arXiv subjects

Shahid Nawaz

Publications and source records attributed to Shahid Nawaz.

11 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↗

arXiv2025

RaFD: Flow-Guided Radar Detection for Robust Autonomous Driving

Radar has shown strong potential for robust perception in autonomous driving; however, raw radar images are frequently degraded by noise and "ghost" artifacts, making object detection based solely on semantic features highly challenging. To address this limitation, we introduce RaFD, a radar-based object detection framework that estimates inter-frame bird's-eye-view (BEV) flow and leverages the resulting geometric cues to enhance detection accuracy. Specifically, we design a supervised flow estimation auxiliary task that is jointly trained with the detection network. The estimated flow is further utilized to guide feature propagation from the previous frame to the current one. Our flow-guided, radar-only detector achieves achieves state-of-the-art performance on the RADIATE dataset, underscoring the importance of incorporating geometric information to effectively interpret radar signals, which are inherently ambiguous in semantics.

cs.RO↗

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↗

arXiv2016

Entropic Dynamics on Curved Spaces

Entropic dynamics is a framework in which quantum theory is derived as an application of entropic methods of inference. Entropic dynamics on flat spaces has been extensively studied. The objective of this paper is to extend the entropic dynamics of $N$ particles to curved spaces. The important new feature is that the displacement of a particle does not transform like a vector because fluctuations can be large enough to feel the effects of curvature. The final result is a modified Schrödinger equation in which the usual Laplacian is replaced by the Laplace-Beltrami operator.

quant-ph↗

arXiv2014

A Quasi-Unary Representation of Discrete Taxicab Geometry

In this paper we represent $n-$dimensional discrete Taxicab geometry by base--($4n+1$) numeral system. The algebraic structure of this base--($4n+1$) system is similar to unary system, we call it quasi-unary (QU) representation. QU representation generalizes translation and rotation to transform any geometrical object (shape) into another shape.

math.MG↗

arXiv2014

Ultra low noise YBCO nanoSQUIDs implementing nanowires

We present results on ultra low noise YBa$_2$Cu$_3$O$_{7-δ}$ nano Superconducting QUantum Interference Devices (nanoSQUIDs). To realize such devices, we implemented high quality YBCO nanowires, working as weak links between two electrodes. We observe critical current modulation as a function of an externally applied magnetic field in the full temperature range below the transition temperature $T_C$. The white flux noise below 1 $μΦ_0/\sqrt{\mathrm{Hz}}$ at T = 8 K makes our nanoSQUIDs very attractive for the detection of small spin systems.

cond-mat.supr-con↗

arXiv2013

Josephson-like behavior in YBa$_2$Cu$_3$O$_{7-δ}$ nano-bridges carrying the depairing current

We have investigated the zero-field critical supercurrent of YBa$_2$Cu$_3$O$_{7-δ}$ bridges patterned from 50 nm thick films as a function of bridge width, ranging from 2 $μ$m to 50 nm. The critical current density monotonically increases for decreasing bridge width even for widths smaller than the Pearl length. This behavior is accounted for by considering current crowding effects at the junction between the bridge and the wider electrodes. Comparison to numerical calculations of the current distributions in our bridge geometries of various widths yields a (local) critical current density at 4.2 K of $1.3\times 10^8$ A/cm$^2$, the Ginzburg Landau depairing current density. The observation of up to 160 Shapiro-like steps in the current voltage characteristics under microwave irradiation substantiates the pristine character of our nano bridges with cross sections as small as $50\times 50$ nm$^2$.

cond-mat.supr-con↗

arXiv2011

Momentum and Uncertainty Relations in the Entropic Approach to Quantum Theory

In the Entropic Dynamics (ED) approach to quantum theory the particles have well-defined positions but since they follow non differentiable Brownian trajectories they cannot be assigned an instantaneous momentum. Nevertheless, four different notions of momentum can be usefully introduced. We derive relations among them and the corresponding uncertainty relations. The main conclusion is that momentum is a statistical concept: in ED the momenta are not properties of the particles; they are attributes of the probability distributions.

quant-ph↗

arXiv2010

The Topological Structure of Question Theory

A question is identified with a topology on a given set of irreducible assertions. It is shown that there are three types of a question. Type-I question generates sub-question, type-II question has a definite answer and type-III question is irrelevant. We suggest that the most intelligent machine asks type-II questions. We also claim that a truly intelligent machine cannot be desireless. This work may prove useful in machine learning and may open up new ways to understand mind.

math.GM↗

arXiv2009

Geometrized Symbols and the Related Codes

In this paper geometry is studied with a novel approach. Every geometrical object is defined as a symbol which satisfies some properties. These symbols are then coded into a class of numbers which are named here as many dots numbers (MDN). The algebraic structure of MDN is established. Assuming the universe as a symbol, the existence of dark matter is explained qualitatively. Moreover, it is shown that dark matter increases as the universe expands.

physics.gen-ph↗