Finite size effects in neutron star and nuclear matter simulations

Abstract

In this work we study molecular dynamics simulations of symmetric nuclear matter using a semi-classical nucleon interaction model. We show that, at sub-saturation densities and low temperatures, the solutions are non-homogeneous structures reminiscent of the "nuclear pasta" phases expected in Neutron Star Matter simulations, but shaped by artificial aspects of the simulations. We explore different geometries for the periodic boundary conditions imposed on the simulation cell: cube, hexagonal prism and truncated octahedron. We find that different cells may yield different solutions for the same physical conditions (i.e. density and temperature). The particular shape of the solution at a given density can be predicted analitically by energy minimization. We also show that even if this behavior is due to finite size effects, it does not mean that it vanishes for very large systems and it actually is independent of the system size: The system size sets the only characteristic length scale for the inhomogeneities.We then include a screened Coulomb interaction, as a model of Neutron Star Matter, and perform simulations in the three cell geometries. In this case, the competition between competing interactions of different range produces the well known nuclear pasta, with (in most cases) several structures per cell. However, we find that the results are affected by finite size in different ways depending on the geometry of the cell. In particular, at the same physical conditions and system size, the hexagonal prism yields a single structure per cell while the cubic and truncated octahedron show consistent results with more than one structure per cell. In this case, the results in every cell are expected to converge for systems much larger than the characteristic length scale that arises from the competing interactions.

Low-density nuclear matter with quantum molecular dynamics: The role of the symmetry energy

“…To see if these conclusions are affected by the finite size effects, as discussed in Ref. [40], we plan to use larger system in future.…”

Equations of state for supernovae and compact stars

“…In the classical molecular dynamics (CMD) approach (Dorso, Molinelli, and Lopez, 2011;Horowitz et al, 2011;Dorso, Giménez Molinelli, Nichols, and Lopez, 2012;Piekarewicz and Toledo Sanchez, 2012;Schneider et al, 2013;Giménez Molinelli et al, 2014;Giménez Molinelli and Dorso, 2015), a certain number of nucleons is placed inside a box of given volume to reproduce a fixed density. The velocities of the particles are chosen to represent a Maxwellian distribution at given temperature.…”

Domains and defects in nuclear pasta

“…Despite plenty of investigations using several different approaches a phase-diagram of nuclear pasta [64][65][66][67][68][69][70][71] and all of its possible topologies [65,[72][73][74][75][76][77][78][79][80] is still elusive. Amongst the issue faced are that analytical computations are limited to few symmetries [3,56,79,80], numerical simulations that use simplified nucleon-nucleon potentials are constrained by finite size effects [12,13,42,52,[81][82][83], while computational power is an impediment for detailed quantum approaches [55,63]. Furthermore, strong magnetic fields such as the ones in NSs or produced during CCSNe may significantly alter the topology of the pasta [35,[84][85][86], but are rarely taken into account.…”

“…However, those calculations are computationally expensive and, to date, are limited to hundreds to a few thousand nucleons [24,55,63,68]. Molecular dynamics (MD) simulations show that finite size effects and boundary conditions are important for such small simulations and influence the pasta shapes formed [42,52,83]. Moreover, to determine transport properties of nuclear pasta simulations with hundreds of thousands of nucleons or even more may be necessary [7,9,12,14].…”