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Spectral analysis papers 35 papers
Spectral analysis. Spectra, eigen-structures and bounds Tagged papers: 35.
Helical Electron Structure at the Compton Scale: Geometric Origin of the Fine-Structure Constant and Corrections to the Anomalous Magnetic Moment
The fine-structure constant $\alpha$ governs the strength of electromagnetic interactions, yet in the Standard Model it remains an unexplained dimensionless input, and the electron is treated as a point particle. This leaves open the question of whether $\alpha$ and the electron's anomalous magnetic…
The Algebraic Origin of Zitterbewegung: A Hierarchy of Ownership from Clifford Structure to Observed Oscillation
Zitterbewegung (ZB) — the rapid trembling of a relativistic quantum particle's position — is usually presented as a kinematic curiosity of the Dirac equation, and simulator experiments in cold atoms and engineered Dirac-like systems must interpret observed oscillations without a criterion for when…
Quantization as Hydrodynamic Relaxation: Eigenstates as Attractor Basins in a Dissipative Madelung Fluid
We develop a research program in which quantum jumps are reinterpreted as continuous, deterministic relaxation events in the Madelung hydrodynamic picture of quantum mechanics, where the wavefunction $\psi=\sqrt{\rho}\,e^{iS/\hbar}$ becomes a compressible fluid with density $\rho$ and velocity…
Ensemble Drafting Under Broadcast Control: Throughput Algebra, Variance Reduction, and Vandermonde Conditioning
Ensemble control studies populations of structurally identical dynamical systems, differing only in a parameter, that must be steered by a single broadcast input without individual state feedback. We formalize ensemble drafting — a population of draft generators whose candidate tokens are checked by…
Thresholded Readout of Continuous Classical Fields: A Formalization and Counterexample to the Uniqueness Claim for Quantum Mechanics
A family of contemporary foundational programs asserts that reality is a continuum of local deterministic fields and that quantum mechanics is the unique calculus bridging this continuum to discrete measurement outcomes. If that uniqueness claim were correct, research seeking additional physical…
Zitterbewegung as an Archimedean–2-adic Adelic Mixing Signature: Spectral-Gap Formalization, Numerical Anchors, and a Falsifiable Simulation Program
Zitterbewegung (ZBW) — the trembling motion of a Dirac wave packet at angular frequency $\omega = 2mc^{2}/\hbar$ — is conventionally treated as an interference artifact of the Dirac Hamiltonian. We propose and partially formalize a stronger claim: ZBW is the observable trace of mixing between the…
Spectral Decomposition of the Bruhat–Tits Tree as a Candidate Origin of Particle Mass Hierarchies: Exact Radial Spectrum, Finite Truncations, Semigroup Tests, and a Falsification Analysis
The Bruhat–Tits tree $\mathcal{T}_p$ of $\mathbb{Q}_p$ is the infinite $(p+1)$-regular tree that serves as the bulk of $p$-adic AdS/CFT. We test the conjecture that a natural Laplacian on $\mathcal{T}_p$ — or the prime-indexed arithmetic of the tree — encodes Standard Model mass ratios. We compute,…
The Exponential Arena: A Reconciled Quantitative Account of Hilbert-Space Growth with Qubit Number
A recurring question in quantum information is what "space" the state of a quantum computer inhabits, and how that space grows as the number of qubits $n$ increases. This paper treats the question quantitatively, formalizing the arena of an $n$-qubit register as the complex projective Hilbert space…
Error Correction Properties of Covariant Bosonic Encodings: A Quantitative Assessment
Bosonic modes provide a hardware‑efficient substrate for quantum error correction (QEC) because logical information can be encoded in continuous‑variable states with built‑in symmetries. Recent work introduced a representation‑theoretic framework in which a physical representation of a finite group,…
Exact Maximum-Likelihood Quantum Decoding beyond Treewidth: A Structural Analysis of Rank-Decomposition Dynamic Programming
Maximum-likelihood (ML) decoding is the optimal decoding rule for quantum error correction under stochastic Pauli noise, but exact evaluation of logical-class probabilities has required tensor-network contraction whose cost grows exponentially in the treewidth of the syndrome graph, blocking…
