Capabilities of object-oriented programming for the construction of quantum-kinetic BBGKY equations of high orders

TL;DR

This paper introduces an object-oriented Python framework for efficiently deriving high-order quantum-kinetic BBGKY equations, simplifying complex calculations in open quantum systems.

Contribution

The authors develop a novel object-oriented approach that automates the derivation of high-order BBGKY equations using Python classes and operator algebra principles.

Findings

Derivation of fourth-order correlation matrix equations in under a minute

Framework automates complex quantum equation derivations

Enables systematic construction of equations for many-particle systems

Abstract

Theoretical methods based on the density matrix are powerful tools to describe 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 in the quantum chain of BBGKY hierarchy 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 data. It is shown that this framework allows one to derive the equations of motion of the fourth-order correlation matrix in less than a minute.