Table of contents

At the core of every frustrated system, one can identify the existence of frustrated rings that are usually interpreted in terms of single–particle physics. We check this point of view through a careful analysis of the entanglement entropy of both models that admit an exact single–particle decomposition of their Hilbert space due to integrability and those for which the latter is supposed to hold only as a low energy approximation. In particular, we study generic spin chains made by an odd number of sites with short-range antiferromagnetic interactions and periodic boundary conditions, thus characterized by a weak, i.e. nonextensive, frustration. While for distances of the order of the correlation length the phenomenology of these chains is similar to that of the non-frustrated cases, we find that correlation functions involving a number of sites scaling like the system size follow different rules. We quantify the long-range correlations through the von Neumann entanglement entropy, finding that indeed it violates the area law, while not diverging with the system size. This behavior is well fitted by a universal law that we derive from the conjectured single–particle picture.

In an exact quantum-mechanical framework we show that space-time expectation values of the second-quantized electromagnetic fields in the Coulomb gauge in the presence of a classical conserved source automatically lead to causal and properly retarded ℏ-independent electromagnetic field strengths. The classical ℏ-independent and gauge invariant Maxwell's equations naturally emerge in terms of quantum-mechanical expectation values and are therefore also consistent with the classical special theory of relativity. The fundamental difference between interference phenomena due to the linear nature of the classical Maxwell theory as considered in, e.g., classical optics, and interference effects of quantum states is clarified. In addition to these issues, the framework outlined also provides for a simple approach to invariance under time-reversal, some spontaneous photon emission and/or absorption processes as well as an approach to Vavilov-Čherenkov radiation. The inherent and necessary quantum uncertainty, limiting a precise space-time knowledge of expectation values of the quantum fields considered, is, finally, recalled.

Independently of the image modality (x-rays, neutrons, etc), image data analysis requires normalization, a preprocessing step. While the normalization can sometimes easily be generalized, the analysis is, in most cases, specific to an experiment and a sample. Although many tools (MATLAB, ImageJ, VG Studio...) offer a large collection of pre-programmed image analysis tools, they usually require a learning step that can be lengthy depending on the skills of the end user. We have implemented Jupyter Python notebooks to allow easy and straightforward data analysis, along with live interaction with the data. Jupyter notebooks require little programming knowledge and the steep learning curve is bypassed. Most importantly, each notebook can be tailored to a specific experiment and sample with minimized effort. Here, we present the pros and cons of the main methods to analyse data and show the reason why we have found that Jupyter Python notebooks are well suited for imaging data processing, visualization and analysis.

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which differs from the usual Ostrogradsky approach to higher derivative theories, are elaborated for mechanical systems and illustrated for simple examples. Both a canonical space and a set of constraints emerge naturally from the transformation rule for the variables. In other words, the setting for quantization and the procedure for eliminating instabilities arise naturally.

The paper describes the investigations of a low-current discharge in airflow with the electrode configuration of coaxial plasmatron. An inner diameter of the plasmatron nozzle is of 0.5 cm and the mass airflow rate is from 0.1 to 0.3 g s⁻¹. Typical averaged discharge current is varied from 0.06 to 0.2 A. In these conditions, due to airflow the so-called plasma jet forms in the plasmatron nozzle and at its exit. The total current in plasmatron mainly flows via the constricted plasma column of the glow discharge and only a small fraction of current is carried by the jet. The principal idea of the experiments is to reveal the mechanism of the jet formation and to elucidate how the nonsteady discharge regimes influence on the jet properties. We have proposed the method for the jet diagnostics, which is based on measuring the currents to the additional diagnostic electrodes located outside the nozzle. The obtained data show that the jet current forms due to electrons that are emitted from the boundary of plasma column. The temporal behavior of the jet current is determined by the position of the column inside the plasmatron nozzle, which changes with time. Hence, the term 'plasma jet' has to be used with care, since the charged particles in the jet area are the electrons. The estimated electron density in the jet is of about 10⁹ cm^–3.

