Understanding quantum systems embedded into environment is of
particular theoretical and practical importance. The situation becomes
particularly interesting and complex when the system itself is already
an interacting many-body system, which provides novel perspectives to
quantum many-body physics. In this talk, I will present two examples
to show how the conspiracy of dissipation and interaction can
significantly change the behaviors of the quantum systems and give
rise to novel phenomena, including the algebraic decoherence behavior
and a dissipation-induced localization. Our numerical methods can be
applied to various open quantum many-body systems ranging from the
Rydberg atoms and trapped ions to quantum computational systems based
on solid-state devices (e.g. rf-SQUIDs, Solid-state qubits in diamonds
nanostructures and quantum wells).