  We study the spectral properties of classical and quantum Markovian processes
that are reset at random times to a specific configuration or state with a
reset rate that is independent of the current state of the system. We
demonstrate that this simple reset dynamics causes a uniform shift in the
eigenvalues of the Markov generator, excluding the zero mode corresponding to
the stationary state, which has the effect of accelerating or even inducing
relaxation to a stationary state. Based on this result, we provide expressions
for the stationary state and probability current of the reset process in terms
of weighted sums over dynamical modes of the reset-free process. We also
discuss the effect of resets on processes that display metastability. We
illustrate our results with two classical stochastic processes, the totally
asymmetric random walk and the one-dimensional Brownian motion, as well as two
quantum models: a particle coherently hopping on a chain and the dissipative
transverse field Ising model, known to exhibit metastability.
