Effective Hamiltonian Approach to Open Systems and Its Applications

TL;DR

This paper introduces a self-consistent effective Hamiltonian framework for analyzing geometric phases and decoherence-free subspaces in open quantum systems, extending to non-Markovian dynamics and providing solutions for dissipative two-level systems.

Contribution

It develops a unified effective Hamiltonian approach for open systems, including non-Markovian cases, and applies it to solve specific quantum dynamics problems.

Findings

Extended effective Hamiltonian approach to non-Markovian systems

Derived adiabatic condition for non-Markovian evolution

Solved dissipative two-level system dynamics

Abstract

By using the effective Hamiltonian approach, we present a self-consistent framework for the analysis of geometric phases and dynamically stable decoherence-free subspaces in open systems. Comparisons to the earlier works are made. This effective Hamiltonian approach is then extended to a non-Markovian case with the generalized Lindblad master equation. Based on this extended effective Hamiltonian approach, the non-Markovian master equation describing a dissipative two-level system is solved, an adiabatic evolution is defined and the corresponding adiabatic condition is given.