  Quantum circuit theory has emerged as an essential tool for the study of the
dynamics of superconducting circuits. Recently, the problem of accounting for
time-dependent driving via external magnetic fields was addressed by
Riwar-DiVincenzo in their paper - 'Circuit quantization with time-dependent
magnetic fields for realistic geometries' in which they proposed a technique to
construct a low-energy Hamiltonian for a given circuit geometry, taking as
input the external magnetic field interacting with the geometry. This result
generalises previous efforts that dealt only with discrete circuits. Moreover,
it shows through the example of a parallel-plate SQUID circuit that assigning
individual, discrete capacitances to each individual Josephson junction, as
proposed by treatments of discrete circuits, is only possible if we allow for
negative, time-dependent and even singular capacitances. In this report, we
provide numerical evidence to substantiate this result by performing
finite-difference simulations on a parallel-plate SQUID. We furnish continuous
geometries with a uniform magnetic field whose distribution we vary such that
the capacitances that are to be assigned to each Josephson junction must be
negative and even singular. Thus, the necessity for time-dependent capacitances
for appropriate quantization emerges naturally when we allow the distribution
of the magnetic field to change with time.
