The theory of wave turbulence describes the equilibrium and out-of-equilibrium states of continuous systems possessing many dispersive interacting waves. It can be thought of as the statical mechanics of an interacting wave system, allowing to predict the long-time behaviour of the system via a wave kinetic equation. It has many applications including ocean waves, nonlinear optics, and quantum fluids.
This theory can also be applied to discrete nonlinear dispersive systems such as anharmonic chains in solid-state physics. However, a formal mathematical derivation of the wave kinetic equation is still lacking. Moreover, due to the discreteness, the nonlinear interaction timescale can sometimes be unexpectedly large, especially in systems of reduced dimensionality. Other exotic behaviours, like anomalous thermal conduction, may also emerge when studying such discrete systems in out-of-equilibrium conditions. Understanding the route towards equilibrium, its fluctuations, and some out-of-equilibrium regimes, becomes of paramount importance, particularly when considering that physicists are nowadays able to craft nanoscale devices, like graphene structures, superconducting circuit networks, and nanophotonic networks that can be mimicked via semi-classical and/or quantum discrete nonlinear dispersive models.
This PhD project aims at addressing some of the open questions on the applicability, predictions, and validity of the wave turbulence theory to discrete nonlinear dispersive systems. It involves mixing branches of physics (nonlinear physics, statistical mechanics) and applied mathematics (nonlinear ODEs/PDEs). Also, much of the work will be carried out using extensive numerical simulations. The project is in collaboration with Prof. Miguel Onorato (Turin, Italy) and visits to his institution will be highly encouraged.
We are looking for an enthusiastic, talented, and extremely motivated applicant with a degree in Physics, Mathematics, or Computer Sciences (or similar). Highly desirable skills are knowledge of nonlinear waves and statistical mechanics, and excellent ability in numerical coding.