arXiv subjects

Abhiram Sripat

Publications and source records attributed to Abhiram Sripat.

4 recordsLinked to original sources

arXiv2026

Non-Hausdorff Incidence Completions of Finite Coverings: Monodromy, Transport, and Defect Posets

Let X be a connected Hausdorff surface, let Sigma be a finite subset of X, and let pi from Y to X minus Sigma be a finite sheeted covering. Peripheral monodromy at each marked point determines a finite set of peripheral component germs together with their local degree labels. We introduce incidence completions by adjoining an exceptional fibre at each marked point and prescribing a closed many to many incidence relation between peripheral component germs and exceptional points. The resulting tail saturated topology realizes the prescribed endpoint relation intrinsically. A fixed regular lift extends through a defect precisely when its exceptional value lies in the intersection of the endpoint sets associated with all accumulated peripheral germs. For finite discrete exceptional fibres, a bipartite incidence graph determines the local fundamental group and low dimensional homology. Power probes recover peripheral degrees, while multi arm probes recover higher endpoint intersections and reconstruct the discrete incidence relation by Mobius inversion. For finite exceptional fibres, the completion data are equivalently described by a weighted specialization poset with an antitone incidence map. This yields a structured monodromy classification, automorphism and quotient results, and relation valued and multiplicity valued transport through isolated defects. Varying the exceptional topology and incidence produces a finite defect poset described by a Grothendieck construction. Its total order complex forgets the incidence direction, while vertical incidence complexes and their survival under topology degeneration retain incidence dependent information.

math.GN↗

arXiv2026

Quantum Mechanics on Non-Hausdorff One-Manifolds with Finite Graph Resolutions: Analytic Completion, Branching, and Invariant-Sector Scattering

We develop a systematic framework for quantum mechanics on a finite graph-resolved class of second-countable, T1, non-Hausdorff one-manifolds. The central problem is that local differential expressions do not by themselves determine the quantum theory: non-Hausdorff incidence, bundle transport, smooth extension, and analytic completion can impose additional global constraints on the operator domain. We formulate these constraints using transported jets, Whitney realisability, Sobolev traces, and formal return holonomy, obtaining exact closure results for finite smooth graph resolutions. At first Sobolev order, scalar dynamics reduce to a weighted quantum graph whose edge weights arise from a marked resolving presentation, leading naturally to weighted Kirchhoff Hamiltonians. Multiple-origin lines and circles, branching junctions, finite trees, and split-and-rejoin geometries then yield explicit deficiency indices, reflection and transmission laws, interference conditions, compact dark states, and embedded cavity modes. For finite-rank Hermitian bundles, unitary gluing selects a transmitting fixed subspace, so scattering becomes projection onto the invariant sector of the subgroup generated by the gluing matrices. Compact-group representations therefore turn non-Hausdorff incidence into an invariant-sector selection mechanism; connected compact semisimple groups require at most two relative gluing matrices for full invariant completion, with explicit SU(3) examples. The resulting theory separates topological non-Hausdorff data from the analytic and representation-theoretic structures that remain detectable by quantum dynamics.

quant-ph↗

arXiv2025

Quantum Approximate Optimization Algorithm and Quantum-enhanced Markov Chain Monte Carlo: A Hybrid Approach to Data Assimilation in 4DVAR

We propose a novel hybrid quantum-classical framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) and Quantum-enhanced Markov Chain Monte Carlo (QMCMC) with variational particle filters to tackle the computational challenges in Four-Dimensional Variational Data Assimilation (4DVAR). 4DVAR, widely used in numerical weather prediction, suffers from inefficiencies in high-dimensional, non-linear systems. Our approach, the Quantum Variational Particle Filter (QVPF), uses QAOA to optimize particle proposals and QMCMC to efficiently compute particle weights and resample, accelerating convergence while reducing the computational load. The QVPF framework addresses the curse of dimensionality by minimizing the number of particles required for accurate state estimation, thus improving efficiency in systems with complex dynamics. The hybrid model offers enhanced accuracy by integrating quantum algorithms into the variational particle filter, making it particularly suited for applications in climate modeling, space weather prediction, and defense. The potential for achieving unprecedented resolution in predictive models could transform sectors that rely on high-resolution forecasting. We present the mathematical foundations of the approach, along with discussions on algorithmic implementation and hardware requirements. Early results suggest that this hybrid framework could significantly improve data assimilation, with future implementations on near-term quantum devices offering a practical pathway for scaling up. This work demonstrates how quantum computing can address the growing need for more accurate and computationally feasible methods in large-scale data assimilation.

quant-ph↗

arXiv2025

Quantum Algorithms for Optimizing Mycorrhizal Inoculants Using Mycoponics: A Novel Framework for Nutrient Transfer and Protein Discovery in Precision Agriculture

Mycorrhizal fungi form vast subterranean networks that are critical for plant nutrient uptake, carbon sequestration, and ecosystem resilience. Despite their ecological importance, optimizing these networks for precision agriculture, forestry,and carbon sequestration remains an open challenge, particularly when it comes to understanding the complex molecular and quantum-scale processes that govern nutrient exchange. In this paper, we propose a novel experimental framework using mycoponics, a controlled, soil-less environment for the study of plant fungal symbiosis integrated with isotopic labeling and quantum dots to track real-time nutrient transfer.

physics.bio-ph↗