Ashim Roy

Topological aspects of a fermion and the chiral anomaly

It is here shown that the chiral anomaly is related to the topological properties of a fermion. The quantization procedure of a relativistic particle requires that the particle be an extended one, and to quantize a Fermi field, it is necessary to introduce an anisotropic feature in the internal space of the particle so that it gives rise to two internal helicities corresponding to a particle and an antiparticle. This specific quantum geometry of a Dirac particle gives rise to the solitonic feature as envisaged by Skyrme and the Skyrme term appears as an effect of quantization. When in the Lagrangian formulation the effect of this topological property is taken into account, it is found that the anomaly vanishes.

New approximate phase functions: test for nonspherical particles

Abstract In a recent paper, we described two approximate phase functions for the scattering of light by monodisperse particles. One phase function for particles of size small or comparable to the wavelength of scattering radiation and the other for larger particles. Validity of these phase functions was established by comparing their predictions against Mie phase functions. In this paper we examine the validity of these phase functions for monodisperse aligned nonspherical particles. The nonspherical particles employed for examining approximate phase functions are spheroids and infinitely long cylinders. Results show that the predictions of our approximate phase functions are equally valid for nonspherical particles too.

NEW APPROXIMATE PHASE FUNCTIONS FOR SCATTERING OF UNPOLARIZED LIGHT BY DIELECTRIC PARTICLES

Abstract We present two new phase functions, one for particles small compared to the wavelength of the scattering radiation and the other for particles large compared to the wavelength of the scattering radiation. These phase functions have been validated for the case of Mie scatterers. For small particles, the results of the new phase function are found to be identical with the Mie results. For large particles, comparison with the Mie results show that the phase function presented here is an extremely good approximation to the Mie phase function. We believe that these phase functions can be expediently used in problems relating to solutions of the radiative transfer equations.

A simple analysis of the extinction spectrum of a size distribution of Mie particles

In the context of the inverse scattering problem in optics, the extinction spectra generated by smooth size distributions of Mie particles are analysed. It is seen that an extinction spectrum, in general, has some easily identifiable characteristic regions where the extinction–frequency relationship can be approximated by simple empirical formulae involving the first four moments of the particle size distribution function. Also, some remarkable features associated with the symmetric (Gaussian) distributions are observed and explained in this context. This analysis clearly exhibits the manner in which essential features of a particle size distribution gets coded into its extinction spectrum.

On the validity of soft particle approximations for the light scattering by a homogeneous dielectric sphere

Abstract The validity of various soft particle approximations has been examined for the scattering of light by a homogeneous dielectric sphere. A scalar analogue of the S-approximation has been presented. It is shown that this much simpler approximation could be nearly as good as the sophisticated S-approximation itself. Numerical results for the extinction and the scattered intensities are examined over a wide refracted index and size parameter domain. The anomalous diffraction approximation has also been included in numerical comparisons.

Inverse scattering problem involving soft Mie particles

The inverse-scattering problem for a polydispersion f(a) of Mie particles is discussed. A new approach based on the mean value theorem and the method of employing Lagrange multipliers is developed. We show that the mean value theorem enables us to obtain easily the key parameters associated with the distribution function f(a). The method of Lagrange multipliers may then be used to construct f(a), the formal solution to the inverse-scattering problem. The workability and the effectiveness of this approach are also demonstrated.

Large diamagnetic persistent currents

Magnetization of finite size systems in the form of mesoscopic rings has intrigued physicists for a long time. Theories to date predict paramagnetic behavior, but experiments consistently show diamagnetic behavior. We show that the evanescent modes that are always present in rings of finite thicknesses can carry very large diamagnetic currents that are also very sensitive to disorder. Their contribution has always been ignored so far. Their contribution has features similar to that observed in experiments.

A semi-analytic approach within the framework of the anomalous diffraction approximation for transverse magnetic scattering of light by an infinitely long cylinder at normal incidence

Near-forward scattering of light by an infinitely long homogeneous right circular cylinder has been considered using the anomalous diffraction approximation. The scattering function is shown to be expressible in terms of known functions by means of a series expansion. Simple formulae have been obtained for the specific cases of (i) near-forward scattering and (ii) a large-diameter cylinder. The validity of these formulae is examined numerically. The corresponding large-sphere formula is also examined to check that the analysis is not limited to particles of cylindrical geometry only.

Topological aspects of SU(2) Weyl fermion and global anomaly

It is argued here that the global anomaly of SU(2) Weyl fermions is related to the residual topological properties of massive Dirac fermions leading to the topological index corresponding to the fermion number. As in the case of the chiral anomaly with Dirac fermions, the SU(2) anomaly with a Weyl fermion vanishes when the effect of this topological property is taken into account in the Lagrangian formulation.

GRAVITATIONAL ANOMALY AND THE WORLD TOPOLOGY

Here it is shown that the gravitational anomaly is compensated by the torsion term in the Einstein–Cartan action when the geometrical and topological origin of torsion is considered in the context of quantum geometry characterizing the quantization procedure of a fermion. The relationship of this anomaly with Pontryagin index is then established. The relevance of this index in the origin of topological fixtures like wormholes in space-time has also been discussed.