Correlation functions of in- and out-of-equilibrium integrable models

Since the birth of the scientific method it became widespread in the physical sciences the idea that natural phenomena can always be understood by studying the physics of each of their elementary constituents. While this attitude led to immense discoveries on the sub-atomic particles, on the other hand it left many big questions with no proper answer. For example, one of the most fasci- nating concepts of modern-day physics is emergence, the process whereby complex macroscopic properties arise from the interaction of many simple-behaved constituents. For example, when interactions among the single constituents of a system becomes large, the properties of the whole are in general completely different from the properties of the single element. New undiscovered physics therefore emerges from the presence of such non-trivial interactions which cannot usually be treated perturbatevely, namely they cannot be addressed assuming that the interactions are small. When the constituents are confined to a one-dimensional geometry for example interac- tions become more and more effective and when prepared in an out-of-equilibrium situation they reorganize themselves in a unusual, hard-to-predict manner that possibly leads to new exotic states of matter.
My PhD research focused on non-equilibrium aspects of some one-dimensional interacting quan- tum models which are exactly solvable by Bethe Ansatz such as the Heisenberg spin chain or the Bose gas with contact interactions. The presence of an exact solution, together with the well-established experimental relevance, makes these models a perfect playground where to study the role of interactions in equilibrium and out-of-equilibrium many-body quantum systems.