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 analytically 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.

arXiv comment17 pages, 10 figures

References in corpus (19)

• Neutrino-pasta scattering: the opacity of nonuniform neutron-rich matter
• Dynamical response of the nuclear pasta in neutron star crusts
• Quantum Molecular Dynamics Approach to the Nuclear Matter Below the Saturation Density
• Phase diagram of nuclear "pasta" and its uncertainties in supernova cores
• Theory for the phase behaviour of a colloidal fluid with competing interactions
• Nuclear "pasta" structures in low-density nuclear matter and neutron star crust
• Microscopic Study of Slablike and Rodlike Nuclei: Quantum Molecular Dynamics Approach
• Phases of hot nuclear matter at subnuclear densities
• Topological characterization of neutron star crusts
• Phase diagram for Coulomb-frustrated phase separation in systems with negative short-range compressibility
• Three dimensional structure of low-density nuclear matter
• Gyroid Phase in Nuclear Pasta
• Dynamical aspects of isoscaling
• Enhanced molecular dynamics performance with a programmable graphics processor
• What is the limit $\hslash \to 0$ of quantum theory ?
• From the Plateau problem to periodic minimal surfaces in lipids, surfactants and diblock copolymers
• A Quasi-Classical Model of Intermediate Velocity Particle Production in Asymmetric Heavy Ion Reactions
• Effect of Coulomb Screening Length on Nuclear Pasta Simulations
• Isoscaling and the nuclear EOS

Cited by in corpus (8)

• Equations of state for supernovae and compact stars
• Phases of dense matter in compact stars
• Pasta Nucleosynthesis: Molecular dynamics simulations of nuclear statistical equilibrium
• Nuclear Equation of state for Compact Stars and Supernovae
• Impact of the neutron-star deformability on equation of state parameters
• Quantum Simulations of Nuclei and Nuclear Pasta with the Multi-resolution Adaptive Numerical Environment for Scientific Simulations
• Domains and defects in nuclear "pasta"
• Low density nuclear matter with quantum molecular dynamics : The role of the symmetry energy