fe_{2-y}Se_2 with a critical temperature Tc = 31 K have been modeled in the normal state using the Bruggeman effective medium approximation for metallic inclusions in an insulating matrix. The volume fraction for the inclusions is estimated to be ~ 10%; however, they appear to be highly distorted, suggesting a filamentary network of conducting regions joined through weak links. The value for the Drude plasma frequency in the inclusions is much larger than the volume average, which when considered with the reasonably low values for the scattering rate, suggests that the transport in the grains is always metallic. Estimates for the dc conductivity and the superfluid density in the grains places the inclusions on the universal scaling line close to the other homogeneous iron-based superconductors.Comment: 6 pages, 3 figure

Optimal CUR Matrix Decompositions

The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank matrix $U$ such that the matrix $C U R$ approximates the matrix $A,$ that is, $|| A - CUR ||_F^2 \le (1+\epsilon) || A - A_k||_F^2$, where $||.||_F$ denotes the Frobenius norm and $A_k$ is the best $m \times n$ matrix of rank $k$ constructed via the SVD. We present input-sparsity-time and deterministic algorithms for constructing such a CUR decomposition where $c=O(k/\epsilon)$ and $r=O(k/\epsilon)$ and rank$(U) = k$. Up to constant factors, our algorithms are simultaneously optimal in $c, r,$ and rank$(U)$.Comment: small revision in lemma 4.

Joint effect of lattice interaction and potential fluctuation in colossal magnetoresistive manganites

Taking into account both the Jahn-Teller lattice distortion and the on-site electronic potential fluctuations in the orbital-degenerated double-exchange model, in which both the core-spin and the lattice distortion are treated classically, we investigate theoretically the metal-insulator transition (MIT) in manganites by considering the electronic localization effect. An inverse matrix method is developed for calculation in which we use the inverse of the transfer matrix to obtain the localization length. We find that within reasonable range of parameters, both the lattice effect and the potential fluctuation are responsible to the occurrence of the MIT. The role of the orbital configuration is also discussed.Comment: 4 figure