Quantum phase transition in skewed ladders: an entanglement entropy and fidelity study

Entanglement entropy (EE) of a state is a measure of correlation or entanglement between two parts of a composite system and it may show appreciable change when the ground state (GS) undergoes a qualitative change in a quantum phase transition (QPT). Therefore, the EE has been extensively used to characterise the QPT in various correlated Hamiltonians. Similarly fidelity also shows sharp changes at a QPT. We characterized the QPT of frustrated antiferromagnetic Heisenberg spin-1/2 systems on 3/4, 3/5 and 5/7 skewed ladders using the EE and fidelity analysis. It is noted that all the non-magnetic to magnetic QPT boundary in these systems can be accurately determined using the EE and fidelity, and the EE exhibits a discontinuous change, whereas fidelity shows a sharp dip at the transition points. It is also noted that in case of the degenerate GS, the unsymmetrized calculations show wild fluctuations in the EE and fidelity even without actual phase transition, however, this problem is resolved by calculating the EE and the fidelity in the lowest energy state of the symmetry subspaces, to which the degenerate states belong.Comment: 9 pages, 10 figure

Enhanced dynamics of active Brownian particles in periodic obstacle arrays and corrugated channels

We study the motion of an active Brownian particle (ABP) using overdamped Langevin dynamics on a two-dimensional substrate with periodic array of obstacles and in a quasi-one-dimensional corrugated channel comprised of periodically arrayed obstacles. The periodic arrangement of the obstacles enhances the persistent motion of the ABP in comparison to its motion in the free space. Persistent motion increases with the activity of the ABP. We note that the periodic arrangement induces directionality in ABP motion at late time, and it increases with the size of the obstacles. We also note that the ABP exhibits a super-diffusive dynamics in the corrugated channel. The transport property is independent of the shape of the channel; rather it depends on the packing fraction of the obstacles in the system. However, the ABP shows the usual diffusive dynamics in the quasi-one-dimensional channel with flat boundary

Probing defects in chemically synthesized ZnO nanostrucures by Positron Annihilation and Photoluminescence Spectroscopy

The present article describes the size induced changes in the structural arrangement of intrinsic defects present in chemically synthesized ZnO nanoparticles of various sizes. Routine X-ray diffraction (XRD) and Transmission Electron Microscopy (TEM) have been performed to determine the shapes and sizes of the nanocrystalline ZnO samples. Detailed studies using positron annihilation spectroscopy reveals the presence of zinc vacancy. Whereas analysis of photoluminescence results predict the signature of charged oxygen vacancies. The size induced changes in positron parameters as well as the photoluminescence properties, has shown contrasting or non-monotonous trends as size varies from 4 nm to 85 nm. Small spherical particles below a critical size (~ 23 nm) receive more positive surface charge due to the higher occupancy of the doubly charge oxygen vacancy as compared to the bigger nanostructures where singly charged oxygen vacancy predominates. This electronic alteration has been seen to trigger yet another interesting phenomenon, described as positron confinement inside nanoparticles. Finally, based on all the results, a model of the structural arrangement of the intrinsic defects in the present samples has been reconciled

Initial‐valued first‐order fuzzy differential equation in Bi‐level inventory model with fuzzy demand

In the present paper, two methods for the solution of an initial valued first ordered fuzzy differential equation are presented and applied in a fuzzy EOQ model. The constructed model is a bi‐level inventory problem involving wholesaler‐retailers‐customers. The wholesaler buys and sells the item instantaneously to several retailers. In the next level, the retailers sell the units to customers with a time dependent imprecise demand, which introduce the fuzzy nature in the differential equation. The selling price of the item is a step‐wise time dependent decreasing function. The fuzzy objectives are transformed into crisp one following fuzzy extension principle and centroid formula. The model is illustrated through Interactive Fuzzy Decision Making (IFDM) and Multi Objective Genetic Algorithm (MOGA) and the results from two methods are compared. First Published Online: 14 Oct 201