arXiv subjects

Dalaver H. Anjum

Publications and source records attributed to Dalaver H. Anjum.

6 recordsLinked to original sources

arXiv2026

Unified Entropic Dynamics Framework for Classical, and Quantum Wave Equations

Entropic Dynamics (ED) provides a statistical-inferential foundation for physical laws, deriving motion and field equations from principles of entropy maximization rather than quantization postulates. ED reconstructs quantum mechanics by treating the evolution of probability distributions on configuration space as driven by information constraints, yielding the Schrodinger equation as a non-dissipative diffusion process. Building on this foundation, the present work extends the ED framework into a Unified Entropic Dynamics (UED) formulation that encompasses classical, quantum, relativistic, thermodynamic, and gravitational phenomena within a single information geometric principle. By maximizing entropy subject to constraints on diffusion, drift, and gauge covariance over a manifold endowed with a supermetric H_ab, we derive a universal field equation that merges the Fokker-Planck and Hamilton-Jacobi structures into one covariant form. When specialized to different dynamical variables, this equation reproduces the harmonic oscillator, Schrodinger, Maxwell, Klein-Gordon, and gravitational wave equations, thereby revealing a deep equivalence between probabilistic inference and dynamical law. The UED framework demonstrates that spacetime geometry, quantum coherence and thermodynamic diffusion emerge as complementary expressions of the same entropic process, establishing a unified inferential foundation for both microscopic and macroscopic physics. In this formulation, energy, probability, and entropy are intertwined aspects of information geometry, providing a consistent inferential foundation for understanding classical, quantum, and gravitational dynamics as complementary expressions of a single entropic law.

physics.gen-ph↗

arXiv2026

Non-Relativistic Quantum Mechanics in Multidimensional Geometric Frameworks

A generalized formulation of non-relativistic quantum mechanics is developed within multidimensional geometric (NG) frameworks characterized by a power-law dispersion relation \(E \propto |p|^{j}\), where \(j = N - 1\). Starting from the generalized Minkowski distance in \(L^j\)-normed spaces, the conventional quadratic kinetic structure of three-dimensional geometry is extended to higher-order spatial derivatives, yielding a consistent \(j\)-th order Schrödinger equation. The formalism is applied to free particles and to particles confined within a one-dimensional infinite potential well for 2G, 3G, 4G, and 5G geometries. While plane-wave solutions and translational invariance are preserved, the spectral structure is modified, with bound-state energies scaling as \((2n+1)^{j}\), leading to cubic and quartic growth in higher geometries. The corresponding eigenfunctions exhibit mixed exponential, trigonometric, and hyperbolic forms determined by the roots of negative unity. A generalized probability framework based on \(j\)-fold conjugation is introduced, ensuring a real-valued probability density and consistent expectation values. Despite these generalizations, the Heisenberg uncertainty principle is preserved. The formulation presents quantum mechanics as a geometry-dependent theory in which dispersion relations, spectral properties, and probabilistic structure emerge from the underlying spatial metric.

quant-ph↗

arXiv2023

Approach to Data Science with Multiscale Information Theory

Data Science is a multidisciplinary field that plays a crucial role in extracting valuable insights and knowledge from large and intricate datasets. Within the realm of Data Science, two fundamental components are Information Theory (IT) and Statistical Mechanics (SM), which provide a theoretical framework for understanding dataset properties. IT enables efficient storage and transmission of information, while SM focuses on the behavior of systems comprising numerous interacting components. In the context of data science, SM allows us to model complex interactions among variables within a dataset. By leveraging these tools, data scientists can gain a profound understanding of data properties, leading to the development of advanced models and algorithms for analysis and interpretation. Consequently, data science has the potential to drive accurate predictions and enhance decision-making across various domains, including finance, marketing, healthcare, and scientific research. In this paper, we apply this data science framework to a large and intricate quantum mechanical system composed of particles. Our research demonstrates that the dynamic and probabilistic nature of such systems can be effectively addressed using a Multiscale Entropic Dynamics (MED) approach, derived from the Boltzmann methods of SM. Through the MED approach, we can describe the system's dynamics by formulating a general form of the Nonlinear Schrödinger equation and how it can be applied to various systems with particles and quasi-particles, such as electrons, plasmons, polarons, and solitons. By employing this innovative approach, we pave the way for a deeper understanding of quantum mechanical systems and their behaviors within complex materials.

physics.data-an↗

arXiv2017

Impacts of Doping on Epitaxial Germanium Thin Film Quality and Si-Ge Interdiffusion

Ge-on-Si structures with three different dopants (P, As and B) and those without intentional doping were grown and annealed. Several different materials characterization methods have been performed to characterize the Ge film quality. All samples have a smooth surface (roughness < 1.5 nm), and the Ge films are almost entirely relaxed. On the other hand, B doped Ge films have threading dislocations above 1 x 10^8 cm-2. While P and As doping can reduce the threading dislocation density to be less than 10^6 cm-2 without annealing. The interdiffusion of Si and Ge of different films have been investigated experimentally and theoretically. A quantitative model of Si-Ge interdiffusion under extrinsic conditions across the full x_Ge range and with the dislocation mediated diffusion term was established. The Kirkendall effect has been observed. The results are of technical significance for the structure, doping, and process design of Ge-on-Si based devices, especially for photonic applications.

cond-mat.mtrl-sci↗

arXiv2016

Study Of Si-Ge Interdiffusion With a High Phosphorus Doping Concentration

Si-Ge interdiffusion with a high phosphorus doping level was investigated by both experiments and modeling. Ge/Si1-xGex/Ge multi-layer structures with 0.75<x_Ge<1 , a mid-10^18 to low-10^19 cm-3 P doping and a dislocation density of 10^8 to 10^9 cm-2 range were studied. The P-doped sample shows an accelerated Si-Ge interdiffusivity, which is 2-8 times of that of the undoped sample. The doping dependence of the Si-Ge interdiffusion was modelled by a Fermi-enhancement factor. The results show that Si-Ge interdiffusion coefficient is proportional to n^2/n_i^2 for the conditions studied, which indicates that the interdiffusion in high Ge fraction range with n-type doping is dominated by V^(2-) defects. The Fermi-enhancement factor was shown to have a relatively weak dependence on the temperature and the Ge fraction. The results are relevant to structure and thermal processing condition design of n-type doped Ge/Si and Ge/SiGe based devices such as Ge/Si lasers.

cond-mat.mtrl-sci↗

arXiv2013

Electron irradiation induced reduction of the permittivity in chalcogenide glass (As2S3) thin film

We investigate the effect of electron beam irradiation on the dielectric properties of As2S3 Chalcogenide glass. By means of low-loss Electron Energy Loss Spectroscopy, we derive the permittivity function, its dispersive relation, and calculate the refractive index and absorption coefficients under the constant permeability approximation. The measured and calculated results show, to the best of our knowledge, a heretofore unseen phenomenon: the reduction in the permittivity of <40%, and consequently a modification of the refractive index follows, reducing it by 20%, hence suggesting a significant change on the optical properties of the material. The plausible physical phenomena leading to these observations are discussed in terms of the homopolar and heteropolar bond dynamics under high energy absorption.

cond-mat.mtrl-sci↗