Many particle simulations of the quantum electron gas using momentum-dependent potentials

A simple quasiclassical model of the quantum electron gas based on a quasiclassical dynamics with an effective momentum-dependent Hamiltonian is developed. The quantum mechanical effects corresponding to the Pauli and the Heisenberg principles are modeled by constraints in the Hamiltonian. By using the concept of minimum uncertainty wave packets, momentum-dependent effective potentials are derived. Monte Carlo and molecular dynamics calculations are carried out for ensembles of 64\char21{}512 electrons and calculations of the internal energy at several temperatures are given. A comparison with quantum Monte Carlo calculations of the mean energy for low temperatures and with Pad\'e approximations for several finite temperatures show that at least in thermodynamic equilibrium our simple model yields reasonable results.