By exact numerical solutions of the Gross–Pitaevskii (GP) equation in 3D, we assess the validity of 1D and 2D approximations in the study of Bose–Einstein condensates confined in harmonic trap potentials. Typically, these approximations are performed when one or more of the harmonic frequencies are much greater than the remaining ones, using arguments based on the adiabatic evolution of the initial approximated state. Deviations from the 3D solution are evaluated as a function of both the effective interaction strength and the ratio between the trap frequencies that define the reduced dimension where the condensate is confined. The observables analyzed are both of stationary and dynamical character, namely, the chemical potential, the wave function profiles, and the time evolution of the approximated 1D and 2D stationary states, considered as initial states in the 3D GP equation. Our study, besides setting quantitative limits on approximations previously developed, should be useful in actual experimental studies where quasi-1D and quasi-2D conditions are assumed. From a qualitative perspective, 1D and 2D approximations certainly become valid when the anisotropy is large, but in addition the interaction strength needs to be above a certain threshold.

The energy spectrum of atomic clusters with a fractal structure corresponding to a Sierpiński triangle on a hexagonal lattice are studied theoretically using a simple tight-binding Hamiltonian. The evolution of the energy levels and degeneracy with the growing generation of the fractal cluster is investigated. The energy states are classified into two groups: growing states and temporary states. States belonging to the first group continue to grow after appearing at a certain generation, while those of the second group do not grow. The self-similar structure of the cluster model is reflected in the growing states, which consist of three distinct types. The energy levels of the growing states, whose degeneracy obeys a recurrence relation, can be expressed by an iterated or multi-nested function including the infinitely nested square root function.

MCViNE is an open source, object-oriented Monte Carlo neutron ray-tracing simulation software package. Its design allows for flexible, hierarchical representations of sophisticated instrument components such as detector systems, and samples with a variety of shapes and scattering kernels. Recently this flexible design has enabled several applications of MCViNE simulations at the Spallation Neutron Source (SNS) at Oak Ridge National Lab, including assisting design of neutron instruments at the second target station and design of novel sample environments, as well as studying effects of instrument resolution and multiple scattering. Here we provide an overview of the recent developments and new features of MCViNE since its initial introduction (Jiao et al 2016 Nucl. Instrum. Methods Phys. Res., Sect. A 810, 86–99), and some example applications.

Single Cu₂O nanowires (NWs) were fabricated by the two-step method we reported previously (Wang et al 2014 RSC Advances4 37542). Band-edge exciton photoluminescence (PL) was observed from individual NWs at room temperature using excitation at 325 nm. The PL signals were assigned to Fabry–Perot (F-P) type standing waves in a right cylindrical dielectric cavity (resonator) for a representative range of different wire lengths and diameters. We found that the mode spacing of F-P resonances varied inversely as the NW length as expected. For the region of NW diameters from 140 to 200 nm, and NW length between 2–5 mm, E-field simulations by COMSOL Multiphysics finite element analysis indicate that the main F-P mode propagating inside the NW is the HE₁₁ mode. When the diameter exceeds 200 nm, there are at least two F-P type modes supported in the NWs. Our results further the understanding of exciton photoluminescence in Cu₂O NWs and demonstrates the existence of enhanced mode frequencies based on the geometry of the optical micro-cavity. We further identify potential applications in exciton-driven optoelectronic devices and light emission enhanced by optical micro-cavities.

In this work, we solve the problem of modeling the generation of an acoustic pulse produced by the incidence of a pulsed laser light upon an elastic material. Our concern is about the heat transport during the absorption of electromagnetic radiation. We assume that the pulse duration is of the order of nanoseconds, and asses if under these conditions the contribution of the heat transport in the sample is an essential consideration in the description of the phenomena or if we can ignore it in the model. We begin with the energy balance analysis over the initial interaction of radiation with matter in the context of the formulation Meixner-Prigonine which is called the linear irreversible thermodynamics to describe the induced temperature field. Then we carry a momentum balance which yields the macroscopic elasticity equations with a heat source for the induced pressure field. Once established the equations for temperature and displacement fields, we solve them for the one-dimensional case, showing that the induced pressure has two components, one fast component and one slow component which is due to heat transport in the sample, which is one of the main contributions of the paper.

