Path-Integral and Real-Time Dynamics Simulations of Quantum Systems

Abstract

While classical molecular dynamics (MD) and Monte Carlo (MC) simulations have become standard theoretical tools in studies of condensed matter and material science [1], treatments of quantum systems via computer simulations are more scarce. Early proposals for studies of quantum systems have been hampered by prohibitive computational demands. However, progress in the area of computers coupled with theoretical advances brought about renewed endeavors in quantum simulations [1–8] resulting in the formulation, implementation and application of several methods to studies of quantum field theory, many-fermion systems, quantum fluids and crystals, models of nuclear matter, electronic structure of molecules, electron localization in fluids and small clusters and quantum adsorption systems. Among the methods which were developed we note [1–8] the quantum Monte Carlo (QMC) methods, Green’s function Monte Carlo (GFMC), Quantum Path-Integral Molecular Dynamics (QUPID), Path-Integral Monte Carlo (PIMC), and time-dependent self-consistent-field (TDSCF) methods in conjunction with the fast Fourier transform (FFT) method for the solution of the time-dependent Schrodinger equation and with classical molecular dynamics. In this chapter we focus on the QUPID and MD-TDSCF techniques. Following brief reviews of the methods in the next section, we turn to several illustrations of their use in recent studies. The examples which we choose are drawn from investigations performed in our laboratory. For entrance into the growing body of literature on these subjects the reader is referred to recent reviews [7,8] and to the cited references.