In this article we provide a review of geometrical methods employed in the analysis of
quantum phase transitions and non-equilibrium dissipative phase transitions. After a …

Topological phases of matter have revolutionised the fundamental understanding of band
theory and hold great promise for next-generation technologies such as low-power …

We study the connection between Berry phases and quantum phase transitions of generic
quantum many-body systems. Consider sequences of Berry phases associated to …

When the parameters of a physical system are varied, the eigenvalues of observables can
undergo crossings and avoided crossings among themselves. It is relevant to be aware of …

The large mass difference between nuclei and electrons makes the Born–Oppenheimer
approximation a central tool in the modelling of molecular systems. The mass difference …

The main objective of this thesis is the developement of geometrical methods for the
investigation of critical phenomena. In particular, a novel approach based on the Uhlmann …