Twisted Demazure modules, fusion product decomposition and twisted Q--systems

In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the twisted current algebras. These modules are indexed by an $|R^+|$-tuple of partitions \bxi=(\xi^{\alpha})_{\alpha\in R^+} satisfying a natural compatibility condition. We give three equivalent presentations of these modules and show that for a particular choice of \bxi these modules become isomorphic to Demazure modules in various levels for the twisted affine algebras. As a consequence we see that the defining relations of twisted Demazure modules can be greatly simplified. Furthermore, we investigate the notion of fusion products for twisted modules, first defined in \cite{FL99} for untwisted modules, and use the simplified presentation to prove a fusion product decomposition of twisted Demazure modules. As a consequence we prove that twisted Demazure modules can be obtained by taking the associated graded modules of (untwisted) Demazure modules for simply-laced affine algebras. Furthermore we give a semi-infinite fusion product construction for the irreducible representations of twisted affine algebras. Finally, we prove that the twisted $Q$-sytem defined in \cite{HKOTT02} extends to a non-canonical short exact sequence of fusion products of twisted Demazure modules

Borel-de Siebenthal theory for affine reflection systems

We develop a Borel-de Siebenthal theory for affine reflection systems by classifying their maximal closed subroot systems. Affine reflection systems (introduced by Loos and Neher) provide a unifying framework for root systems of finite-dimensional semi-simple Lie algebras, affine and toroidal Lie algebras, and extended affine Lie algebras. In the special case of nullity $k$ toroidal Lie algebras, we obtain a one-to-one correspondence between maximal closed subroot systems with full gradient and triples $(q,(b_i),H)$, where $q$ is a prime number, $(b_i)$ is a $n$-tuple of integers in the interval $[0,q-1]$ and $H$ is a $(k\times k)$ Hermite normal form matrix with determinant $q$. This generalizes the $k=1$ result of Dyer and Lehrer in the setting of affine Lie algebras

Measures and dynamics of entangled states

We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular emphasis is given to the derivation of reliable estimates which allow for an efficient evaluation of a specific entanglement measure, concurrence, for further implementation in the monitoring of the time evolution of multipartite entanglement under incoherent environment coupling. The flexibility of the technical machinery established here is illustrated by its implementation for different, realistic experimental scenarios.Comment: Physics Reports, in pres

Superconducting properties of MgB2 thin films prepared on flexible plastic substrates

Superconducting MgB2 thin films were prepared on 50-micrometer-thick, flexible polyamide Kapton-E foils by vacuum co-deposition of Mg and B precursors with nominal thickness of about 100 nm and a special ex-situ rapid annealing process in an Ar or vacuum atmosphere. In the optimal annealing process, the Mg-B films were heated to approximately 600 C, but at the same time, the backside of the structures was attached to a water-cooled radiator to avoid overheating of the plastic substrate. The resulting MgB2 films were amorphous with the onset of the superconducting transition at T_(c,on) about 33 K and the transition width of approximately 3 K. The critical current density was > 7x10^5 A/cm^2 at 4.2 K, and its temperature dependence indicated a granular film composition with a network of intergranular weak links. The films could be deposited on large-area foils (up to 400 cm^2) and, after processing, cut into any shapes (e.g., stripes) with scissors or bent multiple times, without any observed degradation of their superconducting properties.Comment: 3 figure

The Global and Local in Phillips Curve\ud

The debate over the Phillips Curve - as the relation between level of unemployment rate and inflation rate - in historical economics is shortly reviewed. By using the analysis in the Extreme Value Theory, i.e.: the rank order statistics the unemployment and inflation data over countries from various regions are observed. The calculations brought us to conjecture that there exists the general pattern that could lead from the relation between unemployment and inflation rate. However, the difference patterns as observed in the Phillips Curve might could be reflected from the range of values of the local variables of the incorporated model.\u

