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

The Wigner formulation of quantum mechanics is used to derive a new path integral representation of the quantum density of state. A path integral Monte Carlo approach is developed for the numerical investigation of the 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