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The hierarchical equations of motion (HEOM), derived from the exact Feynman-Vernon path integral, is one of the most powerful numerical methods to simulate the dynamics of open quantum systems that are embedded in thermal environments.…

量子物理 · 物理学 2025-10-07 Meng Xu , Yaming Yan , Qiang Shi , J. Ankerhold , J. T. Stockburger

Over the last two decades, the hierarchical equations of motion (HEOM) of Tanimura and Kubo have become the equation of motion-based tool for numerically exact calculations of system-bath problems. The HEOM is today generalized to many…

量子物理 · 物理学 2023-05-15 Robert Fuchs , Marten Richter

The hierarchical equations of motion (HEOM) approach is an accurate method to simulate open system quantum dynamics, which allows for systematic convergence to numerically exact results. To represent the effects of the bath, the reservoir…

强关联电子 · 物理学 2023-05-31 Xiaohan Dan , Meng Xu , J. T. Stockburger , J. Ankerhold , Qiang Shi

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic…

化学物理 · 物理学 2020-07-10 Yoshitaka Tanimura

The hierarchical equations of motion (HEOM) provide a numerically exact approach for computing the reduced dynamics of a quantum system linearly coupled to a bath. We have found that HEOM contains temperature-dependent instabilities that…

化学物理 · 物理学 2019-05-13 Ian S. Dunn , Roel Tempelaar , David R. Reichman

The hierarchical equations of motion (HEOM) provide a numerically exact approach for simulating the dynamics of open quantum systems coupled to a harmonic bath. However, its applicability has traditionally been limited to specific spectral…

量子物理 · 物理学 2023-08-07 Meng Xu , Joachim Ankerhold

The Hierarchical equations of motion (HEOM) method is an important non-perturbative technique, allowing numerically exact treatment of open quantum systems with strong coupling and non-Markovian memory. However, its encoding of bath memory…

量子物理 · 物理学 2026-03-25 Po-Rong Lai , Jhen-Dong Lin , Yi-Te Huang , Po-Chen Kuo , Neill Lambert , Yueh-Nan Chen

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…

化学物理 · 物理学 2013-10-15 Jeremy M. Moix , Jianshu Cao

We investigate the quantum dynamics of Coulomb potential systems in thermal baths. We study these systems within the framework of open quantum dynamics theory, focusing on preserving the rotational symmetry of the entire system, including…

量子物理 · 物理学 2026-03-18 Yankai Zhang , Yoshitaka Tanimura

The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling…

化学物理 · 物理学 2022-08-17 Thomas P Fay

In non-perturbative non-Markovian open quantum systems, reaching either low temperatures with the hierarchical equations of motion (HEOM) or high temperatures with the Thermalized Time Evolving Density Operator with Orthogonal Polynomials…

We rigorously investigate the quantum non-Markovian dissipative dynamics of a system coupled to a harmonic oscillator bath by deriving hierarchical Schrodinger equations of motion (HSEOM) and studying their dynamics. The HSEOM are the…

量子物理 · 物理学 2018-07-11 Kiyoto Nakamura , Yoshitaka Tanimura

Dissipaton-equation-of-motion (DEOM) theory [Y. J. Yan, J. Chem. Phys. 140, 054105 (2014)] is an exact and nonperturbative many-particle method for open quantum systems. The existing dissipaton algebra treats also the dynamics of hybrid…

化学物理 · 物理学 2020-01-24 Yao Wang , Rui-Xue Xu , YiJing Yan

We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath…

量子物理 · 物理学 2026-04-09 Kai Müller , Walter T. Strunz

We introduce an efficient method TTN-HEOM for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme to the…

量子物理 · 物理学 2025-10-01 Xinxian Chen , Ignacio Franco

Time- and frequency resolved optical signals provide insights into the properties of light harvesting molecular complexes, including excitation energies, dipole strengths and orientations, as well as in the exciton energy flow through the…

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the…

The Hierarchical Equations of Motion (HEOM) method has become one of the cornerstones in the simulation of open quantum systems and their dynamics. It is commonly referred to as a non-perturbative method. Yet, there are certain instances,…

量子物理 · 物理学 2024-08-13 Malte Krug , Jürgen Stockburger

Excitonic models of light-harvesting complexes, where the vibrational degrees of freedom are treated as a bath, are commonly used to describe the motion of the electronic excitation through a molecule. Recent experiments point toward the…

量子物理 · 物理学 2011-07-19 Christoph Kreisbeck , Tobias Kramer , Mirta Rodriguez , Birgit Hein

Molecular vibrations in solutions, especially OH stretching and bending in water, drive ultrafast energy relaxation and dephasing in chemical and biological systems. We present a machine learning approach for constructing system-bath models…

化学物理 · 物理学 2026-03-18 Kwanghee Park , Ju-Yeon Jo , Yoshitaka Tanimura
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