• open quantum system
• stochastic collision models
• quantum transport
• quantum delocalization
• quantum decohrence
• noise engineering
• quantum collision models

As quantum technologies and condensed matter physics advance, the study of open quantum systems becomes increasingly necessary beyond the fact that any actual, measurable system in the laboratory cannot be perfectly isolated. In fact, under certain conditions the presence of interaction with the environment can lead to the occurrence of interesting physical phenomena, not observable in closed systems. Current technological developments of quantum systems, including their tailored coupling to their environment, create new paradigms where dissipative engineering represents a new way in which we can program and control quantum matter. The main consequence of considering the interaction between the system we are interested in, and the environment around it, is the manifestation of effects such as decoherence and dissipation. Quantum decoherence describes the loss of coherence of a quantum state and constitutes an essential concept in quantum information. Dissipation, on the other hand, is the common effect in an open system characterized by the loss of energy into the environment, which can include the loss of particles. These features of open systems have been exploited to discover new quantum regimes, via e.g. the cooling of the system, or dissipative state preparation, and also explore the emergence of new phases of matter. The use of this new physics requires, however, an understanding and modeling of the interaction between system and environment. This description is generally very complicated because of the large number of degrees of freedom of the environment itself. In this regard, approximations are often used to describe the environment, also called bath, in simpler terms. One of the descriptions of open systems in vogue in recent years is provided by quantum collision models, also denoted as repeated interaction schemes. In this description, the bath is modeled as a set of small subunits called ancillas, that interact one at a time with the system or a part of it. These interactions are assumed to be pairwise and instantaneous. This simplified discretization of the bath allows to drastically simplify the problem: this is why such models are increasingly involved in the study of quantum non-Markovian dynamics, quantum optics, and quantum thermodynamics. While these models are applied to a wide range of systems, in this thesis we will be focusing on Markovian dynamics, which implies the absence of memory effects. In particular, we want to study the transport properties of noisy media with links to biology, delocalization aspects in quantum complex networks and to quantum transport in 1D-lattices. We also analyse how transport can be favored or inhibited by acting both on the environment and the interactions inside the system. For this work, we consider a specific sub-branch of collision models, that are the stochastic collision models. In this specific formulation, the collisions are governed by a stochastic process and the unraveling of the system’s evolution can be described in terms of individual random realizations. Thus, an important role is played by the specific stochastic process that we have chosen to describe the time lapsed between two collisions. As our aim is to consider the most general noise distribution, we resort to the concept of Weibull process. In fact, the Weibull distribution allows to explore a variety of bath-induced noise regimes, by tailoring both the number of collisions occurring over time and their space and time homogeneity. We perform a systematic study by simulating a number of realizations, each sampled from the distribution leading to a particular collision configuration, and average over them to obtain the effective evolution of our system. As a prototype for our analysis, we choose an anisotropic quantum spin chain, a paradigmatic system also known as the Heisenberg XXZ model. We work at fixed magnetization, which allows us to reduce the computational complexity of the problem as the magnetization is preserved in the anisotropic Heisenberg model. We first carry out a thorough analysis of the convergence of our numerical method. Then, we move on to the study of transport and delocalization. In order to do so, we first focus on the evolution of a spin chain with one single spin impurity (excitation) and analyse the relevant observables over time. We study the magnetization and how the excitation spreads over the chain, also considering the inverse participation ratio (IPR) which is a quantitative measure of localization for an excitation, often used in quantum networks. We then address the role of noise in stochastic collision models in the presence of interactions, that in our model appear in the form of anisotropy. To do so, we need to increase the number of excitations. We thus switch to two of them and introduce the inverse ergodicity ratio (IER), which - contrary to IPR - allows us to quantify ergodicity and localization in the system case of more than one excitation. Our studies reveal that noise can be engineered to control the system transport properties. While normal structure-less noise leads to transport slowdown, we find specific regimes where we can minimize this effect, tailor the amount of coherent oscillations of the dynamics, or even enhance transport in the case where the particles are pinned together due to their interaction. This suggests that further scenarios can be found, where other competing mechanisms preventing transport, like it occurs in disordered systems or randomly connected networks, can be overcome by the engineering of collision models. We believe our study constitutes one of first step in building this understanding.