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Anyons & topology papers 36 papers
Anyons & topology. Anyons, braiding and topological order Tagged papers: 36.
Passive Error Rejection via Cryo-Fluidic Topological Phases: A Feasibility Analysis of the Topological Matter Engine
Active quantum error correction imposes a large and growing overhead of physical qubits, control electronics, and entropy-exporting measurement cycles on every scalable quantum processor. This paper examines a proposed alternative: a "Topological Matter Engine" in which errors are rejected…
Corrected Condensation Indices and the Sixteen-Fold Way: A Quantitative Bulk-Boundary Dictionary for Ising-Type Anyon Condensates
A companion preprint (https://papers.qnfo.org/papers/a-two-index-framework-for-the-bulk-boundary-correspondence-of-anyon-condensation/) introduced computable indices for anyon condensation: the dimension ratio $\kappa = D_C^2/D_D^2$, the chirality-sensitive index $\mu = 2\,\Delta c$, and the…
Braid Group Representations and the Uniqueness of Modular Data: The Ising Test Case and General Limitations
We investigate whether the unitary braid group representation carried by a collection of non‑Abelian anyons uniquely determines the modular data—namely the $S$ and $T$ matrices—of the underlying modular tensor category (MTC). Using the Ising anyon theory as a concrete laboratory, we reconstruct the…
Quantitative Bulk–Boundary Correspondence for Anyon Condensation: Two Computable Indices with Explicit Arithmetic
When a $(2+1)$-dimensional topologically ordered phase terminates at a boundary where a subset of anyons condenses, the boundary becomes gapped, and the bulk–boundary correspondence acquires sharp quantitative content: which boundary phenomena are forced by the bulk condensation data, and which…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in Two-Dimensional Topological Superconductors
Majorana zero modes (MZMs) bound to vortices of a two-dimensional topological superconductor (2D TSC) realize non-Abelian anyons whose exchange is described by a projective representation of the braid group $B_N$. The associated anyon theory is encoded in a modular tensor category (MTC) with fusion…
A Taxonomy of Exchange Statistics from Configuration-Space Topology: Non-Abelian Flux Attachment and a Pre-Registered Thermal Hall Projection
The statistics of identical particles is fixed by the fundamental group of their configuration space: in $d \geq 3$ spatial dimensions this group is the symmetric group $S_N$, permitting only the bosonic ($+1$) and fermionic ($-1$) exchange phases, while in $d = 2$ it is the braid group $B_N$, whose…
Projective Braid Group Representations from a Microscopic Long-Range Kitaev Chain
We construct an explicit projective representation of the braid group from the microscopic Hilbert space of a Kitaev chain extended with algebraically decaying long-range hopping and pairing. The construction proceeds in three steps. First, we identify the topological phase of the long-range Kitaev…
A Two-Index Framework for the Bulk-Boundary Correspondence of Anyon Condensation and Boundary Majorana Statistics
The bulk-boundary correspondence asserts that topological data of a (2+1)-dimensional phase determine the physics of its boundary, but in the setting of anyon condensation the correspondence is usually stated structurally rather than quantitatively. We propose a set of computable indices that…
Why Vertices, Not Points? Vertex-Anchored Braiding, Stabilizer Arithmetic, and Displacement Gaps on Bruhat–Tits Buildings
Bruhat–Tits buildings are the canonical combinatorial-geometric objects attached to reductive groups over non-Archimedean local fields, and the recent QNFO constructions of p-adic braid groups [12], p-adic anyon models [13], and a p-adic Temperley–Lieb parameter [14] anchor their discrete braiding…
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…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
Majorana zero modes (MZMs) localized on vortices of a two-dimensional topological superconductor carry a projective representation of the braid group, and the associated anyon theory is encoded in a modular tensor category whose fusion rules and modular data ($S$ and $T$ matrices) determine the…
Braid Group Representations, Modular Data, and the Classification of Majorana Zero Mode Fusion Rules in 2D Topological Superconductors
We investigate whether the braid group representation on $N$ anyons uniquely determines the modular data ($S$ and $T$ matrices) of a non-Abelian topological order, and whether this framework classifies all fusion rules for Majorana zero modes (MZMs) in 2D topological superconductors. We show that…
Majorana Zero-Mode Parity, the Hexagon Equation, and Chiral Edge Modes in 2D Topological Superconductors
In a two-dimensional topological superconductor hosting vortices with Majorana zero modes (MZMs), the exchange of vortices yields a projective representation of the braid group. We investigate whether the full anyonic exchange matrix is uniquely determined by the MZM parity operators and whether…
Arithmetic Anyons: The Bounded-Occupation Family, Gentile Statistics, and the Roots of Unity That Carry Braid Phases
Three spatial dimensions admit exactly two exchange statistics for identical particles, and a recent record reads the two occupation distributions as maximum-entropy occupations of one integer lattice under two multiplicity rules, closing with an open correspondence: the bounded-occupation family…
One Table, Two Regimes: Standard-Model Particles and Condensed-Matter Excitations as Patterns on the Bruhat-Tits Tree
Physics maintains two particle catalogs that never meet in one framework: the Standard Model's finite table of elementary fermions and bosons, and the open-ended zoo of quasiparticles and anyons discovered in condensed matter. This paper assembles both catalogs into a single pattern table on the…
Configuration-Space Topology and the Distinction Calculus: The Exchange Scalar, Its ±1 Shadow, and a Pre-Registered Derivation Program
Configuration-space topology (CST) derives exchange statistics from the topology of the space in which identical particles move: the fundamental group pi_1(C_N(M)) is the symmetric group S_N in d >= 3 spatial dimensions (exactly two exchange phases: boson +1, fermion -1) and the braid group B_N in d…
Vanishing ZBW Signal: The ZBW-Majorana Hypothesis as a Unified Framework for Topological Fermion Distinction
The ZBW-Majorana hypothesis, developed across four companion papers (P1--P4), establishes that Zitterbewegung (ZBW) --- the rapid trembling motion of Dirac fermions at the Compton scale --- is a $\mathbb{Z}_2$ topological observable that distinguishes Dirac from Majorana fermions at the hardware…
Cryptochrome Magnetoreception: The Radical Pair Mechanism and Its Implications for Quantum Biology
Review of radical pair mechanism in cryptochrome and avian magnetoreception.