Classical Floquet Drives from Quantized Cavity Fields: Error Budgets, Geometric Phases, Gauge Consistency, and Entanglement Bounds at Large Photon Number
Floquet engineering treats periodically driven quantum systems with classical time-periodic Hamiltonians, while cavity quantum electrodynamics (QED) treats the drive itself as a quantized field. The precise connection between the two descriptions beyond weak coupling has remained subtle. Building on…
Braid Group Representations and Modular Data: Non-Uniqueness, Finite Images, and the Ising Test Case
A central question in the theory of topological order asks whether the braid group representation $B_N$ carried by $N$ non-Abelian anyons uniquely determines the modular data — the $S$ and $T$ matrices — of the underlying topological quantum field theory. We reconcile three lines of analysis into a…
Decoherence Times and Quantum Speed Limits in Spin-Chain Systems: A Many-Body Testbed for Energy-Time Uncertainty
Spin chains are the canonical many-body testbed for quantum memories and quantum wires, and the question of what bounds their useful computation time is usually answered in one of two vocabularies that are rarely placed on the same scale: the decoherence time T2 set by the environment, and the…
Discriminating the Arithmetic Cut: Matched-Level-Density Null Models for the Primon-Gas Specific Heat and Spectral Correlations
The arithmetic-statistics program reads the two exchange statistics of identical particles as two multiplicity rules on one integer lattice, and its published observable is the specific heat of the primon gas: a computable deviation from the smooth ideal gas at every sampled temperature. The…
Harmonic Analysis is Langlands — The Fast Fourier Transform as the Computational Langlands Correspondence for GL(1)
We identify the Fast Fourier Transform (FFT) as the computational Langlands correspondence for the general linear group GL(1). Harmonic analysis on the finite cyclic group Z/nZ decomposes functions into irreducible characters -- the FFT -- and this structure generalises directly to harmonic analysis…
The RG-Harmonic Isomorphism: Renormalization Group Similarities with Harmonic Quantum Mechanics
The renormalization group (RG) and harmonic quantum mechanics share a deep structural isomorphism rooted in the spectral decomposition of self-adjoint operators under scale transformations. We identify five pillars of this isomorphism and apply it retrospectively to evaluate Planck's UV catastrophe…
Architecture of Experience
The universe is saturated with a chaotic ocean of energy that we call the electromagnetic spectrum. This spectrum stretches from the longest radio waves, which can be miles long, to the shortest gamma rays, which are smaller than an atom. Between these two extremes lies an infinite gradation of…
Riemannian-Geometric Approach to Superdeterministic Bell-Violations
The foundational conflict between the probabilistic non-locality of quantum mechanics and the geometric determinism of general relativity remains the central challenge of modern physics. This paper addresses the tension by proposing a locally causal framework where Bell-inequality violations emerge…
Spectral Analysis of Anomalous Diffusion on p-Adic Fractals
The reconcilement of continuous Riemannian geometry with the discrete arithmetic of the integers remains one of the most profound challenges in mathematical physics, particularly regarding the spectral interpretation of the Riemann zeros (Berry & Keating, 1999). While standard diffusion on…
Spectral Dynamics on Bruhat-Tits Trees
The probabilistic nature of prevalent primality tests, such as Miller-Rabin, presents a fundamental limitation where certainty is achieved only asymptotically. This study proposes a deterministic alternative rooted in the non-Archimedean geometry of p-adic numbers, specifically leveraging the…
Topological Aliasing and Holographic Readout
URL: https://papers.qnfo.org/papers/topological-aliasing-and-holographic-readout/ Date: 2026-03-23 Version: 1.0 The foundation of modern physical theories relies heavily on the continuous nature of real numbers. This mathematical framework assumes that space and time can be divided infinitely…
Topological Signal Processing
The inherent limitations of conventional digital signal processing—specifically the latency and energy bottlenecks imposed by analog-to-digital conversion—represent a critical barrier for next-generation systems like 6G networks. This paper introduces a novel physical computing paradigm that…
