Séminaire

Stochastic differential equations (SDEs) can be used to describe cosmic ray transport in an efficient way suited for modelling on modern computing architectures. In this talk I will give an overview on how to transform Fokker-Planck (partial differential) equations into their corresponding set of SDEs and show how to solve them numerically.

Dissipation and noise arise across physics, from condensed matter to cosmology, whenever a system evolves in the presence of an unknown medium. The Schwinger–Keldysh formalism provides a systematic framework for describing such non-equilibrium and open-system dynamics. In this talk, I present an approach to cosmology that combines General Relativity with the Schwinger-Keldysh formalism. I show how symmetry, locality, and unitarity constrain the possible forms of dissipation and noise, and use these principles to derive the most general conservative and dissipative dynamics of scalar and tensor perturbations in a Friedmann–Lemaître–Robertson–Walker background. I then discuss how dissipative effects leave characteristic imprints on primordial non-Gaussianities and gravitational waves, and conclude with future prospects for dissipative dark sectors in the late universe.
Gamma-ray bursts (GRBs) and active galactic nuclei (AGNs) launch plasma outflows moving at nearly the speed of light from their central engines, and they create relativistic shock waves. Due to their extreme energies, these shocks are expected to accelerate particles via first-order Fermi acceleration, in which particles gain energy by repeatedly crossing the shock front, potentially explaining the origin of cosmic rays, especially ultra-high-energy cosmic rays. However, whether charged particles can indeed be efficiently accelerated at relativistic shocks remains under debate. A key condition for such acceleration is the presence of strong magnetic turbulence around the shock, which allows particles to be scattered and cross the shock multiple times. Yet, the physical mechanism that generates such intense turbulence is still poorly understood. In this study, we investigate a scenario where turbulence is driven downstream of the shock through the interaction between the shock front and density fluctuations pre-existing in the upstream medium. We perform 3D relativistic magnetohydrodynamic (MHD) simulations to model the turbulent structure, followed by test-particle simulations to trace particle trajectories in the resulting fields. Our results show that strong magnetic turbulence develops in the downstream region, where the magnetic field is amplified by the turbulence through the small-scale dynamo, leading to efficient shock acceleration by particle scattering. In my talk, we will discuss the conditions under which particle acceleration occurs, the nature of acceleration within magnetic turbulence, and the properties of the generated turbulence in comparison with GRB observations.