  The static and dynamical properties of a one-dimensional quantum system
described by a non-Hermitian Hamiltonian of the so-called Hatano-Nelson type; a
tight-binding model with asymmetric (or non-reciprocal) hopping, are studied.
The static properties of the model have been much studied; the complex
spectrum, skin effect and its topological interpretation, etc. Effects of
disorder and inter-particle interaction, especially, when they coexist, may be
less understood. Here, we will also focus on its dynamical properties and
reveal some unique features in the wave-packet and entanglement (entropy)
dynamics. For that some latest (original) results based on improved numerics
(with this a system of larger system size $L$ becomes accessible) are shown.
