Hierarchical equations for open system dynamics in fermionic and bosonic environments

Abstract

We present novel approaches to the dynamics of an open quantum system coupled linearly to a non-Markovian fermionic or bosonic environment. In the first approach, we obtain a hierarchy of stochastic evolution equations of the diffusion type. For the bosonic case such a hierarchy has been derived and proven suitable for efficient numerical simulations recently [arXiv:1402.4647]. The stochastic fermionic hierarchy derived here contains Grassmannian noise, which makes it difficult to simulate numerically due to its anti-commutative multiplication. Therefore, in our second approach we eliminate the noise by deriving a related hierarchy of density matrices. A similar reformulation of the bosonic hierarchy of pure states to a master equation hierarchy is also presented.

12 pages

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Cited by in corpus (30)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Efficient simulation of open quantum systems coupled to a fermionic bath
• Hierarchical Schrödinger Equations of Motion for Open Quantum Dynamics
• The Driven Liouville von Neumann Equation in Lindblad Form
• Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
• 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
• Single-photon absorption by single photosynthetic light-harvesting complexes
• Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States
• Quantum parameter estimation in a dissipative environment
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
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• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation
• How Electronic Dynamics with Pauli Exclusion Produces Fermi-Dirac Statistics
• Simulation of absorption spectra of molecular aggregates: a Hierarchy of Stochastic Pure States approach
• Effects of counter-rotating-wave terms on the non-Markovianity in quantum open systems
• Flexible scheme to truncate the hierarchy of pure states
• Realization of hierarchical equations of motion from stochastic perspectives
• Stable bipolarons in open quantum systems
• Non-Markovian Quantum State Diffusion for Spin Environments
• Open Fermi-Hubbard model: Landauer's vs. master equation approaches
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• Path-Integral Approach to Quantum Acoustics
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• Markovian Embeddings of Non-Markovian Open System Dynamics