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

Abstract

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.

Pressure of Coulomb systems with volume-dependent long-range potentials

“…We call relationship (20) between the pressure P and the potential energy of the Coulomb system as the virial theorem. To calculate W from equation (15), the following relations were used:…”

“…Many interesting features of Coulomb systems arise from the long-range nature of the potential. These include stability and thermodynamic limit [7,8] problems, thermodynamic and dielectric properties of dense plasmas [9,10], and atomistic simulation [11][12][13][14][15]. The latter faces many difficulties because the slow decrease of the potential involves many particles in the calculation of the interaction energy.…”