This paper exposes how to obtain a relation that have to be hold for all free-divergence velocity fields that evolve according to Navier–Stokes equations. However, checking the violation of this relation requires a huge computational effort. To circumvent this problem it is proposed an additional ansatz to free-divergence Navier–Stokes fields. This makes available six degrees of freedom which can be tuned. When they are tuned adequately, it is possible to find finite L² norms of the velocity field for volumes of ${{\mathbb{R}}}^{3}$ and for $t\in [{t}_{0},\infty )$. In particular, the kinetic energy of the system is bounded when the field components u_i are class C³ functions on ${{\mathbb{R}}}^{3}\times [{t}_{0},\infty )$ that hold Dirichlet boundary conditions. This additional relation lets us conclude that Navier–Stokes equations with no-slip boundary conditions have not unique solution. Moreover, under a given external force the kinetic energy can be computed exactly as a funtion of time.

The samples Fe_73.5-xCr_xNb₃Cu₁Si_13.5B₉ [x = 7, 9, 10 and 12.5 are prepared in the amorphous state in the form of thin ribbons by rapid quenching technique at wheel speed of 25 m s⁻¹ in an Ar atmosphere. The composition was sintered at the temperature 450–8000 C for half an hour. The saturation magnetization (Ms) and Curie temperature (Tc) of these alloys decrease linearly with the increase of Cr content for the entire composition range due to dilution of Fe magnetic moment and weakening of exchange interaction between of magnetic atoms. The critical composition for disappearance of ferromagnetism fall of curve Ms with the replacement Fe by Cr, where the nearest neighbor coupling is longer dominant and intermediate range occur, giving rise to a significant portion of antiferromagnetic interaction. The Curie temperature decreases due the weaker interaction among the Fe magnetic moment. The structural relaxation is associated with the magnetization up to the annealed temperature 600 °C and the chemical disorderness arise with reference to enhancement of M of annealed samples. M versus H curves sharply rise which indicates the formation of crystallization and it seems to ferromagnetic and for x = 12.5 which is paramagnetic in the amorphous condition with Tc = 246 K. This increase of M for the four samples are due to the evolution of ferromagnetic α-Fe (Si) nanograin crystal.

In this paper a coplanar waveguide (CPW) periodically loaded with resonant tunneling diodes (RTDs) and air bridges (AB) is presented as a travelling wave (TW) structure for modelling the FitzHugh-Nagumo (FHN) equation and emulating the behaviour of the nerve axon. Based upon an electrical equivalent circuit, the principle of operation is discussed in the context of a lumped-element circuital model being compared to a distributed structure. The phenomena of wave formation and propagation are studied by computer experiments of the underlying nonlinear ordinary difference-differential equations (ODEs) and that of the approximated model nonlinear partial differential equations (PDEs). A key achievement is that this medium supports stable propagating shock waves (kinks and antikinks) when effects of AB are neglected as well as stable traveling pulses only determined by the parameters of the circuit. As a result, compact electronic circuits with features of real neural systems are developed to be an experimental medium mimicking neural activity and to be applied in ultra-fast signal processing.

Post-annealing of superconducting Bi₂Sr₂Ca_n-1Cu_nO_x (BSCCO) thin films deposited by sputtering is essential for obtaining a single 2223 phase. However, optimum annealing temperature is limited to a very narrow range, needing to pass liquid phase for 2223 crystallization while not exceeding re-evaporation point. In this study, we optimized annealing conditions and observed the crystal growth process. As a result, single phase 2223 thin films with critical temperature of 108 K were obtained at 850 °C, while mixed phase thin films of 2223 and 2212 were grown above 855 °C. This is due to the re-evaporation of the thin film compounds, and these results reflect the recrystallization process after melting.

