Inter-Site Fluctuation Mechanics and Quasiparticle Generation-Recombination Noise in Kinetic Inductance Detectors (KID)

Kinetic Inductance Detectors (KIDs) represent a cornerstone of modern millimeter-wave, sub-millimeter, and far-infrared astronomical instrumentation, offering unmatched multiplexing capabilities for large-format focal planes in cosmic microwave background (CMB) polarimetry and spectroscopic survey telescopes. Operating at deep cryogenic temperatures () via the modulation of superconducting surface impedance under photon-induced pair breaking [11], KIDs rely on the kinetic inductance effect to translate Cooper-pair density variations into resonant frequency and phase shifts. However, their ultimate sensitivity is frequently limited by excess low-frequency phase and amplitude noise that traditional quasiparticle generation-recombination (G-R) and Two-Level System (TLS) surface defect models fail to fully resolve. In this work, we extend our first-principles inter-site fluctuation mechanics —previously established for Transition-Edge Sensors (TES) and cryogenic field-effect transistors—to the dissipative electrodynamic transport regime of superconducting microresonators. We present a rigorous field-theoretic derivation of the inter-site fluctuation matrix governing amorphous dielectric-superconductor interfaces and grain boundaries in high-Q superconducting microstrip and coplanar waveguide (CPW) geometries. By decoupling classical thermal activation from quantum zero-point phase dispersion, we formulate a unified stochastic master equation that couples quantum inter-site tunneling, superconductive order-parameter phase dynamics, and non-equilibrium quasiparticle generation-recombination kinetics. We derive the exact non-stationary relaxation time distribution and the resulting resonant frequency noise spectral density, and integrate this framework into a modified Mattis-Bardeen surface impedance and phase readout formulation. Finally, we outline a high-performance MATLAB simulation architecture designed to validate the tripartite noise hierarchy across cryogenic operational regimes, providing instrument designers with an uncompromising theoretical foundation for next-generation focal-plane optimization.