Smooth polytopes with negative Ehrhart coefficients

We present examples of smooth lattice polytopes in dimensions 3 and higher where each coefficient of their Ehrhart polynomials that can potentially be negative is indeed negative. This answers a question by Bruns. We also discuss Berline-Vergne valuations as a useful tool in proving Ehrhart positivity results.Comment: 15 pages, 1 figure, 1 table, accepted by Journal of Combinatorial Theory Ser.

Variational matrix product state approach to quantum impurity models

We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows improvements over Wilson's NRG for quantum impurity models, as we illustrate for the one-channel Kondo model. Moreover, we use a variational method for evaluating Green's functions. The proposed method is more flexible in its description of spectral properties at finite frequencies, opening the way to time-dependent, out-of-equilibrium impurity problems. It also substantially improves computational efficiency for one-channel impurity problems, suggesting potentially \emph{linear} scaling of complexity for $n$-channel problems.Comment: revised version with application to Kondo model at large magnetic field (5 pages, 2 figures

Thermodynamics and kinetics of the Mg65Cu25Y10 bulk metallic glass forming liquid

The thermodynamics and kinetics of the bulk metallic glass forming Mg65Cu25Y10 liquid were investigated using differential scanning calorimetry and three-point beam bending. The experiments lead to the determination of the thermodynamic functions as well as the viscosity of the supercooled liquid. The viscosity shows a temperature dependence, which is consistent with that of a strong glass similar to Zr–Ti–Cu–Ni–Be bulk metallic glasses or sodium silicate glasses. This contrasts with more fragile conventional metallic glass formers or pure metals. The relatively weak temperature dependence of the thermodynamic functions of the supercooled liquid is related to these sluggish kinetics in the supercooled liquid. Entropy, viscosity, and kinetic glass transition are compared in the frameworks of the fragility concept and the Adam–Gibbs theory. Strong liquid behavior retards the formation of crystals kinetically and thermodynamically

Magnetic enhancement of Co0.2_{0.2}Zn0.8_{0.8}Fe2_2O4_4 spinel oxide by mechanical milling

We report the magnetic properties of mechanically milled Co$_{0.2}$Zn$_{0.8}$Fe$_2$O$_4$ spinel oxide. After 24 hours milling of the bulk sample, the XRD spectra show nanostructure with average particle size $\approx$ 20 nm. The as milled sample shows an enhancement in magnetization and ordering temperature compared to the bulk sample. If the as milled sample is annealed at different temperatures for the same duration, recrystallization process occurs and approaches to the bulk structure on increasing the annealing temperatures. The magnetization of the annealed samples first increases and then decreases. At higher annealing temperature ($\sim$ 1000$^{0}$C) the system shows two coexisting magnetic phases {\it i.e.}, spin glass state and ferrimagnetic state, similar to the as prepared bulk sample. The room temperature M\"{o}ssbauer spectra of the as milled sample, annealed at 300$^{0}$C for different durations (upto 575 hours), suggest that the observed change in magnetic behaviour is strongly related with cations redistribution between tetrahedral (A) and octahedral (O) sites in the spinel structure. Apart from the cation redistribution, we suggest that the enhancement of magnetization and ordering temperature is related with the reduction of B site spin canting and increase of strain induced anisotropic energy during mechanical milling.Comment: 14 pages LaTeX, 10 ps figure