We investigate how the near field affects partially coherent light scattered from an aperture in an opaque screen. Prior work on this subject has focused on the role of surface plasmons, and how they affect spatial coherence is well documented. Here, we consider other near-field effects that might impact spatial coherence. We do this by examining the statistics of the near-zone field scattered from an aperture in a perfect electric conductor plane—a structure that does not support surface plasmons. We derive the near-field statistics (in particular, cross-spectral density functions) by applying electromagnetic equivalence theorems and the Method of Moments. We find, even in the absence of surface plasmons, that near-field physics can affect the coherence of the scattered field. The analysis and findings presented herein complement the existing coherence-related surface plasmons literature, and could find use in the design of photonic devices built to engineer spatial coherence.

We show that arbitrary quantum evolution, both unitary and non-unitary ones, can be efficiently realized via one-dimensional quantum walk. This is done based on the equivalence between quantum evolution and positive-operated valued measurements, and an algorithm of properly controlling one-dimensional discrete-time quantum walk to realize arbitrary positive-operated valued measurements. Furthermore, our method based on one-dimensional quantum walk can be easily generalized to other platforms Our method enriches technics for quantum information processes, and the applications of quantum walk.

The author investigates the Hooke-Newton transmutation of the electron in the uniform magnetic field. Two results are reported. First, the modulable quantum spectrum and spinor of the magnetic field are given. Spin exhibits its effect, even in the first order approximation of the power series expansion of the spectrum. Since the transmuted Coulomb interaction, attractive or repulsive, is determined by both the signatures of the charge and the total angular momentum, the pure spin states of different orientations experience the reverse Coulomb forces. This feature may be useful in grouping the pure spin states of the same orientation. Second, it is shown that the effect of the effective vector potential due to the geometry of conformal mapping can be generated by the vector potential of two fractional magnetic fluxes with the reverse directions which couple to the different components of the spinor. The equivalence shows the possibility of demonstrating the physics of the 2D electron in conformal space with an isotropic momentum modulation while interacting with the field of the magnetic fluxes.

We study the Riemann geometric approach to be aimed at unifying soliton systems. The general two-dimensional Einstein equation with a constant negative scalar curvature becomes an integrable differential equation. We show that such Einstein equation includes KdV/mKdV/sine-Gordon equations.

Some effects of cationic charge density distribution on single water molecule dissociation of [M(H₂O)₆]³⁺ clusters with M=Cr, Mn, Fe, Co, and Ni have been investigated using first-principles study. The molecular structures, molecular binding energies, hydration enthalpies, cation and water molecules orbitals, infrared vibrational frequencies, and potential energy surfaces/curves had been computed to fulfill the purpose of research. Our investigation results have revealed that the hollow shape of charge density of central Cr(III) makes the Cr-O bonds rigid as indicated by a higher activation energy for releasing one water molecule from [Cr(H₂O)₆]³⁺. The isotropic charge density of Fe(III) affects in lowering water rotational rigidities which is responsible for augmenting the activation energy, while the cones-shape charge density of Ni(III) weakens the ion-dipole interactions by increasing interactions between nearest neighbour water molecules.

The use of analog classical systems for computation is generally thought to be a difficult proposition due to the susceptibility of these devices to noise and the lack of a clear framework for achieving fault-tolerance. We present experimental results for the application of quantum error correction (QEC) techniques to a prototype analog computational device called a quantum emulation device. It is shown that for the gates tested (transversal Z, X and SH) there is a marked improvement in the performance characteristics of the gate operations following error correction using the 5-Qubit Perfect code. In the case of the Z gate, the median fidelity improved from 0.995 to 0.999 98, a reduction in the gate error by over two orders of magnitude. Other transverse gates similarly show strong improvements.

In this contribution, we calculate the light deflection, perihelion shift, time delay and gravitational redshift using an approximate metric that contains the Kerr metric and an approximation of the Erez-Rosen spacetime. The results were obtained directly using (Mathematica 2018 Wolfram Research, Inc., Version 11.3, Champaign). The results agree with the ones presented in the literature, but they are extended until second order terms of mass, angular momentum and mass quadrupole. The inclusion of the mass quadrupole is done by means of the metric; no expansion of the gravitational potential as in the parameterized post-Newtonian is required.