Riccati equation and the problem of decoherence

TL;DR

This paper explores how Riccati operator equations relate to deriving exact reduced dynamics of a qubit interacting with its environment, using block operator matrix theory to simplify the model to a time-independent form.

Contribution

It establishes a novel connection between Riccati equations and qubit decoherence, providing a method to obtain exact reduced dynamics in specific models.

Findings

Model reduced to a time-independent problem

Exact reduced dynamics can be obtained using Riccati equations

Block operator matrix theory facilitates analysis of qubit-environment interactions

Abstract

The block operator matrix theory is used to investigate the problem of a single qubit. We will establish a connection between the Riccati operator equation and the possibility of obtaining an exact reduced dynamics for the qubit in question. The model of the half spin particle in the rotating magnetic field coupling with the external environment is discussed. We show that the model defined in such a way can be reduced to a time independent problem.