On the Calculation of Autocorrelation Functions of Dynamical Variables

Berne, Bruce; Boon, Jean‐Pierre; Rice, Stuart A.

doi:10.1063/1.1727719

Cited by 305 publications

(91 citation statements)

References 13 publications

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“…It is worth noting that-similar to the simulation results-some analytical models also yield a global downscaling of the memory function with increasing mass of the tracer particle. [8][9][10] In all cases the scaling behavior is a result of the respective forms for (t), which fulfil (0) ϭ͗␦F 2 ͘/(Mk B T) by construction. We note that this is one of the sum rules which can be derived for the memory function.…”

Section: ͑18͒mentioning

confidence: 99%

Scaling of the memory function and Brownian motion

Kneller

Sutmann

2004

The Journal of Chemical Physics

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It has been recently shown that the velocity autocorrelation function of a tracer particle immersed in a simple liquid scales approximately with the inverse of its mass ͓J. Chem. Phys. 118, 5283 ͑2003͔͒. With increasing mass the amplitude is systematically reduced and the velocity autocorrelation function tends to a slowly decaying exponential, which is characteristic for Brownian motion. We give here an analytical proof for this behavior and comment on the usual explanation for Brownian dynamics which is based on the assumption that the memory function is proportional to a Dirac distribution. We also derive conditions for Brownian dynamics of a tracer particle which are entirely based on properties of its memory function. © 2004 American Institute of Physics. ͓DOI: 10.1063/1.1642599͔Recently, a numerical method was published which allows one to extract memory functions reliably from molecular dynamics simulations. 1,2 The concept of memory functions was introduced by Zwanzig to describe the dynamics of liquids in terms of a generalized Langevin equation. 3,4 The method proposed in Refs. 1 and 2 is based on an autoregressive model for the time series of the dynamical variable under consideration. This approach was used to examine under which conditions the dynamics of a tracer particle in a simple solvent can be described by Brownian dynamics. 5 For this purpose both the size and the mass of the tracer particle were varied independently. It was demonstrated that the size of a tracer particle strongly influences the form of its velocity memory function, whereas a change of its mass leads essentially to a global scaling of the latter. With increasing mass the amplitude of the memory function is reduced and the corresponding velocity autocorrelation function ͑VACF͒ tends to a slowly decaying exponential. The smaller the tracer particle, the stronger the effect. The scaling behavior for the memory function is exactly understood for time t ϭ0, 4 and more subtle finite size effects predicted by Español and Zuñiga 6 could be reproduced in Ref. 5. As far as we know, a scaling of the memory function for all times upon a change of the particle mass has not yet been reported.Usually the tendency towards an exponential VACF is explained by assuming an increasingly short-ranged memory function, whereas we find that the amplitude of the memory function is globally reduced with increasing mass. This is not a contradiction, since the memory function decays rapidly relative to the VACF. To discuss this point in more detail we start from the memory function equation for the VACF which has been derived by Zwanzig 3,4Here (t) is the normalized VACF of one Cartesian component v(t) of the particle velocityand (t) is the corresponding memory function. The latter can be expressed as (t)ϭ͗v exp(i͓1ϪP͔Lt)v ͘/͗v 2 ͘. Here L is the Liouville operator of the system and P is a projector. Its action on an arbitrary function in phase space f is defined through Pf ϭv͗v f ͘/͗v 2 ͘. Details about the derivation of (t) can be found in the book of ...

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Section: ͑18͒mentioning

confidence: 99%

Scaling of the memory function and Brownian motion

Kneller

Sutmann

2004

The Journal of Chemical Physics

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“…(28) and considering the momentum independent character of the impurity strength U , the Eq. (27) in the integral form reduces to…”

Section: Electron-impurity Interactionmentioning

confidence: 99%

“…(27), it is assumed that the system has cubic symmetry. Thus using the laws of conservation of energy and conservation of momentum, the part of above equation can be written as…”

Section: Electron-impurity Interactionmentioning

confidence: 99%

“…The later, known as the projection operator technique is developed by Mori and Zwanzig and then extended by others [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] . This formalism is novel as it captures the frequency and temperature dependence of a dynamical response function in terms of the corresponding generalized scattering rate.…”

Section: Introductionmentioning

confidence: 99%

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Finite frequency Seebeck coefficient of metals: A memory function approach

Bhalla

Kumar

Das

et al. 2017

Journal of Physics and Chemistry of Solids

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We study the dynamical thermoelectric transport in metals subjected to the electron-impurity and the electron-phonon interactions using the memory function formalism. We introduce a generalized Drude form for the Seebeck coefficient in terms of thermoelectric memory function and calculate the later in various temperature and frequency limits. In the zero frequency and high temperature limit, we find that our results are consistent with the experimental findings and with the traditional Boltzmann equation approach. In the low temperature limit, we find that the Seebeck coefficient is quadratic in temperature. In the finite frequency regime, we report new results: In the electronphonon interaction case, we find that the Seebeck coefficient shows frequency independent behavior both in the high frequency regime (ω ωD, where ωD is the Debye frequency) and in the low frequency regime (ω ωD), whereas in the intermediate frequencies, it is a monotonically increasing function of frequency. In the case of the electron-impurity interaction, first it decays and then after passing through a minimum it increases with the increase in frequency and saturates at high frequencies.

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“…[72][73][74] The exponential correlation functions given by the KA or RECKA models correspond to the Lorentz-Drude spectral densities. By introducing non-delta-function memory kernels, 75 we can treat a structured spectral density and vibronic coupling. 76,77 The effect of the structured spectral density in optical and transport properties of a biological-scale light-harvesting system is being studied in our group.…”

Section: Reorganization Correction To Stochastic Bath Modelmentioning

confidence: 99%

A stochastic reorganizational bath model for electronic energy transfer

Fujita

Huh

Aspuru‐Guzik

2014

The Journal of Chemical Physics

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The fluctuations of optical gap induced by the environment play crucial roles in electronic energy transfer dynamics. One of the simplest approaches to incorporate such fluctuations in energy transfer dynamics is the well known Haken-Strobl-Reineker model, in which the energy-gap fluctuation is approximated as a white noise. Recently, several groups have employed molecular dynamics simulations and excited-state calculations in conjunction to take the thermal fluctuation of excitation energies into account. Here, we discuss a rigorous connection between the stochastic and the atomistic bath models. If the phonon bath is treated classically, time evolution of the exciton-phonon system can be described by Ehrenfest dynamics. To establish the relationship between the stochastic and atomistic bath models, we employ a projection operator technique to derive the generalized Langevin equations for the energy-gap fluctuations. The stochastic bath model can be obtained as an approximation of the atomistic Ehrenfest equations via the generalized Langevin approach. Based on the connection, we propose a novel scheme to correct reorganization effects within the framework of stochastic models. The proposed scheme provides a better description of the population dynamics especially in the regime of strong exciton-phonon coupling. Finally, we discuss the effect of the bath reorganization in the absorption and fluorescence spectra of ideal J-aggregates in terms of the Stokes shifts. For this purpose, we introduce a simple relationship that relates the reorganization contribution to the Stokes shifts - the reorganization shift - to three parameters: the monomer reorganization energy, the relaxation time of the optical gap, and the exciton delocalization length. This simple relationship allows one to classify the origin of the Stokes shifts in molecular aggregates

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On the Calculation of Autocorrelation Functions of Dynamical Variables

Cited by 305 publications

References 13 publications

Scaling of the memory function and Brownian motion

Scaling of the memory function and Brownian motion

Finite frequency Seebeck coefficient of metals: A memory function approach

A stochastic reorganizational bath model for electronic energy transfer

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