A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths

Abstract

We use the "generalized hierarchical equation of motion" proposed in Paper I to study decoherence in a system coupled to a spin bath. The present methodology allows a systematic incorporation of higher order anharmonic effects of the bath in dynamical calculations. We investigate the leading order corrections to the linear response approximations for spin bath models. Two types of spin-based environments are considered: (1) a bath of spins discretized from a continuous spectral density and (2) a bath of physical spins such as nuclear or electron spins. The main difference resides with how the bath frequency and the system-bath coupling parameters are chosen to represent an environment. When discretized from a continuous spectral density, the system-bath coupling typically scales as $\sim 1/\sqrt{N_B}$ where $N_B$ is the number of bath spins. This scaling suppresses the non-Gaussian characteristics of the spin bath and justify the linear response approximations in the thermodynamic limit. For the physical spin bath models, system-bath couplings are directly deduced from spin-spin interactions with no reason to obey the $1/\sqrt{N_B}$ scaling. It is not always possible to justify the linear response approximations. Furthermore, if the spin-spin Hamiltonian and/or the bath parameters are highly symmetrical, these additional constraints generate non-Markovian and persistent dynamics that is beyond the linear response treatments.

30 pages, 9 figures

References in corpus (14)

• Prospects for Spin-Based Quantum Computing
• Non-Markovian dynamics in a spin star system: Exact solution and approximation techniques
• Hierarchical Quantum Master Equation Approach to Electronic-Vibrational Coupling in Nonequilibrium Transport through Nanosystems
• Exact dynamics in the inhomogeneous central-spin model
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
• Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Non-Markovian dynamics of a qubit coupled to an Ising spin bath
• Accurate nonadiabatic quantum dynamics on the cheap: making the most of mean field theory with master equations
• Universal Scaling of Hyperfine-Induced Electron Spin Echo Decay
• Dissipative quantum dynamics with the Surrogate Hamiltonian approach. A comparison between spin and harmonic baths
• From Zeno to anti-Zeno: decoherence-control dependence on the quantum statistics of the bath
• Two-level system in spin baths: Non-adiabatic dynamics and heat transport
• Unifying quantum heat transfer in a nonequilibrium spin-boson model with full counting statistics

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