Semi-classical particle-in-cell simulations of quantum systems

The Particle-In-Cell (PIC) method has been primarily developed for tracking charged particle trajectories subject to electromagnetic fields. Using the power of modern computer technologies, e.g., graphics processing units, it is possible to efficiently track the classical paths of tens of millions of particles at the same time. In the late 1980th, Dawson formulated the idea of applying the PIC method for calculating the classical paths of virtual particles in the semi-classical approach to quantum systems. One could roughly estimate that if thousands of classical paths are needed to describe the dynamics of one quantum particle, then millions of classical paths could describe the dynamics of a whole quantum particle system. A PIC code in the frame of a semi-classical approach would therefore probably enable investigations of a number of quantum phenomena, e.g., optical and electrical properties of matter, or chemical reactions. In this contribution we report the modification of a PIC code (developed by one of the authors), originally devoted to low-temperature plasmas, for the simulation of quantum systems based on the path integral method. Numerical results for simple quantum phenomena as the quantum harmonic oscillator and quantum tunneling are discussed.