  We develop a linear perturbative formalism to compute the response of an
inhomogeneous stellar disk embedded in a non-responsive dark matter halo to
perturbations like bars, spiral arms and satellite galaxy encounters. Without
self-gravity to reinforce it, the response of a Fourier mode phase mixes away
due to an intrinsic spread in the vertical ($\Omega_z$), radial ($\Omega_r$)
and azimuthal ($\Omega_\phi$) frequencies, giving rise to local phase-space
spirals. Collisional diffusion due to scattering of stars by structures like
giant molecular clouds causes super-exponential damping of the phase-spiral
amplitude. The $z-v_z$ phase-spiral is 1-armed (2-armed) for vertically
anti-symmetric (symmetric) bending (breathing) modes. Only transient
perturbations with timescales ($\tau_{\mathrm{P}}$) comparable to the vertical
oscillation period ($\tau_z \sim 1/\Omega_z$) trigger $z-v_z$ phase-spirals.
Each $(n,l,m)$ mode of the response to impulsive
($\tau_{\mathrm{P}}<\tau=1/(n\Omega_z+l\Omega_r+m\Omega_\phi)$) perturbations
is power law ($\sim \tau_{\mathrm{P}}/\tau$) suppressed, but that to adiabatic
($\tau_{\mathrm{P}}>\tau$) perturbations is exponentially weak ($\sim
\exp{\left[-\left(\tau_{\mathrm{P}}/\tau\right)^\alpha\right]}$) except
resonant ($\tau\to \infty$) modes. Slower ($\tau_{\mathrm{P}}>\tau_z$)
perturbations, e.g., distant encounters with satellite galaxies, induce
stronger bending modes. If the Gaia phase-spiral was triggered by a satellite,
Sagittarius is the leading contender as it dominates the Solar neighborhood
response of the Milky Way disk to satellite encounters. However, survival
against collisional damping necessitates that the impact occurred within $\sim
0.6-0.7$ Gyr ago. We discuss how the detailed galactic potential dictates the
phase-spiral shape: phase mixing occurs slower and phase-spirals are less wound
in the outer disk and in presence of an ambient halo.
