Fisica Matematica

One of the points of interest of this line of research is the study of perturbation theory for Hamiltonian systems with many degrees of freedom, in particular for nonlinear chains: applications range from the study of dynamic properties in the thermodynamic limit, looking for particular solutions such as periodic ones and spatially localized ones. This study, highlighting "slightly" chaotic behaviour for systems with many degrees of freedom, has profound consequences on the study of Statistical Mechanics, which usually requires strong chaotic properties of systems. A second theme of this line of research is therefore the development of techniques suitable for treating these systems.

Faculty

Dario Bambusi 
Andrea Carati 
Simone Paleari 
Tiziano Penati 

This research line focuses on the statistical mechanics and dynamical behavior of many-particle systems. We investigate effective behavior of interacting fermionic and bosonic quantum systems, phase transitions such as Bose–Einstein condensation, and their thermodynamic properties. We also study critical phenomena in lattice models for both classical and quantum systems, with particular emphasis on universality and scaling limits.
 

Faculty

Benedikter  
Gallone
Giacomelli

PhD students and post-docs

Diwakar Naidu 
Sabiha Tokus 
Edoardo D’Angelo

Asymptotic behavior of fluids and dispersive PDEs such as Water Waves, Euler and Navier-Stokes equations, equations of magnetohydrodynamics: construction of multi-periodic waves of small and large amplitude, asymptotic dynamics of small waves and vortices. The techniques used come from various fields: Nash-Moser type techniques, micro-local analysis, Quasi-Linear Normal Form techniques, and disruptive theory. A posteriori analysis of approximate solutions of the Navier-Stokes equation, or of magnetohydrodynamic equations; existence for long times of classical solutions of these equations, through the aforementioned post-hoc analysis. General relativity: stability of space-time tunnels, exactly solvable cosmological models with matter and scalar fields.

Faculty

Montalto
Pizzocchero

PhD students and post-docs

Luca Franzoi
Federico Morgante

The activity of this line of research is based on finding new solutions of equations via symmetries and build new integrable systems with algebraic and geometric methods. In fact there are symmetries underlying the existence of most solutions to known ordinary and partial and stochastic differential equations. On the other hand, integrable systems are those evolution systems whose solutions behave regularly, and their existence often originates in some kind of geometric or algebraic symmetry.

Faculty

Gaeta 
Gubbiotti

PhD students and post-docs

Danilo Latini