Chebyshev Hierarchical Equations of Motion for Systems with Arbitrary Spectral Densities and Temperatures

Abstract

The time evolution in open quantum systems, such as a molecular aggregate in contact with a thermal bath, still poses a complex and challenging problem. The influence of the thermal noise can be treated using a plethora of schemes, several of which decompose the corresponding correlation functions in terms of weighted sums of exponential functions. One such scheme is based on the hierarchical equations of motion (HEOM), which is built using only certain forms of bath correlation functions. In the case where the environment is described by a complex spectral density or is at a very low temperature, approaches utilizing the exponential decomposition become very inefficient. Here we utilize an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a hierarchical equations of motion approach up to an arbitrary order in the environmental coupling. These hierarchical equations are similar in structure to the popular exponential HEOM scheme, but are formulated using the derivatives of the Bessel functions. The proposed scheme is tested up to the fourth order in perturbation theory for a two-level system and compared to benchmark calculations for the case of zero-temperature quantum Ohmic and super-Ohmic noise. Furthermore, the benefits and shortcomings of the present Chebyshev-based hierarchical equations are discussed.

arXiv commentThe following article has been submitted to The Journal of Chemical Physics

References in corpus (18)

• Efficient simulation of strong system-environment interactions
• Exact quantum master equation via the calculus on path integrals
• Delocalized excitons in natural light harvesting complexes
• Hierarchy of stochastic pure states for open quantum system dynamics
• High-performance solution of hierarchical equations of motions for studying energy-transfer in light-harvesting complexes
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Quantum coherent biomolecular energy transfer with spatially correlated fluctuations
• Exciton dynamics and Quantumness of energy transfer in the Fenna-Matthews-Olson complex
• Mappings of open quantum systems onto chain representations and Markovian embeddings
• An exact equilibrium reduced density matrix formulation I: The influence of noise, disorder, and temperature on localization in excitonic systems
• Propagation Scheme for Non-Equilibrium Dynamics of Electron Transport in Nanoscale Devices
• Analytic Representations of Bath Correlation Functions for Ohmic and Superohmic Spectral Densities Using Simple Poles
• Variational dynamics of the sub-Ohmic spin-boson model on the basis of multiple Davydov ${\mathrm{D}}_1$ states
• Efficient calculation of open quantum system dynamics and time-resolved spectroscopy with Distributed Memory HEOM (DM-HEOM)
• Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures
• Lessons on electronic decoherence in molecules from exact modeling
• A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians
• A Chebychev propagator for inhomogeneous Schrödinger equations

Cited by in corpus (21)

• 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 5: The Quantum Toolbox in Python
• Efficient low temperature simulations for fermionic reservoirs with the hierarchical equations of motion method: Application to the Anderson impurity model
• Time-Dependent Atomistic Simulations of the CP29 Light-Harvesting Complex
• 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
• Unraveling current-induced dissociation mechanisms in single-molecule junctions
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
• Survey of the Hierarchical Equations of Motion in Tensor-Train format for non-Markovian quantum dynamics
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Higher-order corrections to the Redfield equation with respect to the system-bath coupling based on the hierarchical equations of motion
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach
• Managing Temperature in Open Quantum Systems Strongly Coupled with Structured Environments
• Exact description of excitonic dynamics in molecular aggregates weakly driven by light
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• Quantum Mpemba Effect Induced by Non-Markovian Exceptional Points
• Path integral Lindblad master equation through transfer tensor method & the generalized quantum master equation
• Impact of Loss Mechanisms on Linear Spectra of Excitonic and Polaritonic Aggregates
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Adaptive Kink Filtration: Achieving Asymptotic Size-Independence of Path Integral Simulations Utilizing the Locality of Interactions