Density of states of a 2D system of soft--sphere fermions by path integral Monte Carlo simulations

The Wigner formulation of quantum mechanics is used to derive a new path integral representation of quantum density of states. A path integral Monte Carlo approach is developed for the numerical investigation of density of states, internal energy and spin–resolved radial distribution functions for a 2D system of strongly correlated soft–sphere fermions. The peculiarities of the density of states and internal energy distributions depending on the hardness of the soft–sphere potential and particle density are investigated and explained. In particular, at high enough densities the density of states rapidly tends to a constant value, as for an ideal system of 2D fermions.