  The laws of thermodynamics require any initial macroscopic inhomogeneity in
extended many-body systems to be smoothed out by the time evolution through the
activation of transport processes. In generic, non-integrable quantum systems,
transport is expected to be governed by a diffusion law, whereas a sufficiently
strong quenched disorder can suppress it completely due to many-body
localization of quantum excitations. Here we show that the confinement of
quasi-particles can also lead to transport suppression even if the dynamics are
generated by homogeneous Hamiltonians. We demonstrate this in the quantum Ising
chain with transverse and longitudinal magnetic fields in the paradigmatic case
of the evolution of domain-wall states. We perform extensive numerical
simulations of the dynamics which turn out to be in excellent agreement with an
effective analytical description valid within both weak and strong confinement
regimes. Our results show that the energy flow from "hot" to "cold" regions of
the chain is suppressed for all accessible times. We argue that this phenomenon
is connected with the presence of atypical states in the many-body energy
spectrum which violate the eigenstate thermalization hypothesis, as recently
reported in the literature.
