Hierarchical Equations for Open System Dynamics in Fermionic and Bosonic Environments

Suess, Dieter; Strunz, Walter T.; Eisfeld, Alexander

doi:10.1007/s10955-015-1236-7

Cited by 51 publications

(61 citation statements)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Current approaches include quantum master equations have successfully simulated situations with weak molecule-lead coupling via a pertubative treatment 13,14 . Another promising approach is that of hierarchical equations of motion, which works well for high temperatures and unstructured spectral densities 15,64 . In contrast, fTE-DOPA is expected to work well for arbitrary temperatures and makes no assumption on the system-bath interaction strength.…”

Section: Discussionmentioning

confidence: 99%

Efficient simulation of open quantum systems coupled to a fermionic bath

et al. 2020

View full text Add to dashboard Cite

We present and analyze the fermionic time evolving density matrix using orthogonal polynomials algorithm (fTEDOPA), which enables the numerically exact simulation of open quantum systems coupled to a fermionic environment. The method allows for simulating the time evolution of open quantum systems with arbitrary spectral densities at zero or finite temperatures with controllable and certified error. We demonstrate the efficacy of the method towards the simulation of quintessential fermionic open quantum systems including the resonant level model and quantum dot coupled to an impurity and towards simulating hitherto intractable problems in quantum transport. Furthermore, we demonstrate significant efficiency gains in the computational costs by performing simulations in the Heisenberg picture. Finally, we compare different approaches for simulating finite-temperature situations and provide guidelines for choosing between these approaches. arXiv:1909.09589v1 [quant-ph]

show abstract

Section: Discussionmentioning

confidence: 99%

Efficient simulation of open quantum systems coupled to a fermionic bath

et al. 2020

View full text Add to dashboard Cite

show abstract

“…Similar functional derivative expressions appear in the nonMarkovian quantum state diffusion stochastic Schrödinger equation [18,19] for open system dynamics. Only recently a numerically exact hierarchical scheme was developed to treat those functional derivatives [20][21][22]. In the GKSL regime, using the Born-Markov approximation, however, allows us to deal with the memory integrals over the bath correlation functions, getting rid of the functional derivatives in (7) as we will now show.…”

Section: Derivation Of the 1-master Equationmentioning

confidence: 97%

Total State Dynamics in the GKSL Regime

Megier

Strunz

2017

Open Syst. Inf. Dyn.

View full text Add to dashboard Cite

Abstract. We develop a framework that allows us to describe the dynamics of the total state of an open quantum system and its bosonic environment in the usual Born (weak coupling) and Markov approximation. By shifting the whole time-dependence into an unnormalized s-operator of the open system, the full dynamics is captured by an s-master equation of similar structure than the well-known Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation for the reduced dynamics. By varying the ordering parameter s (0 ≤ s ≤ 1) we obtain the partial Husimi representation (s = 0) and the partial GlauberSudarshan representation (s = 1) for the dynamics of the total state. For the reduced density operator the GKSL master equation can be derived easily. The case of s = 1/2, leading to a partial Wigner representation, is helpful to study the overlap of states in the total Hilbert space of system and environment.

show abstract

“…The basic equation of the HOPS approach is a stochastic hierarchy of differential equations 18,22 , which for the molecular aggregate described in the previous section takes the form (here and in the following we use ψ t = ψ(t) interchangeably)…”

Section: B the Hops Approachmentioning

confidence: 99%

“…(6). Previous works with HOPS have always used this TT scheme (with a slightly more sophisticated terminator) 18,22,35 . Convergence is checked by increasing D and recording the difference between the results for D and D − 1.…”

Section: A Triangular Truncation (Tt)mentioning

confidence: 99%

“…In Ref. 22 it was shown that HEOM can be directly derived from HOPS. Our studies indicate that as well as reducing the size (wavefunction versus density matrix), HOPS also converges faster with the depth of the hierarchy (this is related to the fact that the n-th order of HOPS already contains terms that appear in the n 2 th order of HEOM).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Flexible scheme to truncate the hierarchy of pure states

Zhang

Bentley

Eisfeld

2018

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The hierarchy of pure states (HOPS) is a wavefunction-based method that can be used for numerically modeling open quantum systems. Formally, HOPS recovers the exact system dynamics for an infinite depth of the hierarchy. However, truncation of the hierarchy is required to numerically implement HOPS. We want to choose a "good" truncation method, where by "good" we mean that it is numerically feasible to check convergence of the results. For the truncation approximation used in previous applications of HOPS, convergence checks are numerically challenging. In this work, we demonstrate the application of the "n-particle approximation" to HOPS. We also introduce a new approximation, which we call the "n-mode approximation." We then explore the convergence of these truncation approximations with respect to the number of equations required in the hierarchy in two exemplary problems: absorption and energy transfer of molecular aggregates.

show abstract

Hierarchical Equations for Open System Dynamics in Fermionic and Bosonic Environments

Cited by 51 publications

References 45 publications

Efficient simulation of open quantum systems coupled to a fermionic bath

Efficient simulation of open quantum systems coupled to a fermionic bath

Total State Dynamics in the GKSL Regime

Flexible scheme to truncate the hierarchy of pure states

Contact Info

Product

Resources

About