Generalization of the hierarchical equations of motion theory for efficient calculations with arbitrary correlation functions
arXiv:2003.06134 · doi:10.1063/5.0007327
Abstract
The hierarchical equations of motion (HEOM) theory is one of the standard methods to rigorously describe open quantum dynamics coupled to harmonic environments. Such a model is used to capture non-Markovian and non-perturbative effects of environments appearing in ultra-fast phenomena. In the regular framework of the HEOM theory, the environment correlation functions are restricted into linear combinations of exponential functions. In this article, we present a new formulation of the HEOM theory including treatments of non-exponential correlation functions, which enables us to describe general environmental effects more efficiently and stably than the original theory and other generalizations. The library and its Python binding we developed to perform simulations based on our approach, named LibHEOM and PyHEOM respectively, are provided as supplementary material.
arXiv comment18 pages, 6 figures
References in corpus (23)
- Efficient simulation of strong system-environment interactions
- Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach
- Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
- Methods for molecular dynamics with nonadiabatic transitions
- Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity
- Exact quantum master equation via the calculus on path integrals
- Long-Lived Electronic Coherence in Dissipative Exciton-Dynamics of Light-Harvesting Complexes
- Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
- Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
- Decoherence and lead induced inter-dot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach
- Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
- Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two- dimensionalcorrelation spectroscopy
- Impact of environmentally induced fluctuations on quantum mechanically mixed electronic and vibrational pigment states in photosynthetic energy transfer and 2D electronic spectra
- Transport through an Anderson impurity: Current ringing, non-linear magnetization and a direct comparison of continuous-time quantum Monte Carlo and hierarchical quantum master equations
- Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
- Dynamics of quantum dissipation systems interacting with Fermion and Boson grand canonical bath ensembles: Hierarchical equations of motion approach
- Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities
- Influence of measurement on the life-time and the line-width of unstable systems
- Hierarchical Schrödinger Equations of Motion for Open Quantum Dynamics
- Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
- Low-Temperature Quantum Fokker-Planck and Smoluchowski Equations and Their Extension to Multistate Systems
- Probing photoisomerization processes by means of multi-dimensional electronic spectroscopy: The multi-state quantum hierarchical Fokker-Planck equation approach
- Prerequisites for relevant spectral density and convergence of reduced density matrices at low temperatures
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- Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
- Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
- QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
- Universal Prony fitting decomposition for optimized hierarchical quantum master equations
- A Multisite Decomposition of the Tensor Network Path Integrals
- Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
- Tree tensor network state approach for solving hierarchical equations of motion
- Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
- Non-Markovian Quantum Exceptional Points
- Mapping Electronic Decoherence Pathways in Molecules
- Heat transport through a superconducting artificial atom
- HierarchicalEOM.jl: An efficient Julia framework for hierarchical equations of motion in open quantum systems
- Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach
- Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics
- A simple improved low temperature correction for the hierarchical equations of motion
- Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
- Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach
- Minimal quantum thermal machine in a bandgap environment: non-Markovian features and anti-Zeno advantage
- QuantumDynamics.jl: A modular approach to simulations of dynamics of open quantum systems
- Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments
- Thermodynamic quantum Fokker-Planck equations and their application to thermostatic Stirling engine
- Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion
- A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions
- Controlling Matter Phases beyond Markov
- Heat Current in Non-Markovian Open Systems
- Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation
- Bexcitonics: Quasi-particle approach to open quantum dynamics
- Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
- Gate Operations for Superconducting Qubits and Non-Markovianity
- Strong Exciton-Vibrational Coupling in Molecular Assemblies. Dynamics using the Polaron Transformation in HEOM Space
- Spectral theory of non-Markovian dissipative phase transitions
- General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. II. Numerical Validation and the Role of Non-Markovianity
- About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
- Input-Output Hierarchical Equations Of Motion
- Dissipation Pathways in a Photosynthetic Complex
- Spectral Densities, Structured Noise and Ensemble Averaging within Open Quantum Dynamics
- Comparison between explicit and implicit discretization strategies for a dissipative thermal environment
- General framework for quantifying dissipation pathways in open quantum systems. III. Off-diagonal system-bath couplings
- A Non-Hermitian State-to-State Analysis of Transport in Aggregates with Multiple Endpoints
- Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
- Moment expansion method for composite open quantum systems including a damped oscillator mode
- Entanglement dynamics and performance of two-qubit gates for superconducting qubits under non-Markovian effects
- A tensor network representation of path integrals: Implementation and analysis
- Testing bath correlation functions for open quantum dynamics simulations
- Markovian Embeddings of Non-Markovian Open System Dynamics
- Adaptive Kink Filtration: Achieving Asymptotic Size-Independence of Path Integral Simulations Utilizing the Locality of Interactions