Dissipative and stochastic geometric phase of a qubit within a canonical Langevin framework

TL;DR

This paper investigates how dissipation and randomness influence the geometric phase of a qubit using a Langevin approach, providing exact and numerical results that extend understanding of open quantum system dynamics.

Contribution

It introduces a geometrical framework incorporating dissipative and stochastic effects into the geometric phase of a qubit, extending the Hopf fibration to open systems.

Findings

Exact geometric phase derived for a dissipative qubit.

Numerical analysis of finite temperature effects on the geometric phase.

Framework extends geometric phase concepts to open quantum systems.

Abstract

Dissipative and stochastic effects in the geometric phase of a qubit are taken into account using a geometrical description of the corresponding open--system dynamics within a canonical Langevin framework based on a Caldeira--Leggett like Hamiltonian. By extending the Hopf fibration $S^{3}\to S^{2}$ to include such effects, the exact geometric phase for a dissipative qubit is obtained, whereas numerical calculations are used to include finite temperature effects on it.