Zitterbewegung as the Physical Realization of p-Adic Anyon Braiding
Shows that the ZBW-induced oscillatory trajectory of a Dirac fermion in a Bruhat-Tits building generates the braid group B_n, establishing ZBW as a physical mechanism for p-adic anyon braiding in topological quantum computation.
Majorana Zitterbewegung Current Correlator: Vanishing ZBW Signal as a Z2 Topological Invariant
Computes the Majorana ZBW current correlator in free-field theory. Shows that the reality condition enforces a vanishing expectation value, establishing a Z_2 topological distinction between Dirac and Majorana fermions accessible via ZBW measurement.
Zitterbewegung as a p-Adic Observable: Ultrametric Readout and Intrinsic Topological Protection
Formulates Zitterbewegung as a p-adic topological observable. Establishes that the ZBW current J_mu_ZBW carries a Z_2 invariant encoding the Dirac/Majorana distinction, and proposes ultrametric readout protocols via Bruhat-Tits buildings.
p-Adic Anyon Fusion and Braiding: Quantum Groups at Roots of Unity, Verma Modules, and Ultrametric Anyon Models
Constructs p-adic anyon models via restricted quantum groups at roots of unity with fusion and braiding.
Adelic Synthesis: The Pattern-Particle Correspondence and the Complete Arithmetic Theory of Anyons
Unifies all place-specific constructions into an adelic synthesis: anyons are adelic patterns, not particles. Proposes Adelic Topological Quantum Computation (ATQC).
p-Adic Braid Groups on Bruhat-Tits Buildings
Constructs p-adic braid groups on Bruhat-Tits buildings, establishing the geometry of discrete braiding.
Quantum Architectonics
The engineering of robust, decoherence-resistant topological qubits is currently impeded by a fragmented approach to material design that often treats control parameters in isolation. This study introduces and computationally supports the “Superconducting Quadrangle,” a unified framework integrating…
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 Origins of Number Theory
This establishes a theoretical framework wherein number-theoretic structures, particularly prime factorization, emerge as causal signatures of topological organization in quantum critical systems. We posit a foundational ontological inversion: physical reality, including particles and spacetime, is…
Winding Number as Hidden Variable
This paper proposes that physical reality emerges from a pre-geometric substrate based on the circle \(S^1\), with its integer winding numbers providing a deterministic foundation for physics. A universal computation of pattern writing, evolution, and projection generates spacetime and particles,…
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…
ASYMMETRIC ELECTRON TRANSPORT ARISING FROM INTRINSIC STRUCTURAL CHIRALITY
A central objective in modern condensed matter physics is to establish a direct, predictive link between the microscopic quantum properties of a material’s electronic structure and its macroscopic, functional responses. Recent advances in spectroscopy have provided unprecedented insight into the…
EMERGENT CORRELATION IN A LOCAL-DETERMINISTIC UNIVERSE
This paper investigates the foundational schism between the ontological coherence of superdeterminism and its epistemic rejection by the scientific community. Superdeterminism, a proposed solution to quantum non-locality, preserves locality and realism by rejecting the axiom of Measurement…
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…
Double Pendulum as a Topological Bridge
The double pendulum serves as the paradigmatic model for the transition from integrability to chaos, yet its potential as a rigorous bridge between classical nonlinear dynamics and quantum open systems remains underutilized. By treating the system’s phase space as a topologically tiled manifold…
Hamiltonian Engineering of Topological Deconfinement in Weyl Semimetals
The theoretical existence of the magnetic monopole has long represented a foundational prediction in physics, with significant implications for technology. However, astrophysical constraints (the Parker Bound) render the extraction of cosmic monopoles physically and economically non-viable. This…
Operationalizing Generalized Symmetries
The experimental realization of Fractional Chern Insulators (FCIs) in twisted moiré superlattices has opened a new frontier for topological physics, yet the classification of their underlying generalized symmetries remains theoretically abstract. This study operationalizes the framework of…
Wave-Built World
The observable universe, in all its astonishing diversity and intricate organization, is not a static collection of isolated objects but a ceaseless dance of dynamic processes. From the quantum fluctuations that shape the very fabric of spacetime itself to the rhythmic swing of pendulums, the…
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