### Thermalization in closed quantum systems

The question of whether, and how, a closed quantum system approaches equilibrium after a sufficiently long time has received renewed interest in the past few years. This interest was in particular triggered by experiments with trapped ultracold gases which, due to their isolation from the environment, are not coupled to any heat bath to a very good approximation. My research focuses on the situation where, although thermalization occurs in principle, it does so on a time scale that diverges with the system size *N*, and is therefore unobservable for macroscopic systems. Read more...

### Many-particle systems with long-range interactions

Long-range interactions are ubiquitous in nature. Nonetheless, many fundamental results or theorems in thermostatistics are restricted to short-range interacting systems. A prime example is the equivalence of statistical ensembles (like the microcanonical and the canonical one), a property that may be violated in the presence of long-range interactions [1]. In that case, the familiar thermodynamic stability conditions do not necessarily hold, specific heat can be negative, and much else. Read more...

### Energy landscapes in statistical physics

Many physical systems are characterized by an energy function. In principle, such an energy function encodes the physical behaviour of the system, as for example the trajectories of classical particles. *In praxi*, however, this information is difficult to access, as exact solutions are an exception rather than the rule. A strategy to deal with this situation consists in viewing the energy “landscape” through the eyes of a hiker, seeking his way in the mountains by focussing on peaks, valleys, and saddles. Some of my recent work has been aiming towards applying energy landscape methods in analytical calculations of statistical physical properties of classical many-body systems. Read more...

### Geometry of quantum phase transitions

Upon variation of some control parameter *λ*, a phase transition is associated with an abrupt change of the properties of the system at some critical value *λ _{c}*. Accordingly, in an information geometric language, states below, respectively above,

*λ*should be separated by a large distance with respect to a suitable metric on the space of density operators. I have worked on the fiber bundle formulation of this idea, the problems arising in the presence of level crossings, and on the application to the Lipkin-Meshkov-Glick model of fully connected SU(2) spins. Read more...

_{c}### Localization in nonlinear dynamics

The study of dynamic localization in nonlinear systems has attracted quite some interest in recent years, in particular due to the fact that it is a *generic* phenomenon in spatially discrete systems (like lattices or networks). Such localized excitations (or “discrete breathers”) can be found in a variety of systems in nonlinear optics, solid state physics, or biophysics. My research activities in this field have been focussing on exact asymptotic results, valid in the limit of small oscillation amplitudes, for time-periodic, spatially localized oscillations. Read more...