  We study a superconducting transmission line (TL) formed by distributed LC
oscillators and excited by external magnetic fluxes which are aroused from
random magnetization (A) placed in substrate or (B) distributed at interfaces
of a two-wire TL. Low-frequency dynamics of a random magnetic field is
described based on the diffusion Langevin equation with a short-range source
caused by (a) random amplitude or (b) gradient of magnetization. For a TL
modeled as a two-port network with open and shorted ends, the effective
magnetic flux at the open end has non-local dependency on noise distribution
along the TL. The flux-flux correlation function is evaluated and analyzed for
the regimes (Aa), (Ab). (Ba), and (Bb). Essential frequency dispersion takes
place around the inverse diffusion time of random flux along the TL. Typically,
noise effect increases with size faster than the area of TL. The flux-flux
correlator can be verified both via the population relaxation rate of the
qubit, which is formed by the Josephson junction shunted by the TL with flux
noises, and via random voltage at the open end of the TL.
