Perturbative dynamics of open quantum systems by renormalization group method

2017/05/30 by Shingo Kukita · 1 citation
Computer Science · Physics and Astronomy · #Boson #Density matrix renormalization group #Dynamics (music) #Master equation #Mathematical physics #Physics #Quantum #Quantum Information and Cryptography #Quantum dynamics #Quantum master equation #Quantum mechanics #Quantum optics and atomic interactions #Quantum system #Renormalization group #Spectroscopy and Quantum Chemical Studies #Statistical physics #quant-ph

paper · pdf · doi:10.1103/physreve.96.042113

published in Physical review. E 96(4), 042113 (American Physical Society) · 15 pages, 1 figure

arxiv created 2017/05/30 · openalex publication_date 2017/10/09 · arxiv updated 2017/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We analyze perturbative dynamics of a composite system consisting of a quantum mechanical system and an environment by the renormalization group (RG) method. The solution obtained from the RG method has no secular terms and approximates the exact solution for a long time interval. Moreover, the RG method causes a reduction of the dynamics of the composite system under some assumptions. We show that this reduced dynamics is closely related to a quantum master equation for the quantum mechanical system. We compare this dynamics with the exact dynamics in an exactly solvable spin-boson model.

Citations

• Non-Markovian dynamics of a qubit
• Completely positive post-Markovian master equation via a measurement approach
• On the assumption of initial factorization in the master equation for weakly coupled systems I: General framework
• The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory
• Invariant Manifolds