Propagator

Matrix (chemical analysis)

Diagrammatic reasoning

Quantum entanglement

Physics

Statistical physics

Path integral formulation

Matrix multiplication

Chemistry

Programming language

Pure mathematics

Path (computing)

Dimension (graph theory)

Mathematics

Computer science

Chromatography

Density matrix

Quantum mechanics

Quantum

Dissipative system

Journal of Chemical Theory and Computation

A small matrix decomposition of the path integral expression (SMatPI) that yields the reduced density matrix of a system interacting with a dissipative harmonic bath is obtained by recursively spreading the entangled influence functional terms over longer time intervals while simultaneously decreasing their magnitude until these terms become negligible. This allows summation over the path integral variables one by one through multiplication of small matrices with dimension equal to that of the bare system. The theoretical framework of the decomposition is described using a diagrammatic approach. Analytical and numerical calculations show that the necessary time length for the temporal entanglement to become negligible is practically the same as the bath-induced memory. The properties and structure of the propagator matrices are discussed, and applications to multistate systems are presented.

Small Matrix Path Integral for System-Bath Dynamics