Exactly solvable approximating models for Rabi Hamiltonian dynamics

The interaction between an atom and a one mode external driving field is an ubiquitous problem in many branches of physics and is often modeled using the Rabi Hamiltonian. In this paper we present a series of analytically solvable Hamiltonians that approximate the Rabi Hamiltonian and compare our results to the Jaynes-Cummings model which neglects the so-called counter-rotating term in the Rabi Hamiltonian. Through a unitary transformation that diagonlizes the Jaynes-Cummings model, we transform the counter-rotating term into separate terms representing several different physical processes. By keeping only certain terms, we can achieve an excellent approximation to the exact dynamics within specified parameter ranges

Pengaruh Kecepatan Putar terhadap Hasil Coran pada Metode Pengecoran Sentrifugal dalam Pembuatan Produk Pisau Pakan Ternak dengan Material Ni-Hard1

Animal feed knife is a tool that serves to cut and chop animal feed consisting of grass as the main ingredient with additives such as bran, herbs, centrate, cassava, tofu pulp and others. Therefore, as a cutting tool must have the properties of friction resistance, impact resistance, and have good sharpness, so that the material chosen is Ni-Hard 1. The use of centrifugal casting method was chosen because it has the advantage of being able to make castings with relatively thin thickness this is due to the influence of the centrifugal force on the distribution of metal liquids throughout the cavity in the mold. Case study in this study is the use of centrifugal casting methods as an alternative to gravity casting methods to overcome defects of misruns. This research was conducted to investigate the effect of speed on the formation of castings products. The method that was carried out began with a literature study on centrifugal casting, and continued by determining the material, the temperature of the cast is in the range 1250ºC - 1300ºC, and the type of mold. The next step is to do work drawings, pattern making, mold making, casting processes, fettling processes, and analysis. With variations in speed of 200 rpm, 300 rpm and 400 rpm, it can be seen the optimal speed for making this product. The results of this study obtained optimal speed at a speed of 300 rpm to make good quality of animal feed knife products

Identities of the multi-variate independence polynomials from heaps theory

We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially commutative algebras we show how the multi-variate version of Godsil type identity as well as the fundamental identity can be obtained from weight preserving bijections. Finally, we obtain a new multi-variate identity involving connected bipartite subgraphs similar to the Christoffel-Darboux type identities obtained by Bencs

Ground state potential energy surfaces and bound states of M-He dimers (M=Cu,Ag,Au): A theoretical investigation

We present an ab initio investigation on the ground state interaction potentials [potential energy surface (PES)] between helium and the group 11 metal atoms: copper, silver, and gold. To the best of our knowledge, there are no previous theoretical PESs proposed for Cu-He and Au-He, and a single one for Ag-He [Z. J. Jakubek and M. Takami, Chem. Phys. Lett. 265, 653 (1997)], computed about 10 years ago at MP2 level and significantly improved by our study. To reach a high degree of accuracy in the determination of the three M-He potentials (M=Cu,Ag,Au), we performed extensive series of test computations to establish the appropriate basis set, the theoretical method, and the computational scheme for these systems. For each M-He dimer we computed the PES at the CCSD(T) level of theory, starting from the reference unrestricted Hartree-Fock wave function. We described the inner shells with relativistic small core pseudopotentials, and we adopted high quality basis sets for the valence electrons. We also performed CCSDT computations in a limited set of M-He internuclear distances, adopting a medium-sized basis set, such as to define for each dimer a CCSD(T) to CCSDT correction term and to improve further the quality of the CCSD(T) interaction potentials. The Cu-He complex has minimum interaction energy (E(min)) of -28.4 mu hartree at the internuclear distance of 4.59 A (R(min)), and the short-range repulsive wall starts at 4.04 A (R(E=0)). Quite interestingly, the PES of Ag-He is more attractive (E(min)=-33.8 mu hartree) but presents nearly the same R(min) and R(E=0) values, 4.60 and 4.04 A, respectively. The interaction potential for Au-He is markedly deeper and shifted at shorter distances as compared to the lighter complexes, with E(min)=-69.6 mu hartree, R(min)=4.09 A and R(E=0)=3.60 A. As a first insight in the structure of M-He(n) aggregates, we determined the rovibrational structure of the three M-He dimers. The Cu-He and Ag-He potentials support just few rotational excitations, while the Au-He PES admits also a bound vibrational excitation