A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

Abstract

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Forster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

20 pages, 6 figures

References in corpus (6)

• Sudden Death of Entanglement
• Long-Lived Electronic Coherence in Dissipative Exciton-Dynamics of Light-Harvesting Complexes
• An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems
• Non-Canonical Statistics of a Spin-Boson Model: Theory and Exact Monte-Carlo Simulations
• Higher-Order Kinetic Expansion of Quantum Dissipative Dynamics: Mapping Quantum Networks to Kinetic Networks
• A Novel Construction of Complex-valued Gaussian Processes with Arbitrary Spectral Densities and its Application to Excitation Energy Transfer

Cited by in corpus (55)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
• Efficient simulation of non-Markovian system-environment interaction
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. II. Beyond Linear Response of Spin Baths
• Initial System-Environment Correlations via the Transfer Tensor Method
• Forster resonance energy transfer, absorption and emission spectra in multichromophoric systems: III. Exact stochastic path integral evaluation
• Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
• Hierarchical Schrödinger Equations of Motion for Open Quantum Dynamics
• Local Temperatures Out of Equilibrium
• New Phase Space Formulations and Quantum Dynamics Approaches
• Negative Zero-Point-Energy Parameter in the Meyer-Miller Mapping Model for Nonadiabatic Dynamics
• Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation
• The hierarchical and perturbative forms of stochastic Schrödinger equations and their applications to carrier dynamics in organic materials
• Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics
• Nonadiabatic Field on Quantum Phase Space: A Century after Ehrenfest
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira-Leggett Hamiltonian
• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
• Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime
• Nonadiabatic Field with Triangle Window Functions on Quantum Phase Space
• Asymptotic Floquet states of a periodically driven spin-boson system in the nonperturbative coupling regime
• A Continued Fraction Resummation Form of Bath Relaxation Effect in the Spin-Boson Model
• Nonadiabatic Field: A Conceptually Novel Approach for Nonadiabatic Quantum Molecular Dynamics
• The Role of Protein Fluctuation Correlations in Electron Transfer in Photosynthetic Complexes
• Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction
• Realization of hierarchical equations of motion from stochastic perspectives
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• MLQD: A package for machine learning-based quantum dissipative dynamics
• Stochastic decoupling approach to the quantum dissipative dynamics: Perturbative and non-perturbative treatments
• Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath
• Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps
• Transient dynamical phase diagram of the spin-boson model
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Quantum corrections of the truncated Wigner approximation applied to an exciton transport model
• Minimalistic analytical approach to non-Markovian open quantum systems
• Input-Output Hierarchical Equations Of Motion
• Stochastic Wave-Function Simulation of Irreversible Emission Processes for Open Quantum Systems in a Non-Markovian Environment
• Noise-Assisted Quantum Exciton and Electron Transfer in Bio-Complexes with Finite Donor and Acceptor Bandwidths
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• Decoherence and Spin Echo in Biological Systems
• Simulation of Open Quantum Dynamics with Bootstrap-Based Long Short-Term Memory Recurrent Neural Network
• Photon counting statistics in the presence of spectral diffusion induced by nonequilibrium environmental fluctuations