Path Integral Monte Carlo with Importance Sampling for Excitons Interacting with an Arbitrary Phonon Bath

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Path Integral Monte Carlo with Importance Sampling for Excitons Interacting with an Arbitrary Phonon Bath

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Title: Path Integral Monte Carlo with Importance Sampling for Excitons Interacting with an Arbitrary Phonon Bath
Author: Shim, Sangwoo; Aspuru-Guzik, Alan

Note: Order does not necessarily reflect citation order of authors.

Citation: Shim, Sangwoo, and Alán Aspuru-Guzik. 2012. Path integral Monte Carlo with importance sampling for excitons interacting with an arbitrary phonon bath. The Journal of Chemical Physics 137(22): 22A538.
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Abstract: The reduced density matrix of excitons coupled to a phonon bath at a finite temperature is studied using the path integral Monte Carlo method. Appropriate choices of estimators and importance sampling schemes are crucial to the performance of the Monte Carlo simulation. We show that by choosing the population-normalized estimator for the reduced density matrix, an efficient and physically-meaningful sampling function can be obtained. In addition, the nonadiabatic phonon probability density is obtained as a byproduct during the sampling procedure. For importance sampling, we adopted the Metropolis-adjusted Langevin algorithm. The analytic expression for the gradient of the target probability density function associated with the population-normalized estimator cannot be obtained in closed form without a matrix power series. An approximated gradient that can be efficiently calculated is explored to achieve better computational scaling and efficiency. Application to a simple one-dimensional model system from the previous literature confirms the correctness of the method developed in this manuscript. The displaced harmonic model system within the single exciton manifold shows the numerically exact temperature dependence of the coherence and population of the excitonic system. The sampling scheme can be applied to an arbitrary anharmonic environment, such as multichromophoric systems embedded in the protein complex. The result of this study is expected to stimulate further development of real time propagation methods that satisfy the detailed balance condition for exciton populations.
Published Version: doi:10.1063/1.4751487
Other Sources: http://arxiv.org/abs/1203.6674
Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10288716
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