Path integral Monte Carlo

Path integral Monte Carlo (PIMC) is a quantum Monte Carlo method in the path integral formulation of quantum statistical mechanics. The equations often are applied assuming that quantum exchange does not matter (the particles are assumed to be Boltzmann particles, not the physically realistic fermion and boson particles). The theory usually is applied to calculate thermodynamic properties such as the internal energy, heat capacity, or free energy. As with all Monte Carlo method based approaches, a large number of points must be calculated. As more 'replicas' are used to integrate the path integral, the more quantum and the less classical the result is. But, the answer might become less accurate initially as more beads are added, until a point where the method starts to converge to the correct quantum answer. Because it is a statistical sampling method, PIMC takes into account all the anharmonicity, and because it is quantum, it takes into account all quantum effects (with the exception of the exchange interaction usually). An early application was to the study of liquid helium. It has been extended to include the grand canonical ensemble and the microcanonical ensemble. With agent-based PIMC the perimeter and sum borderlines of objects can be calculated.