Prin SOPHYA

The project aims at investigating the time evolution of the out-of-equilibrium system produced in the early universe or in the early stage of ultrarelativistic nuclear collisions towards a plasma of quarks and gluons (quark-gluon plasma, QGP). This is a widespread problem in fundamental and applied science, as well as in very different areas. Despite the different features of the evolving systems, the problem is generally afforded assuming a deterministic law for the process, and algorithms are required for the resolution of systems of partial differential equations (PDEs).

The ultimate goal is to understand how ordinary matter formed and establish if the QGP evolution can be considered as a prototype for a larger class of evolving systems.

Efficient algorithms for the analysis of the QGP evolution will be developed, aiming at:

• versatility, in order to be suitable for several different use cases
• optimisation and sustainability, in order to challenge the paradigm of unlimitedly scaling the computer power to face problems with increasing complexity.

Experimental studies have shown that the QGP is a strongly coupled nearly perfect fluid. The QGP evolution cannot be treated perturbatively and is not accessible through Euclidean lattice simulations. New analytical and numerical methods are necessary to gain insights in properties like thermalisation time, low viscosity, and energy loss mechanisms.

In the project, three complementary paths will be followed to approach the dynamical problem:

• study of the evolution of an out-of-equilibrium hot and dense medium in holographic models inspired by the gauge/gravity duality, addressing the numerical instabilities in PDEs near the black-hole horizon;
• study of the plasma dynamics in the early universe during a first-order phase transition, and of the dynamics of the nucleated bubbles;
• study of the Yang-Mills equations describing the evolution of an out-of-equilibrium system with strong anisotropic pressures in a gauge invariant way on a lattice, with appropriate initialisations for proton-proton, proton-nucleus and nucleus-nucleus collisions, and the implementation of a particle-in-cell (PIC) algorithm for the diffusion of heavy quarks in the out-of-equilibrium gluonic system in the early stages of these collisions; the gluon spectrum resulting from the Yang-Mills evolution will be computed and used in a relativistic kinetic theory algorithm.

For such studies, the evolution algorithms will be optimized, with the purpose of making them suitable for similar problems in different areas.