FeynDyn: A MATLAB program for fast numerical Feynman integral calculations for open quantum system dynamics on GPUs

Abstract

This MATLAB program calculates the dynamics of the reduced density matrix of an open quantum system modeled either by the Feynman–Vernon model or the Caldeira–Leggett model. The user gives the program a Hamiltonian matrix that describes the open quantum system as if it were in isolation, a matrix of the same size that describes how that system couples to its environment, and a spectral distribution function and temperature describing the environment’s influence on it, in addition to the open quantum system’s initial density matrix and a grid of times. With this, the program returns the reduced density matrix of the open quantum system at all moments specified by that grid of times (or just the last moment specified by the grid of times if the user makes this choice). This overall calculation can be divided into two stages: the setup of the Feynman integral, and the actual calculation of the Feynman integral for time propagation of the density matrix. When this program calculates this propagation on a multi-core CPU, it is this propagation that is usually the rate-limiting step of the calculation, but when it is calculated on a GPU, the propagation is calculated so quickly that the setup of the Feynman integral can actually become the rate-limiting step. The overhead of transferring information from the CPU to the GPU and back seems to have a negligible effect on the overall runtime of the program. When the required information cannot fit on the GPU, the user can choose to run the entire program on a CPU. Program summaryProgram title: FeynDyn.Catalogue identifier: AEPX_v1_0.Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPX_v1_0.html.Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland.Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html.No. of lines in distributed program, including test data, etc.: 703.No. of bytes in distributed program, including test data, etc.: 11026.Distribution format: tar.gz.Programming language: MATLAB R2012a.Computer: See “Operating system”.Operating system: Any operating system that can run MATLAB R2007a or above.Classification: 4.4.Nature of problem: Calculating the dynamics of the reduced density operator of an open quantum system.Solution method: Numerical Feynman integral.Running time: Depends on the input parameters. See the main text for examples.