In this seminar, I will discuss the applications of linear and
non-linear stochastic Schroedinger equations in quantum foundations as well as in the study of transport phenomena in open quantum systems.

In quantum foundations, non-linear stochastic Schroedinger equations play a fundamental role in collapse models. In these models, the wavefunction collapse in space is described by a non-linear interaction with an external classical noise, resolving the measurement problem. From a mathematical point of view, the evolution of the state of the system is described by a class of non-linear stochastic Schroedinger equations, which will be discussed.

Transport phenomena in open quantum systems are relevant in a large class of interesting systems. The study of the dynamics of a chain of harmonic oscillators locally connected to baths at an arbitrary temperature will be discussed. The advantages of solving the system dynamics using stochastic unravellings instead of working directly with the master equation will be highlighted. The study is relevant in the field of quantum thermodynamics as well as for exciton transfer in biological networks.