Realization of hierarchical equations of motion from stochastic perspectives

Abstract

The hierarchical equations of motion (HEOM) for a generalized quantum dissipative system is rigorously constructed in the frameworks of two different stochastic dynamical descriptions, i.e., the non-Markovian quantum state diffusion approach as well as the stochastic decoupling scheme. We demonstrated that the HEOMs obtained by these two different stochastic dynamical methods are identical. Moreover, we present some numerical examples to verify the feasibility of our formalism.

References in corpus (16)

• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Non-Markovian Quantum Trajectories Versus Master Equations: Finite Temperature Heat Bath
• Non-Markovian Relaxation of a Three-Level System: Quantum Trajectory Approach
• Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
• Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach
• Forster resonance energy transfer, absorption and emission spectra in multichromophoric systems: III. Exact stochastic path integral evaluation
• Hierarchical equations for open system dynamics in fermionic and bosonic environments
• Non-Markovian Quantum State Diffusion for Temperature-Dependent Linear Spectra of Light Harvesting Aggregates
• Quantum Zeno and anti-Zeno effects in quantum dissipative systems
• Experimental quantum Zeno effect in NMR with entanglement-based measurement
• Exact stochastic simulation of dissipation and non-Markovian effects in open quantum systems
• Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems
• Effect of bath temperature on the decoherence of quantum dissipative systems

Cited by in corpus (9)

• Quantum parameter estimation in a dissipative environment
• Non-Markovian temperature sensing
• A new approach for open quantum systems based on a phonon number representation of a harmonic oscillator bath
• Stochastic decoupling approach to the quantum dissipative dynamics: Perturbative and non-perturbative treatments
• Quantum speed limit from a quantum-state-diffusion method
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Effects of counter-rotating-wave terms on the noisy frequency estimation
• Quantum Mpemba Effect Induced by Non-Markovian Exceptional Points
• Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time