The accurate modeling of mode hybridization and calculation of radiative
relaxation rates have been crucial to the design and optimization of
superconducting quantum devices. In this work, we introduce a spectral theory
for the electrohydrodynamics of superconductors that enables the extraction of
the relaxation rates of excitations in a general three-dimensional distribution
of superconducting bodies. Our approach addresses the long-standing problem of
formulating a modal description of open systems that is both efficient and
allows for second quantization of the radiative hybridized fields. This is
achieved through the implementation of finite but transparent boundaries
through which radiation can propagate into and out of the computational domain.
The resulting spectral problem is defined within a coarse-grained formulation
of the electrohydrodynamical equations that is suitable for the analysis of the
non-equilibrium dynamics of multiscale superconducting quantum systems.Comment: 21 pages, 12 figures, journal pape