SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach (Communications in Computational Physics, 2012)
We present Path Integral Monte Carlo C code for calculation of quantummechanical transition amplitudes for 1D models. The SPEEDUP C code is based on theuse of higher-order short-time effective actions and implemented to the maximal order $p$=18 in the time of propagation (Monte Carlo time step), which substantially improvesthe convergence of discretized amplitudes to their exact continuum values. Symbolicderivation of higher-order effective actions is implemented in SPEEDUP Mathematicacodes, using the recursive Schrödinger equation approach. In addition to the general1D quantum theory, developed Mathematica codes are capable of calculating effectiveactions for specific models, for general 2D and 3D potentials, as well as for a generalmany-body theory in arbitrary number of spatial dimensions.