A Field Theory of Superconducting Fluctuations and Circuit Dissipation: Inter-Site Saddles, Non-Markovian Dielectric Loss, and the cQED Quantum Floor

This paper is the third in a series of long-form summaries, one for each volume of a three-volume monograph on the inter-site field theory of 1/f noise. It summarizes the third and concluding volume, A Field Theory of Superconducting Fluctuations and Circuit Dissipation (Self-published, KDP, ASIN B0HLMS97ZZ), and builds on the classical and quantum papers of the series (10.5281/zenodo.22942255 and 10.5281/zenodo.22981164). It is written to be cited. Energy relaxation, dielectric loss, critical-current noise and flux noise in superconducting circuits are usually treated as separate problems. The standard tunneling model assumes a flat distribution of two-level-system parameters but does not supply a microscopic generator for it. Here the isolated-defect picture is replaced by a continuous, fluctuating electrostatic manifold spanning the tunnel barrier and its interfaces. Morse topology identifies the double wells of the standard tunneling model as rank-1 saddles, and the vector central limit theorem gives a Gaussian density of states whose width is fixed in closed form by the structural correlation length and the barrier thickness. From this single construction the paper derives: critical-current noise with 1/A area scaling, and the dielectric loss tangent, as longitudinal and transverse projections of one field; transmon energy relaxation through capacitive participation ratios; a geometric cross-correlation between Josephson-energy and charging-energy fluctuations that suppresses pure dephasing; a millikelvin quantum floor from soft-phonon bremsstrahlung under non-cancellation phase agitation; SQUID flux noise from a coupled surface-spin manifold; Differential Josephson Spectroscopy (DJS), an operando probe of barrier height and disorder width. Eleven principal results are stated with their assumptions and numbered for citation, together with twelve testable predictions (P1–P12) and their failure conditions. Structural results depend on stated assumptions and not on fitted constants. Quantitative results, such as the roughly 31 μs Ramsey dephasing floor for canonical planar transmons, depend on material inputs and are presented as order-of-magnitude statements.