An open quantum system, whose time evolution is governed by a master equation, can be driven into a given pure quantum state by an appropriate design of the system-reservoir coupling. This points out a route towards preparing many body states and non-equilibrium quantum phases by quantum reservoir engineering. Here we discuss in detail the example of a driven dissipative Bose Einstein Condensate of bosons and of paired fermions, where atoms in an optical lattice are coupled to a bath of Bogoliubov excitations via the atomic current representing local dissipation. In the absence of interactions the lattice gas is driven into a pure state with long range order. Weak interactions lead to a weakly mixed state, which in 3D can be understood as a depletion of the condensate, and in 1D and 2D exhibits properties reminiscent of a Luttinger liquid or a KosterlitzThouless critical phase at finite temperature, with the role of the "finite temperature" played by the interactions.

We investigate the possibility of using a dissipative process to prepare a quantum system in a desired state. We derive for any multipartite pure state a dissipative process for which this state is the unique stationary state and solve the corresponding master equation analytically. For certain states, like the Cluster states, we use this process to show that the jump operators can be chosen quasi-locally, i.e. they act non-trivially only on a few, neighboring qubits. Furthermore, the relaxation time of this dissipative process is independent of the number of subsystems. We demonstrate the general formalism by considering arbitrary MPS-PEPS states. In particular, we show that the ground state of the AKLT-model can be prepared employing a quasi-local dissipative process.

This review discusses the interface between two of the most important types of interactions between species, interspecific competition and predation. Predation has been claimed to increase, decrease, or have little effect on, the strength, impact or importance of interspecific competition. There is confusion about both the meaning of these terms and the likelihood of, and conditions required for, each of these outcomes. In this article we distinguish among three measures of the influence of predation on competitive outcomes: short-term per capita consumption or growth rates, long-term changes in density, and the probability of competitive coexistence. We then outline various theoretical mechanisms that can lead to qualitatively distinct effects of predators. The qualitative effect of predators can depend both on the mechanism of competition and on the definition of competitive strength/impact. In assessing the empirical literature, we ask: (1) What definitions of competitive strength/impact have been assumed? (2) Does strong evidence exist to support one or more of the possible mechanisms that can produce a given outcome? (3) Do biases in the choice of organism or manipulation exist, and are they likely to have influenced the conclusions reached? We conclude by discussing several unanswered questions, and espouse a stronger interchange between empirical and theoretical approaches to this important question.