New solution to quantum master equation for diffusion

TL;DR

This paper introduces an integral form solution to the quantum master equation for diffusion, simplifying the calculation of the density operator's evolution in diffusion channels using an operator integration method.

Contribution

It develops a new integral transformation approach for solving the quantum master equation in diffusion processes, enhancing computational convenience.

Findings

Provides a formalism for easier calculation of density operator evolution.

Utilizes the Kraus-form solution and ordered operator integration.

Facilitates analytical and numerical analysis of quantum diffusion.

Abstract

Based on the Kraus-form solution to the master equation describing diffusion we develop an integral form solution by using the method of integration within ordered product of operators, i.e., the evolution law of density operator in diffusion channel can be considered as an integration transformation from an input to its output density operator. It brings much convenience for obtaining the time evolution law in the diffusion process via this formalism.