## Dynamics in optical lattices with localized dissipation.

Dissipation and decoherence, caused by the irreversible coupling of a quantum system with its environment, represent a major obstacle for a long-time coherent control of quantum states. Only recently it was realized that dissipation can be used to steer the dynamics of complex quantum systems if it can be accurately controlled. We have shown that if we apply localized single particle losses in an optical lattice filled with BEC, we can dynamically create and stabilize coherent nonlinear structures, like discrete breathers and dark solitons. Furthermore, the interplay between strong interparticle interactions and localized losses can be used to prepare either an almost-pure BEC or a macroscopically entangled "breather" state, that is a quantum superposition of discrete breathers which are localized in different lattice sites.

## Non-Equilibrium transport in Bose-Hubbard chains.

Quantum transport has gained recently interest in the context of quantum transport with biological clusters and ultracold atomic gases. In the later case it has been proposed that lattice systems can be used to create bosonic analogues to the mesoscopic systems used in electronic devices like a diode or field-effect transistor, the so-called atomtronics. We are studying the non-equilibrium transport of bosons across quantum-dot like potentials and especially the role of interatomic interactions in such systems.

## Time-Continuous Coherent-State Path Integrals.

The path integral formalism, since it was first introduced by R.P. Feynman, has been proven a powerful tool for understanding and handling quantum mechanics, quantum field theory and statistical mechanics. The introduction of the overcomplete base of coherent states has expanded the concept of path integration into a complexified phase space enlarging its range of possible applications in many areas of physics. However, it is not straightforward to define the coherent-state path integral in a continuous form. We have given a simple recipe to define the coherent-state path integral in the continuum, a definition which can be the starting point for systematic approximations for a variety systems, such as the Bose-Hubbard lattices. Furthermore, with the help of the Feynman-Vernon influence functional formalism this tool can be generalized also for open bosonic systems.