Riccardo Fantoni

We solve numerically exactly a simple toy model to quantum general relativity or more properly to path integral on a curved space. We consider the thermal equilibrium of a quantum many-body problem on the sphere, the surface of constant positive curvature. We use path integral Monte Carlo to measure the kinetic energy, the internal energy, and the static structure of a bosons, fermions, and anyons fluid at low temperatures on the sphere. For bosons we also measure the superfluid fraction and compare its behavior at the critical temperature with the universal jump predicted by Nelson and Kosterlitz in flat space in the thermodynamic limit at the superfluid phase transition. For fermions and anyons it is necessary to use the restricted path integral recipe to overcome the sign problem. Even if this recipe is exact for the noninteracting fluid it reduces to just an approximation for an interacting system. And we make the example of the electron gas at low temperature. Snapshots of the many-body path configuration during the evolution of the computer experiment show that the “speed” of the single-particle path near the poles slows down as a consequence of the “hairy ball theorem” of Poincaré. The influence of curvature on the thermodynamic and structural properties of the many-body fluid is also studied.

We study the electron-proton binary mixture with the path integral Monte Carlo method. In order to lower the discretization error in the approach to the continuum limit we use the (end-point approximation to the) pair-product Coulomb interaction instead of the primitive approximation and a mix of the two keeping the former for the electron-proton component only and the latter for the like components. We determine some thermodynamic properties like the internal energy and the superfluid fractions and structural properties like the partial and total radial distribution functions. We compare the realistic mixture where the like particles obey to the Fermi-Dirac statistics with the artificial one where the particles obey to the Bose-Einstein statistics. While for bosons the method is exact for fermions we employ the approximate restricted path integral method with a free particle restriction. We study the mixture in its hot dense metallic atomic Hydrogen phase. We discuss the importance of approaching the continuum limit in simulations of the interior of giant planets.

In this paper, we review the physics of many bodies in the context of general relativity. Starting from the stress–energy tensor for one body and moving onto those for a swarm of bodies and for a perfect fluid, we review the relativistic hydrodynamics, kinetic theory, and statistical physics of N identical bodies. We conclude our excursion with a thermal equivalence principle in physics.

We review the physics of many bodies in the context of general relativity. Starting from the stress energy tensor for one body, for a swarm of bodies, for a perfect fluid, we review relativistic hydrodynamics, kinetic theory, and statistical physics of N identical bodies. We conclude our excursion with a thermal equivalence principle in physics.

We study the effects of treating the equilibrium of a white dwarf within general relativity. We approximate the electron gas within the star with an ideal, perfect, degenerate one. We determine the magnitude of the correction on the Newtonian (Chandrasekhar) limiting mass for central densities approaching the neutron drip critical one. We also discuss the effect of considering a temperature gradient within the star interior due to heat transfer. We point out that, whereas the degenerate hypothesis is fully legitimate, dropping the ideal and perfect assumption may lead to observable effects. This would require a careful study of the Jellium ground state on curved spacetime.

We compare two kinds of affine localizations in physics: the localization in a short range polaron and the one in a Wick rotated Anderson stochastic model. The conditions on the interaction potential necessary to see the traslational symmetry breaking localization phase transition is identical in the two problems. We therefore suggest that they should belong to the same universality class of the renormalization group for the localization phase transition.