Homogeneity and Markovity of electronic dephasing in liquid solutions

Ka, Being J.; Zhang, Ming Liang; Geva, Eitan

doi:10.1063/1.2354155

Cited by 6 publications

(5 citation statements)

References 34 publications

(24 reference statements)

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“…This finding is not without precedent, as a similar observation has been made in the modeling of photosynthetic light-harvesting systems, 60 line widths in single-molecule spectroscopy, 61,62 as well as coherent single-molecule experiments. 14−17 In these studies, single molecules are seen to have narrower spectral line widths than the ensemble, leading to a distinction between inhomogeneous broadening (present only in the ensemble spectrum) due to static heterogeneity between the transition frequencies of individual molecules and homogeneous broadening due to unresolved dynamic fluctuations in the transition frequency of each molecule during the measurement.…”

Section: Numerical Results and Discussionsupporting

confidence: 67%

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

Dodin

Provazza

Coker

et al. 2022

J. Chem. Theory Comput.

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The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. We observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system−bath entanglement.

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Section: Numerical Results and Discussionsupporting

confidence: 67%

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

Dodin

Provazza

Coker

et al. 2022

J. Chem. Theory Comput.

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“…Considerable progress has already been made toward calculating the aforementioned memory kernels and inhomogeneous terms without resorting to perturbation theory. ,− Much of that progress has been based on the strategy introduced by Shi and Geva, which relies on formally exact relationships between the memory kernel and the inhomogeneous term and projection-free inputs (PFIs) that are given in terms of two-time correlation functions of the overall system. These PFIs can be obtained from quantum-mechanically exact or approximate (e.g., semiclassical or mixed quantum-classical) input methods. ,− , …”

Section: Introductionmentioning

confidence: 99%

Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations

Lyu

Mulvihill

Soley

et al. 2023

J. Chem. Theory Comput.

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The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion and dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a spin-boson model system described by various types of GQMEs. Exact memory kernels and inhomogeneous terms are obtained from short-time quantum-mechanically exact tensor-train thermo-field dynamics (TT-TFD) simulations and are compared with those obtained from an approximate linearized semiclassical method, allowing for assessment of the accuracy of these approximate memory kernels and inhomogeneous terms. Moreover, we have analyzed the computational cost of the full and reduced-dimensionality GQMEs. The scaling of the computational cost is dependent on several factors, sometimes with opposite scaling trends. The TT-TFD memory kernels can provide insights on the main sources of inaccuracies of GQME approaches when combined with approximate input methods and pave the road for the development of quantum circuits that implement GQMEs on digital quantum computers.

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“…24 The Zhang−Ka−Geva approach was also used to calculate the memory kernel for an atomistic model of a two-state chromophore in liquid solution and to study the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics. 25 Rabani and co-workers have calculated the memory kernel of a quantum dot with electron-phonon interaction 27 and the Anderson impurity model 26,28,29,31 from quantum-mechanically exact projection-free inputs within the Zhang−Ka− Geva approach and introduced a method for calculating the memory kernel from the reduced system propagator. 36 The Shi−Geva and Zhang−Ka−Geva approaches were further explored and extended by Montoya-Castillo and Reichman, who introduced new forms of calculating the projection-free inputs.…”

Section: Introductionmentioning

confidence: 99%

“…Efforts over the last two decades have been directed at developing, testing, and applying computational methods for calculating the memory kernel, using either quantum-mechanically exact or approximate semiclassical and mixed quantum-classical methods. − The motivation for doing so comes from the fact that the memory kernel is often short-lived, which makes it possible to limit the use of exact or approximate methods to relatively short times, where they are often more accurate or more cost-effective or both. The short lifetime of the memory kernel combined with its scaling with the number of electronic states (∼ N e 4 , where N e is the number of electronic states) makes the GQME approach most beneficial for systems with a small number of electronic DOF and a memory time that is too long for weak coupling to be valid but shorter than the time scale of system dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The Shi–Geva approach was later extended and streamlined by Zhang, Ka, and Geva in a manner that made it possible to account for a wider class of projection operators and initial conditions . The Zhang–Ka–Geva approach was also used to calculate the memory kernel for an atomistic model of a two-state chromophore in liquid solution and to study the sensitivity of photon echo signals to the heterogeneity and non-Markovity of the underlying solvation dynamics …”

Section: Introductionmentioning

confidence: 99%

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A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation

Mulvihill

Geva

2021

J. Phys. Chem. B

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The generalized quantum master equation (GQME) provides a powerful framework for simulating electronic energy, charge, and coherence transfer dynamics in molecular systems. Within this framework, the effect of the nuclear degrees of freedom on the time evolution of the electronic reduced density matrix is fully captured by a memory kernel superoperator. However, the actual memory kernel depends on the choice of projection operator and is therefore not unique. Furthermore, calculating the memory kernel can be done in multiple ways that use different forms of projection-free inputs. Although the electronic dynamics is invariant to those choices when quantum-mechanically exact projection-free inputs are used, this is not the case when they are obtained via more feasible semiclassical or mixed quantum-classical approximate methods. Furthermore, the accuracy and numerical stability of the resulting electronic dynamics has been observed to be sensitive to the above-mentioned choices when approximate methods are used to calculate the projection-free inputs. In this article, we provide a systematic road map to 30 possible pathways for calculating the memory kernel and highlight how they are related as well as the ways in which they differ. We also compare the performance of different pathways in the context of the spin-boson benchmark model, with the projection-free inputs obtained via a mapping Hamiltonian linearized semiclassical method. In this case, we find that expressing the memory kernel with an exponential operator where the projection operator precedes the Liouvillian yields the most accurate and most numerically stable results.

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Homogeneity and Markovity of electronic dephasing in liquid solutions

Cited by 6 publications

References 34 publications

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

Tensor-Train Thermo-Field Memory Kernels for Generalized Quantum Master Equations

A Road Map to Various Pathways for Calculating the Memory Kernel of the Generalized Quantum Master Equation

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