Dispersive Quantum Non-Demolition Readout, Spontaneous Tri-Sector Hamiltonian Level-Crossing, and Feshbach-Kato Quantum-Anchor Metastability on l^2(N >= 2) (K-PROTOCOL Series 00-E / Core Monograph V Complete 3-Volume Suite & Digital Twin)
Year: 2026
Type: preprint
Abstract: This repository presents the complete 3-volume monograph suite and high-resolution digital-twin simulation package of K-PROTOCOL Series 00-E (Core Monograph V, Companion Guide V, and Experimental Blueprint V). Building directly upon the five fundamental lattice invariants and the Master Vacuum Transfer Operator U_vac established in Core Monograph IV (Series 00-D, DOI: 10.5281/zenodo.23911703), we resolve the quantum measurement and wave-to-particle transition problem on the shifted harmonic Hilbert space l^2(N >= 2) with zero adjustable parameters and zero conditional (if-else) branching. 1. Core Monograph V (00-E_Core_Monograph_V_QND_Wave_Readout_and_Level_Crossing.pdf):We prove that the apparent instantaneous exponential decoherence of a quantum wave packet (V(eta) = exp(-alpha*eta)) is not a universal law of nature, but the N = 1 boundary-truncated special limit of a general N-mode impedance-matching problem on l^2(N >= 2) equipped with the normalized harmonic measure w(k) = 4 / [(k-1)k(k+1)] (Sum_{k=2..inf} w(k) = 1):- Transcendental Orthogonality (zeta(2) perp zeta(3)): Off-diagonal nearest-neighbor hopping J_k^2 = w(k)w(k+1) preserves Euler's quadratic phase invariant zeta(2) = pi^2 / 6 (J_total^2 = (238 - 8*pi^2)/9 = 0.12549937), whereas the diagonal radial self-energy operator [W_w]_{kk} = w(k)^2 / (4k) = 4 / [(k-1)^2 k^3 (k+1)^2] eliminates zeta(2) identically via Step-2 telescopic pairing (+1 - 1 = 0) and condenses into the Apery diagonal vacuum trace Tr(W_w) = 4*zeta(3) - 19/4 = Z_diag = 0.0582276126, locking an exact 24:1 infrared {2,3} doublet hierarchy (eta_{2,3} = 99.3865%) and residual ultraviolet tail Z_tail = Z_diag - 25/432 = 0.0003572423.- Evanescent Jacobi Waveguide Relaxation: An unbuffered single-surface detector (N = 1) erects a rational impedance wall kappa_0 = 2*w(2) + Delta_perp^2(2) = 4/3 + 1/8 = 35/24 = 1.458333 (power reflection R_1 = 121/3481 = 3.4760%). Coupling the entrance port to an evanescently coupled N-mode Jacobi waveguide array relaxes this barrier rationally via K_N(0) = 1 + 11 / [4(N+1)(N+2)] -> 1 (R_12 = 0.0052%, R_50 = 0.000027%).- Spontaneous Tri-Sector Level Crossing & Quantum-Anchor Metastability: The Master Vacuum Transfer Operator U_vac on H_{I_0} = C_eq^2 (+) C_polar^1 generates the linear probe Hamiltonian H(eta) = H_vac - eta * Q_probe with symplectic codimension operator Q_probe = diag(0, 1, 2) (x) I_N, where all gaps (Z_loop = Z_diag + |gamma_vac|^2 = 9.129631%, |gamma_vac| = 18.184800%), confinement stiffnesses (chi_perp = 8, xi_screen = 0.149524, R_23 = 24), and inter-sector couplings (g_01 = (1/4)|gamma_vac|^2 = 0.00826717, g_12 = (1/2)Z_tail = 0.00017862) are fixed without free parameters.- Four Deterministic Regimes: (i) Green Zone (0 <= eta <= Z_loop = 9.1296%) supporting lossless single-shot Wigner-Smith phase readout delta_WS = arcsin(eta) <= 5.2382 deg; (ii) Yellow Zone (9.1296% < eta <= 18.1400%) forming a metastable 24:1 {2,3}-doublet condensate exhibiting 100% hysteresis-free adiabatic quantum revival upon eta -> 0; (iii) Quantum-Anchor Supercooled Window (18.1848% <= eta <= 18.2601%), where Feshbach-Kato second-order level repulsion from the q = 0 wave band (Delta_eta_anchor = +0.0753%) delays the 50:50 particle localization threshold to eta_{c2}^{dressed} = 18.2601% across a hyperbolic gap 2*g_12 = Z_tail = 0.0357% (resolvable for resonator Q > Z_tail^(-1) = 2,800); and (iv) Red Zone (eta > 18.2601%) Step-2 parity collapse onto site k = 2. 2. Companion Guide V (00-E_Companion_Guide_V_Intuitive_Wave_Readout_and_Quantum_Anchor.pdf):Provides two macroscopic/microscopic thought experiments (the 12-satellite asteroid gravitational sensor array and 12 parallel tunable-stiffness sheets), Five Textbook Intuition Models, and step-by-step pocket-calculator walkthroughs. 3. Experimental Blueprint V (00-E_Experimental_Blueprint_V_Modular_Hardware_and_LC_Wind_Tunnel.pdf):Provides full hardware Bills of Materials (BOM) and protocols across three tracks: Track 1 (12-mode, 36-node tabletop high-Q LC Quantum Wind Tunnel at f_0 = 1.591549 MHz), Track 2 (room-temperature, non-vacuum, gravity-invariant 1550 nm SMF-28 all-fiber common-path interferometer and heralded SPDC single-photon Fock-state coincidence benchtop), and Track 3 (N = 50 silicon-photonics CROW chip). 4. Digital-Twin Cinema & Source Code (00-E_Video1_...gif, 00-E_Fig1_...pdf/.png, 00-E_Simulator_V_...py):Includes the 420-frame ultra-slow-motion 4-panel quantum oscilloscope animation and standalone Python engine.
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225173017