Computer-aided cluster expansion: An efficient algebraic approach for open quantum many-particle systems

Abstract We introduce an equation of motion approach that allows for an approximate evaluation of the time evolution of a quantum system, where the algebraic work to derive the equations of motion is done by the computer. The introduced procedures offer a variety of different types of approximations applicable for finite systems with strong coupling as well as for arbitrary large systems where augmented mean-field theories like the cluster expansion can be applied. Program summary Program Title: EoM_main.frm Program Files doi: http://dx.doi.org/10.17632/fjwxr28j3d.1 Licensing provisions: CC By 4.0 Programming language: FORM Nature of problem: Quantum many-particle systems are an important subject in fundamental and applied research. The calculation of the time evolution of such systems is a key aspect to investigate and understand their properties. In most cases the Hilbert space that represents the quantum mechanical system is too big to be processed by numerically exact methods and approximation methods have to be used. Solution method: The program automates an equation-of-motion technique that uses the generalized Ehrenfest equation to derive the time evolution for expectation values of physical observables. The cluster expansion is used to close the hierarchy of the equations of motion. The offered method allows for a variety of different types of approximations to solve such problems with small numerical effort [1]. [1] Leymann, H.A.M., Foerster, A., Wiersig, J., 2014. Expectation value based equation-of-motion approach for open quantum systems: A general formalism. Phys. Rev. B 89 (8), 085308.