SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

TL;DR

The paper introduces SPEEDUP, a C code utilizing higher-order effective actions for efficient and accurate calculation of quantum transition amplitudes in one-dimensional models, with extensions to higher dimensions and many-body systems.

Contribution

Development of SPEEDUP C code that employs up to 18th order effective actions for improved convergence in quantum amplitude calculations, along with Mathematica tools for deriving these actions symbolically.

Findings

Significantly improved convergence of discretized amplitudes.

Capability to handle 1D, 2D, 3D, and many-body quantum models.

Enhanced computational efficiency in quantum transition amplitude calculations.

Abstract

We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use 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 improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schroedinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.