In this talk, I will consider a quantum particle interacting with a target. The target is supposed to be localized and the dynamics of the particle is supposed to be generated by a Lindbladian acting on the space of trace class operators. I will discuss scattering theory for such models associated to a Lindblad operator. First, I will consider situations where the incident particle is necessarily scattered off the target, next situations where the particle may be captured by the target. An important ingredient of the analysis consists in studying scattering theory for dissipative operators on Hilbert spaces.
This is joint work with Marco Falconi, Juerg Froehlich and Baptiste Schubnel.[-]

We consider a general network of harmonic oscillators driven out of thermal equilibrium by coupling to several heat reservoirs at different temperatures. The action of the reservoirs is implemented by Langevin forces. Assuming the existence and uniqueness of the steady state of the resulting process, we construct a canonical entropy production functional $S(t)$ which satisfies the Gallavotti-Cohen fluctuation theorem. More precisely, we prove that cumulant generating function of $S(t)$ has a large-time limit $e(a)$ which is finite on a closed interval centered at $a=1/2$, infinite on its complement and satisfies the Gallavotti-Cohen symmetry $e(1-a)=e(a)$ for all $a$. It follows from well known results that $S(t)$ satisfies a global large deviation principle with a rate function $I(s)$ obeying the Gallavotti-Cohen fluctuation relation $I(-s)-I(s)=s$ for all $s$. We also consider perturbations of $S(t)$ by quadratic boundary terms and prove that they satisfy extended fluctuation relations, i.e., a global large deviation principle with a rate function that typically differs from $I(s)$ outside a finite interval. This applies to various physically relevant functionals and, in particular, to the heat dissipation rate of the network. Our approach relies on the properties of the maximal solution of a one-parameter family of algebraic matrix Ricatti equations. It turns out that the limiting cumulant generating functions of $S(t)$ and its perturbations can be computed in terms of spectral data of a Hamiltonian matrix depending on the harmonic potential of the network and the parameters of the Langevin reservoirs. This makes our approach well adapted to both analytical and numerical investigations. This is joint work with Vojkan Jaksic and Armen Shirikyan.[-]

Photonic quantum systems, which comprise multiple optical modes, have become an established platform for the experimental implementation of quantum walks. However, the implementation of large systems with many modes, this means for many step operations, a high and dynamic control of many different coin operations and variable graph structures typically poses a considerable challenge.
Time-multiplexed quantum walks are a versatile tool for the implementation of a highly flexible simulation platform with dynamic control of the different graph structures and propagation properties. Our time-multiplexing techniques is based on a loop geometry ensures a extremely high homogeneity of the quantum walk system, which results in highly reliable walk statistics. By introducing optical modulators we can control the dynamics of the photonic walks as well as input and output couplings of the states at different stages during the evolution of the walk.
Here we present our recent results on our time-multiplexed quantum walk experiments.[-]