Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
TLDR
The hierarchical equations of motion (HEOM) theory as discussed by the authors can describe numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system.Abstract:
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 oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system--bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article, presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.read more
Citations
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Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
TL;DR: It is shown that the HEOM in real time obtained when the authors include the system-bath coherence of the initial thermal equilibrium state possess the same form as those obtained from a factorized initial state, and it is found that the imaginary-time HEOM allow us to evaluate a number of thermodynamic variables, including the free energy, entropy, internal energy, heat capacity, and susceptibility.
Journal ArticleDOI
Simulation of open quantum systems by automated compression of arbitrary environments
Moritz Cygorek,Michael Cosacchi,Alexei Vagov,Vollrath M. Axt,Brendon W. Lovett,J. Keeling,Erik M. Gauger +6 more
TL;DR: In this article , the authors present a method for simulating open quantum systems with arbitrary environments that consist of a set of independent degrees of freedom, which can be iteratively constructed and compressed using matrix product state techniques.
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Efficient propagation of the hierarchical equations of motion using the Tucker and hierarchical Tucker tensors
TL;DR: In this article, the Tucker and hierarchical Tucker tensors are used to represent the reduced density operator and auxiliary density operators. And the binary tree structure of the hierarchical equations of motion (HEOM) can be used to propagate a short matrix product state constructed from these nodes.
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Finite temperature quantum dynamics of complex systems: Integrating thermo-field theories and tensor-train methods
Raffaele Borrelli,Maxim F. Gelin +1 more
TL;DR: In this paper, the authors provide fundamental theoretical tools for the development of a complete wave function formalism for the study of time-evolution of chemico-physical systems at finite temperature.
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Efficient Exploration of Hamiltonian Parameter Space for Optimal Control of Non-Markovian Open Quantum Systems
TL;DR: In this article, the authors present a general method to efficiently design optimal control sequences for non-Markovian open quantum systems and illustrate it by optimizing the shape of a laser pulse to prepare a quantum dot in a specific state.
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