Analytic solution of the Boltzmann equation in an expanding system

For a massless gas with constant cross section in a homogeneous, isotropically expanding spacetime we reformulate the relativistic Boltzmann equation as a set of non-linear coupled moment equations. For a particular initial condition this set can be solved exactly, yielding the first analytical solution of the Boltzmann equation for an expanding system. The non-equilibrium behavior of this relativistic gas can be mapped onto that of a homogeneous, static non-relativistic gas of Maxwell molecules.Comment: 5 pages, 1 figure; minor changes, accepted for publication in Phys. Rev. Let

Exact solutions of the Boltzmann equation and optimized hydrodynamic approaches for relativistic heavy-ion collisions

Several recent results are reported from work aiming to improve the quantitative precision of relativistic viscous fluid dynamics for relativistic heavy-ion collisions. The dense matter created in such collisions expands in a highly anisotropic manner. Due to viscous effects this also renders the local momentum distribution anisotropic. Optimized hydrodynamic approaches account for these anisotropies already at leading order in a gradient expansion. Recently discovered exact solutions of the relativistic Boltzmann equation in anisotropically expanding systems provide a powerful testbed for such improved hydrodynamic approximations. We present the latest status of our quest for a formulation of relativistic viscous fluid dynamics that is optimized for applications to relativistic heavy-ion collisions.Comment: 4 pages, 1 figure. Talk given at Hard Probes 2015. To appear in the proceeding

Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation

We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.publishe

Massively parallel simulations of relativistic fluid dynamics on graphics processing units with CUDA

Relativistic fluid dynamics is a major component in dynamical simulations of the quark–gluon plasma created in relativistic heavy-ion collisions. Simulations of the full three-dimensional dissipative dynamics of the quark–gluon plasma with fluctuating initial conditions are computationally expensive and typically require some degree of parallelization. In this paper, we present a GPU implementation of the Kurganov–Tadmor algorithm which solves the 3 + 1d relativistic viscous hydrodynamics equations including the effects of both bulk and shear viscosities. We demonstrate that the resulting CUDA-based GPU code is approximately two orders of magnitude faster than the corresponding serial implementation of the Kurganov–Tadmor algorithm. We validate the code using (semi-)analytic tests such as the relativistic shock-tube and Gubser flow