Object-oriented programming as a tool for constructing high-order quantum-kinetic BBGKY equations

Theoretical methods based on the density matrix provide powerful tools for describing open quantum systems. However, such methods are complicated and intricate to be used analytically. Here we present an object-oriented framework for constructing the equation of motion of the correlation matrix at a given order within the quantum BBGKY hierarchy, which is widely used to describe the interaction of many-particle systems. The algorithm of machine derivation of equations includes the implementation of the principles of quantum mechanics and operator algebra. It is based on the description and use of classes in the Python programming environment. Class objects correspond to the elements of the equations that are derived: density matrix, correlation matrix, energy operators, commutator and several operators indexing systems. The program contains a special class that allows one to define a statistical ensemble with an infinite number of subsystems. For all classes, methods implementing the actions of the operator algebra are specified. The number of subsystems of the statistical ensemble for the physical problem and the types of subsystems between which pairwise interactions are possible are specified as an input parameters. It is shown that this framework allows one to derive the equations of motion of the fourth-order correlation matrix in less than one minute.