Padé spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems

Hu, Jie; Luo, Meng; Jiang, Feng; Xu, Rui-Xue; Yan, YiJing

doi:10.1063/1.3602466

Cited by 213 publications

(213 citation statements)

References 24 publications

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“…[34][35][36]. Using the Padé approximant to the Bose-Einstein function in the definition of α j (t) [23] represents α j (t) in the form of Eqn. (6).…”

Section: Resultsmentioning

confidence: 99%

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Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

Wilkins

Dattani

2015

J. Chem. Theory Comput.

107

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We develop and present an improvement to the conventional technique for solving the Hierarchical Equations of Motion which reduces the memory cost by more than 75% while retaining the same convergence rate and accuracy. This allows for a full calculation of the population dynamics of the 24-site FMO trimer for long timescales with very little effort, and we present the first fully converged, exact results for the 7-site subsystem of the monomer, and for the full 24-site trimer.Owing to this new approach, our numerically exact 24-site, 2-exponential results are the most demanding HEOM calculations performed to date, surpassing the 50-site, 1-exponential results of Strumpfer and Schulten [2012, J. Chem. Thy. & Comp., 8, 2808]. We then show where our exact 7-site results deviate from the approximation of Ishizaki and Fleming [2009, Proc. Natl. Acad. Sci. USA, 106, 17255]. Our exact results are then compared to calculations using the incoherent Förster theory, and it is found that the energy transfer from the antenna to the reaction centre occurs more than 50 times faster than the fluorescence lifetime of the excitation, whether or not coherence is considered. This means that coherence is not likely to improve the efficiency of the photosynthesis.In fact, the incoherent theory often tends to over-predict the rates of energy transfer, suggesting that in some cases electronic coherence may actually slow down the photosynthetic process.

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“…[34][35][36]. Using the Padé approximant to the Bose-Einstein function in the definition of α j (t) [23] represents α j (t) in the form of Eqn. (6).…”

Section: Resultsmentioning

confidence: 99%

“…with p jk and γ jk defined by the Padé decomposition that was first introduced in [22], and explained in more detail in [23].…”

Section: Theorymentioning

confidence: 99%

Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

Wilkins

Dattani

2015

J. Chem. Theory Comput.

107

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“…[86][87][88] The present simulations employ a tolerance filter for the auxiliary density operators 89 and the [R − 1/R] Padé decomposition scheme. 90 It was found that the calculations converge at R = 4 for the T = 230 K case and R = 5 for the T = 77 K case. Fig.…”

Section: B Excited-state Proton Transfermentioning

confidence: 99%

Non-equilibrium dynamics from RPMD and CMD

Welsch

Song

Shi

et al. 2016

The Journal of Chemical Physics

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We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t4) and O(t1), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t5) and O(t2), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

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“…50 Padé points is used in the Padé spectrum decomposition (see Eq. (2)) [24]. Figure 4(a) shows the atomic structure and parition scheme for this combined GNR system.…”

Section: B Graphene Nanoribbon System (Tb Model)mentioning

confidence: 99%

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport

Xie

Kwok

Jiang

et al. 2014

The Journal of Chemical Physics

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Based on the complex absorbing potential (CAP) method, a Lorentzian expansion scheme is developed to express the self-energy. The CAP-based Lorentzian expansion of self-energy is employed to solve efficiently the Liouville-von Neumann equation of one-electron density matrix. The resulting method is applicable for both tight-binding and first-principles models, and is used to simulate the transient currents through graphene nanoribbons and a benzene molecule sandwiched between two carbon-atom-chains.

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Padé spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems

Cited by 213 publications

References 24 publications

Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

Non-equilibrium dynamics from RPMD and CMD

Complex absorbing potential based Lorentzian fitting scheme and time dependent quantum transport

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