Relativistic fermion on a ring: Energy spectrum and persistent current

The energy and persistent current spectra for a relativistic fermion on a ring is studied in details. The nonlinear nature of persistent current in relativistic regime and its dependence on particle mass and ring radius are analysed thoroughly. For a particular ring radius we find the existence of a critical mass at which the single ring current doesn't depend on the flux. In lower mass regime the total current spectrum shows plateaus at different height which appears periodically. The susceptibility as well shows periodic nature with amplitude depending on particle mass. As we move from higher mass to lower mass regime, we find that the system turns into paramagnetic from diamagnetic. We also show that same behaviour is observed if one vary the radius of the ring for a fixed particle mass. Hence the larger ring will be diamagnetic while the smaller one will be paramagnetic. Finally we propose an experiment to verify our findings.Comment: LaTex, 11 pages, 11 figure

Persistent current of relativistic electrons on a Dirac ring in presence of impurities

We study the behavior of persistent current of relativistic electrons on a one dimensional ring in presence of attractive/repulsive scattering potentials. In particular, we investigate the persistent current in accordance with the strength as well as the number of the scattering potential. We find that in presence of single scatterer the persistent current becomes smaller in magnitude than the scattering free scenario. This behaviour is similar to the non-relativistic case. Even for a very strong scattering potential, finite amount of persistent current remains for a relativistic ring. In presence of multiple scatterer we observe that the persistent current is maximum when the scatterers are placed uniformly compared to the current averaged over random configurations. However if we increase the number of scatterers, we find that the random averaged current increases with the number of scatterers. The latter behaviour is in contrast to the non-relativistic case.Comment: This is the published versio

Classical and quantum machine learning applications in spintronics

In this article we demonstrate the applications of classical and quantum machine learning in quantum transport and spintronics. With the help of a two-terminal device with magnetic impurity we show how machine learning algorithms can predict the highly non-linear nature of conductance as well as the non-equilibrium spin response function for any random magnetic configuration. By mapping this quantum mechanical problem onto a classification problem, we are able to obtain much higher accuracy beyond the linear response regime compared to the prediction obtained with conventional regression methods. We finally describe the applicability of quantum machine learning which has the capability to handle a significantly large configuration space. Our approach is applicable for solid state devices as well as for molecular systems. These outcomes are crucial in predicting the behavior of large-scale systems where a quantum mechanical calculation is computationally challenging and therefore would play a crucial role in designing nano devices.Comment: 9 pages, 8 figure

On a fundamental physical principle underlying the point location algorithm in computer graphics

The issue of point location is an important problem in computer graphics and the study of e cient data structures and fast algorithms is an important research area for both computer graphics and computational geometry disciplines. When filling the interior region of a planar polygon in computer graphics, it is necessary to identify all points that lie within the interior region and those that are outside. Sutherland and Hodgman are credited for designing the first algorithm to solve the problem. Their approach utilizes vector construction and vector cross products, and forms the basis of the "odd parity" rule. To verify whether a test point is within or outside a given planar polygon, a ray from the test point is drawn extending to infinity in any direction without intersecting a vertex. If the ray intersects the polygon outline an odd number of times, the region is considered interior. Otherwise, the point is outside the region. In dimensional space, Lee and Preparata propose an algorithm but their approach is limited to point location relative to convex polyhedrons with vertices in 3D-space. Although it is rich on optimal data structures to reduce the storage requirement and efficient algorithms for fast execution, a proof of correctness of the algorithm, applied to the general problem of point location relative to any arbitrary surface in 3D-space, is absent in the literature. This paper argues that the electromagnetic field theory and Gauss´s Law constitute a fundamental basis for the "odd parity" rule and shows that the "odd parity" rule may be correctly extended to point location relative to any arbitrary closed surface in 3D-space