Covariant formulation of relativistic quantum molecular dynamics for a system of interacting wave packets

Abstract

We present a new formulation for the mean-field propagation part of relativistic quantum molecular dynamics, simulating an $N$-body system of interacting Gaussian wave packets via Lorentz scalar and vector potentials. Covariant equations of motion are derived based on the principle of least action with a weak form of mass-shell conditions and time-fixation constraints defined with respect to a chosen foliation. However, as is common with traditional relativistic quantum molecular dynamics, the dynamics exhibits a residual dependence on the chosen foliation, which is unavoidable because a finite number of interacting degrees of freedom is not strictly compatible with relativity. Nevertheless, we show that this dependence remains small for physically reasonable choices of the foliation in practical applications. By introducing a new approximation method to the spatial integral in the equations of motion, these covariant equations of motion can be solved with a computational cost comparable to that of conventional noncovariant quantum molecular dynamics. Furthermore, the new equations of motion accurately estimate the density-dependent potential, as demonstrated through comparison of the forces with the numerical integration. We apply them to $N$-body systems interacting via the Skyrme-type potentials or the relativistic mean field to simulate heavy-ion collisions. Our results show that the derived equations of motion provide a robust approximation to the dynamics of the full numerical integrations.

arXiv comment26 pages, 13 figures. published version in PRC

References in corpus (31)

• An Introduction to PYTHIA 8.2
• Microscopic Models for Ultrarelativistic Heavy Ion Collisions
• Transport-theoretical Description of Nuclear Reactions
• Modelling the many-body dynamics of heavy ion collisions: Present status and future perspective
• Parton-Hadron-String Dynamics: an off-shell transport approach for relativistic energies
• Study of relativistic nuclear collisions at AGS energies from p+Be to Au+Au with hadronic cascade model
• Particle production and equilibrium properties within a new hadron transport approach for heavy-ion collisions
• Understanding transport simulations of heavy-ion collisions at 100 and 400 AMeV: Comparison of heavy ion transport codes under controlled conditions
• Comparison of heavy-ion transport simulations: Collision integral in a box
• Parton-Hadron-Quantum-Molecular Dynamics (PHQMD) -- A Novel Microscopic N-Body Transport Approach for Heavy-Ion Collisions, Dynamical Cluster Formation and Hypernuclei Production
• Quantum Molecular Dynamics Approach to the Nuclear Matter Below the Saturation Density
• Mean-Field Effects on Collective Flows in High-Energy Heavy-Ion Collisions at 2-158A GeV energies
• Comparison of heavy-ion transport simulations: Collision integral with pions and $\Delta$ resonances in a box
• Dynamics of clusters and fragments in heavy-ion collisions
• Elliptic flow in intermediate energy heavy ion collisions and in-medium effects
• Constraints on symmetry energy and nucleon effective mass splitting with Heavy Ion Collisions
• Comparison of Heavy-Ion Transport Simulations: Mean-field Dynamics in a Box
• Flow and interferometry results from Au+Au collisions at $\sqrt{{\text{s}}_{NN}}$ = 4.5 GeV
• Momentum-dependent potential and collective flows within the relativistic quantum molecular dynamics approach based on relativistic mean-field theory
• Progress of Quantum Molecular Dynamics model and its applications in Heavy Ion Collisions
• Mean-field update in the JAM microscopic model: Mean-field effects on collective flow in high-energy heavy-ion collisions at $\sqrt{s_{NN}}=2-20$ GeV energies
• Sensitivity of Au+Au collisions to the symmetric nuclear matter equation of state at 2 -- 5 nuclear saturation densities
• Phase transitions and critical behavior in hadronic transport with a relativistic density functional equation of state
• Nucleon Flow and Fragment Flow in Heavy Ion Reactions
• The high-density equation of state in heavy-ion collisions: Constraints from proton flow
• Molecular dynamics description of an expanding $q$/$\bar{q}$ plasma with the Nambu--Jona-Lasinio model and applications to heavy ion collisions at RHIC and LHC energies
• Sensitivity of the excitation functions of collective flow to relativistic scalar and vector meson interactions in the relativistic quantum molecular dynamics model RQMD.RMF
• Relativistic Effects in the Transverse Flow in the Molecular Dynamics Framework
• Nuclear collective dynamics in the lattice Hamiltonian Vlasov method
• Influence of the treatment of initialization and mean-field potential on the neutron to proton yield ratios
• A Poincaré covariant cascade method for high-energy nuclear collisions