Studio di stati a temperatura negativa nel modello di Fermi-Pasta-Ulam-Tsingou attraverso l'equazione cinetica per le onde ​

This thesis focuses on studying negative temperature states within the FPUT model, which describes a one-dimensional anharmonic chain of atoms. In these systems, the thermal energy is described by the kinetic equation of waves, which contains a collision integral that describes the transfer of action/energy between the various modes of the wave. The collision integral contains non-linear terms in the WKE, such as resonant wave-wave interactions between the normal modes of the harmonic chain. The system evolves to a relaxed equilibrium distribution, namely the Rayleigh-Jeans distribution, in which energy and number of particles are conserved. From these initial working conditions, a phase diagram is constructed, and physical regions with negative temperature states are observed, which are a consequence of the presence of an entropy with a limited domain that leads to a non-monotonic increasing trend and thus admits negative temperatures. Finally, it is demonstrated how the system actually evolves thanks to the WKE and how it relaxes precisely on the Rayleigh-Jeans distribution.