Chiral High-Temperature Topological Processing
By replacing active syndrome extraction with passive topological protection derived from the 25 meV spectral gap of 45-degree twisted Bi-2212, the architecture circumvents the cooling power limitations of dilution refrigeration to enable the monolithic integration of classical control logic at 4…
Prime Numbers as Spectral Artifacts
This establishes a mathematical framework demonstrating that prime numbers emerge as spectral artifacts from a continuous quantum geometric substrate, rather than representing fundamental discrete entities. Through formal deduction from five established mathematical facts—base-independence of…
Arithmetic Gauge Concentration
Analytic number theory traditionally relies on probabilistic models to describe the asymptotic distribution of prime numbers, treating them as independent random variables. However, this approach fails to account for the deterministic rigidity observed in ergodic theory and the spectral statistics…
Coherent Tunneling
Standard biological paradigms conceptualize the organism as a stochastic chemical engine governed by reaction-diffusion kinetics. However, this classical view fails to account for the thermodynamic anomaly of living matter, which sustains macroscopic order against the entropic decay of the…
Continuous Topology and Discrete Arithmetic
The tension between the discrete cardinality of prime numbers and the continuous geometry of the complex plane is reconciled by treating primes as spectral residues governed by the explicit formulae of the Riemann zeta function. Sequential enumeration provides a linear coordinate that obscures the…
Relativistic Topological Superfluid
Standard cosmological models assume a static vacuum energy density, yet this premise conflicts with the renormalization group flow of quantum field theory and the fine-tuning required for dark energy. Simultaneously, high-energy astrophysical observations impose a strict “glass floor” on Lorentz…
REYNOLDS FILTER AND THE OBSERVABILITY OF CHAOS
The transition to turbulence is characterized by universal scaling laws, specifically the Feigenbaum constants, which govern the onset of chaos in nonlinear systems. While these constants are traditionally viewed as topological invariants of the underlying dynamical maps, their observability in…
Spectral Schism
Standard analytic number theory treats the Riemann zeros as eigenvalues of a Hermitian operator acting on a rigid symplectic manifold. However, the asymptotic diffraction spectrum of the prime numbers exhibits fluid-like Lebesgue measure rather than the crystalline Bragg peaks required for such a…
TOPOLOGICAL HYDRODYNAMICS AND THE SPECTRAL GAP
Standard quantum field theory conceptualizes the vacuum as a probabilistic void, yet phenomenological isomorphism with superfluid Helium-3 suggests a deeper hydrodynamic ontology. While this topological substrate theoretically supports analog computation via vorticity, the practical realization is…
Computational Benchmark of Geometric and Algebraic Models for Multi-Qubit State Representation
The Bloch sphere provides a powerful yet fundamentally limited geometric model for quantum states, excelling at single-qubit intuition but failing to represent the multi-qubit entanglement that powers quantum advantage. This work addresses the critical tension between the cognitive simplicity of…
Spectral Benchmarking of Holographic Quantum Simulations
The simulation of quantum gravity on near-term quantum processors is hindered by a critical tension between hardware feasibility and physical fidelity, creating an “Artifact Zone” where simplified models produce misleading, non-physical results. This paper addresses this challenge by proposing a…
Information-Theoretic Reformation of Physics
Physics must be reoriented around information-theoretic constraints rather than quantum mechanical assumptions. This reorientation requires a critical reevaluation of Planck’s constant as a curve-fitting parameter and the establishment of finite information capacity as a new axiom. The historical…
Standard Model
The Standard Model (SM) of particle physics represents the most precise and empirically successful framework devised for describing fundamental particles and their interactions. This rigorous empirical success is intrinsically coupled with severe, formally demonstrable theoretical deficiencies that…
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