Amal K. Das

A non‐Fickian diffusion equation

A non‐Fickian diffusion equation, which differs from the usual (Fickian) diffusion equation by having an additional, second‐order derivative term in time, is considered to describe the dynamics of a Brownian particle. Some useful perspectives on this generalized diffusion equation are presented, particularly with respect to the effect of a potential field. Two quantities of physical interest, namely the mean square displacement and the particle flux at an absorbing boundary, are considered in the process of a comparative study of the two diffusion equations. We also discuss the applicability of the non‐Fickian diffusion equation to some systems of physical and practical interest.

Dicluster stopping in a degenerate electron gas

In this paper we report on our theoretical studies of various aspects of the correlated stopping power of two pointlike ions (a dicluster) moving in close but variable vicinity of each other in some metallic target materials, the latter being modeled by a degenerate electron gas with appropriate densities. Within the linear-response theory we have made a comprehensive investigation of correlated stopping power, vicinage function and related quantities for a diproton cluster in two metallic targets, aluminum and copper, and present detailed and comparative results for three approximations to the electron gas dielectric function, namely, the plasmon-pole approximation without and with dispersion as well as with the random-phase approximation. The results are also compared, wherever applicable, with those for an individual projectile.

Radiation damage and surface modification of GaAs(001) by MeV C+ and C2+ co-implantation with Ga2+

Radiation damage and Surface modifications of semi-insulating GaAs(001) substrates upon 1 MeV C+ and 2 MeV C2+ coimplantation with Ga2+ have been studied by X-ray reflectometry, combined Rutherford backscattering/channeling and transmission electron microscopy. Two disordered layers – one near-surface and another deeper – are formed. Additionally the electron density of the near-surface region has been found to be lower compared to bulk GaAs. This has been attributed to vacancy-enrichment in this region. The disorder caused by C2 implantation is higher compared to C. Assuming that the near-surface disorder is partially caused by electronic excitation in the semi-insulating substrate, a possible reason for this difference is the coherent dynamic response of the electrons in the target due to vicinage of C atoms in the C2 cluster. In the deeper layer, overlap of damage cascades might be responsible for the higher damage caused in the cluster implantation.

Numerical Solution for a Non-Fickian Diffusion in a Periodic Potential

Numerical solutions of a non-Fickian diffusion equation belonging to a hyperbolic type are presented in one space dimension. The Brownian particle modelled by this diffusion equation is subjected to a symmetric periodic potential whose spatial shape can be varied by a single parameter. We consider a numerical method which consists of applying Laplace transform in time; we then obtain an elliptic diffusion equation which is discretized using a finite difference method. We analyze some aspects of the convergence of the method. Numerical results for particle density, flux and meansquare-displacement (covering both inertial and diffusive regimes) are presented.

Number-conserving linear-response study of low-velocity ion stopping in a collisional magnetized classical plasma.

The results of a theoretical investigation of the low-velocity stopping power of ions in a magnetized collisional and classical plasma are reported. The stopping power for an ion is calculated through the linear-response (LR) theory. The collisions, which lead to a damping of the excitations in the plasma, are taken into account through a number-conserving relaxation time approximation in the LR function. In order to highlight the effects of collisions and magnetic field, we present a comparison of our analytical and numerical results obtained for nonzero damping or magnetic field with those for vanishing damping or magnetic field. It is shown that the collisions remove the anomalous friction obtained previously [Nersisyan et al., Phys. Rev. E 61, 7022 (2000)] for the collisionless magnetized plasmas at low ion velocities. One of the major objectives of this paper is to compare and to contrast our theoretical results with those obtained through a diffusion coefficient formulation based on the Dufty-Berkovsky relation evaluated for a magnetized one-component plasma modeled with target ions and electrons.

Energy loss of high energy ion beams in a disordered plasma

Within the linear response formalism and using a number-conserving relaxation-time approximation to include disorder in a degenerate electron plasma we show, through analytical and numerical results, that the stopping power and effective charge of energetic extended projectile ions are significantly affected by disorder.

A generalized stopping power sum rule

Abstract The Lindhard–Winther (LW) equipartition sum rule states that within the linear response theory, the stopping power of an energetic point-charge projectile in a degenerate electron gas medium, receives equal contributions from single-particle and collective excitations in the medium. In this Letter we show that the LW sum rule does not necessarily hold for an extended projectile ion and for ion clusters moving in a fully degenerate electron gas. We have derived a generalized stopping power rule for this type of projectiles.

A numerical approach to study the Kramers equation for finite geometries: boundary conditions and potential fields

The Kramers equation for the phase-space function, which models the dynamics of an underdamped Brownian particle, is the subject of our study. Numerical solutions of this equation for natural boundaries (unconfined geometries) have been well reported in the literature. But not much has been done on the Kramers equation for finite (confining) geometries which require a set of additional constraints imposed on the phase-space function at physical boundaries. In this paper we present numerical solutions for the Kramers equation with a variety of potential fields—namely constant, linear, harmonic and periodic—in the presence of fully absorbing and fully reflecting boundary conditions (BCs). The choice of the numerical method and its implementation take into consideration the type of BCs, in order to avoid the use of ghost points or artificial conditions. We study and assess the conditions under which the numerical method converges. Various aspects of the solutions for the phase-space function are presented with figures and discussed in detail.

Gone to pieces

When I was a student at the University of Dhaka, I was given a book on quantum mechanics written by Raziuddin Siddiqui.

Effect of collisions on a one-dimensional plasmon

The dielectric function obtained in the semi-phenomenological relaxation time approximation, and also through a microscopic method, is considered and it is shown that collisions severely affect the one-dimensional plasmon, which now cannot propagate below a critical wavevector. This behaviour is similar to that reported recently for a two-dimensional electron gas. the two methods are briefly compared.