arXiv subjects

James C. Hateley

Publications and source records attributed to James C. Hateley.

6 recordsLinked to original sources

arXiv2025

A Chiral Adelic Dirac Operator and the Spectral Realization of the Riemann Zeros

This paper develops a chiral adelic operator framework in which the functional--equation symmetry of global $L$--functions is realized directly in the spectrum of a Dirac--type Hamiltonian. Working on the idèle class space, we place a real--place Floquet Hamiltonian into an off--diagonal chiral form to obtain a global adelic Dirac operator with an exact involutive symmetry implemented by real reflection and idelic inversion. Arithmetic information is incorporated through a prime--indexed mass deformation built from spherical Hecke operators; when the coefficient functions are even, the perturbed operator preserves the chiral symmetry and produces isolated $\pm$--paired eigenvalues inside the spectral gaps of the Floquet background. These eigenvalues appear as jump discontinuities of the Dirac spectral shift function, while a separated adelic trace formula expresses the trace as a product of a Floquet orbital factor and a prime--indexed Euler--factor--type term whose logarithmic derivatives yield a prime--orbit expansion reminiscent of the explicit formula. This structure motivates a Dirac reinterpretation of the Hilbert--Pólya idea, identifying the nontrivial zeros of $ζ(s)$ not with the raw spectrum of a single operator but with the spectral--shift discontinuities of a chiral adelic Dirac system under controlled prime--indexed deformations, with finite--prime truncations providing computable models that converge distributionally and enable numerical exploration of arithmetic spectral flow.

math-ph↗

arXiv2025

Measurement-Induced Temporal Geometry

We propose a unified theoretical framework, Measurement-Induced Temporal Geometry (MTG), in which time, causality, and spacetime geometry emerge from quantum measurement acting on a fiber-valued internal time field. Each spacetime point supports a local degree of freedom $τ$, modeled as a smooth section of a fiber bundle $π: E \to M$, with projection events $μ[τ]$ generating classical temporal flow. Quantum coherence and entanglement are encoded in the curvature $F = \nabla^2$ of a connection on the time-fiber, while the effective spacetime metric $g_{μν}^{\mathrm{eff}}$ arises as an integral over measurement histories. We derive the dynamical equations governing $τ$, its supersymmetric completions, and the entanglement connection $A_μ$, showing how quantization proceeds via both canonical and path-integral methods. Standard Model fields couple covariantly to the fiber geometry, and gravitational dynamics emerge from variational principles over projection-induced entropy. Cosmological inflation, dark energy, and large-scale structure are reinterpreted as consequences of modular coherence, topological obstruction, and fluctuations in the projection density $ρ(x)$. Within the AdS/CFT correspondence, MTG reinterprets modular Hamiltonians as boundary projections of bulk time flow and identifies entanglement wedges with surfaces minimizing measurement-induced projection current. A UV-complete embedding arises through string theory, where $τ$ descends from compactified moduli and projection corresponds to brane interaction and spontaneous supersymmetry breaking. The framework yields a set of falsifiable predictions, including CMB anisotropies, black hole ringdown echoes, and modular deviations in lab-scale quantum systems, offering a consistent and testable account of spacetime as an emergent property of quantum measurement.

hep-th↗

arXiv2025

Segmentation-Based Regression for Quantum Neural Networks

Recent advances in quantum hardware motivate the development of algorithmic frameworks that integrate quantum sampling with classical inference. This work introduces a segmentation-based regression method tailored to quantum neural networks (QNNs), where real-valued outputs are encoded as base-b digit sequences and inferred through greedy digitwise optimization. By casting the regression task as a constrained combinatorial problem over a structured digit lattice, the method replaces continuous inference with interpretable and tractable updates. A hybrid quantum-classical architecture is employed: quantum circuits generate candidate digits through projective measurement, while classical forward models evaluate these candidates based on task-specific error functionals. We formalize the algorithm from first principles, derive convergence and complexity bounds, and demonstrate its effectiveness on inverse problems involving PDE-constrained models. The resulting framework provides a robust, high-precision interface between quantum outputs and continuous scientific inference.

quant-ph↗

arXiv2020

Fresnel Integral Computation Techniques

This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor series, modified trapezoid rule and an asymptotic expansion for small, medium and large arguments respectively. These special functions can be computed accurately and efficiently up to an arbitrary precision. Error estimates are provided and we give a systematic method in choosing the various parameters for a desired precision. We illustrate this method and verify numerically using double precision.

math.NA↗

arXiv2019

Deep Learning Seismic Substructure Detection using the Frozen Gaussian Approximation

We propose a deep learning algorithm for seismic interface and pocket detection with neural networks trained by synthetic high-frequency displacement data efficiently generated by the frozen Gaussian approximation (FGA). In seismic imaging high-frequency data is advantageous since it can provide high resolution of substructures. However, generation of sufficient synthetic high-frequency data sets for training neural networks is computationally challenging. This bottleneck is overcome by a highly scalable computational platform built upon the FGA, which comes from the semiclassical theory and approximates the wavefields by a sum of fixed-width (frozen) Gaussian wave packets. Data is generated from a forward simulation of the elastic wave equation using the FGA. This data contains accurate traveltime information (from the ray path) but not exact amplitude information (with asymptotic errors not shrinking to zero even at extremely fine numerical resolution). Using this data we build convolutional neural network models using an open source API, GeoSeg, developed using Keras and Tensorflow. On a simple model, networks, despite only being trained on FGA data, can detect an interface with a high success rate from displacement data generated by the spectral element method. Benchmark tests are done for P-waves (acoustic) and P- and S-waves (elastic) generated using the FGA and a spectral element method. Further, results with a high accuracy are shown for more complicated geometries including a three layered model, and a 2D-pocket model where the neural networks trained by both clean and noisy data.

physics.geo-ph↗

arXiv2018

Frozen Gaussian Approximation for 3-D Elastic Wave Equation and Seismic Tomography

The purpose of this work is to generalize the frozen Gaussian approximation (FGA) theory to solve the 3-D elastic wave equation and use it as the forward modeling tool for seismic tomography with high-frequency data. FGA has been previously developed and verified as an efficient solver for high-frequency acoustic wave propagation (P-wave). The main contribution of this paper consists of three aspects: 1. We derive the FGA formulation for the 3-D elastic wave equation. Rather than standard ray-based methods (e.g. geometric optics and Gaussian beam method), the derivation requires to do asymptotic expansion in the week sense (integral form) so that one is able to perform integration by parts. Compared to the FGA theory for acoustic wave equation, the calculations in the derivation are much more technically involved due to the existence of both P- and S-waves, and the coupling of the polarized directions for SH- and SV-waves. In particular, we obtain the diabatic coupling terms for SH- and SV-waves, with the form closely connecting to the concept of Berry phase that is intensively studied in quantum mechanics and topology (Chern number). The accuracy and parallelizability of the FGA algorithm is illustrated by comparing to the spectral element method for 3-D elastic wave equation in homogeneous media; 2. We derive the interface conditions of FGA for 3-D elastic wave equation based on an Eulerian formulation and the Snell's law. We verify these conditions by simulating high-frequency elastic wave propagation in a 1-D layered Earth model. In this example, we also show that it is natural to apply the FGA algorithm to geometries with non-Cartesian coordinates; 3. We apply the developed FGA algorithm for 3-D seismic { wave-equation-based traveltime tomography and full waveform inversion, respectively

physics.geo-ph↗