  We study the single-photon transport in the coupled-resonator waveguide (CRW)
controlled by an imperfect cavity. A Lorentzian spectrum is introduced to
describe the dissipation. We find that the probability current conservation can
be broken, although the imperfect cavity is a Hermitian system. The coupling
strength between the imperfect cavity and the CRW has significant influences
near the resonant frequency. With the increase of the coupling strength, the
transmission coefficient becomes smaller. The spectral width plays a dominant
role under the off-resonant condition, where the transmission coefficient is
greatly suppressed with the increase of the spectral width. We also observe an
abrupt jump of the transmission and reflection coefficients when the hopping
amplitude is large enough. All the distinctive behaviors are closely related to
the complex effective potential induced by the imperfect cavity.
