Non-Markoffian excitation-relaxation processes

Grigolini, Paolo

doi:10.1007/bf02721425

Cited by 40 publications

(3 citation statements)

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“…In the present paper, EXEMs were formulated with the assumption of multi-exponential form of the friction kernel appearing in the GLE. The derived equation of motion for EXEMs is equivalent to (or even more general than 44,45 ) the original GLE, and describes the time evolution of the system only in terms of the current values of the variables (viz. without a memory term) and white noise.…”

Section: Discussionmentioning

confidence: 99%

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On the environmental modes for the generalized Langevin equation

Kawai

2015

The Journal of Chemical Physics

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The generalized Langevin equation (GLE) is used widely in molecular science and time series analysis as it offers a convenient low-dimensional description for large systems. There the dynamical effect of the environment interacting with the low-dimensional system is expressed as friction and random force. The present paper aims to investigate explicit dynamical variables to describe the dynamical modes in the environment that are derived from the GLE and defined solely in terms of the time series of the observed variable. The formulation results in equations of motion without a memory term and hence offers a more intuitive description than the GLE. The framework provided by the present study is expected to elucidate a multi-dimensional dynamics hidden behind the time series of the observed quantity.

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Section: Discussionmentioning

confidence: 99%

“…In fact, there have been several studies 15,18,24,[43][44][45][46][47][48][49][50] to express this retarded effect of the environment by explicit variables. Dynamical variables are introduced to describe the motion that exists in the environment and gives rise to the memory term in the GLE.…”

Section: Introductionmentioning

confidence: 99%

On the environmental modes for the generalized Langevin equation

Kawai

2015

The Journal of Chemical Physics

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“…To elucidate the dynamical modes that are hidden in the environment but are still interacting with the subsystem, one of the present authors, following a long line of studies, 15,19,[26][27][28][29][30][31][32][33][34][35] has recently proposed a formulation that converts the GLE into multidimensional and memoryless equations of motion 36 . The idea of expressing the GLE by equivalent set of ordinary differential equations dates back to the continued-fraction expansion of the friction kernel introduced by Mori.…”

Section: Introductionmentioning

confidence: 99%

Recovering hidden dynamical modes from the generalized Langevin equation

Kawai

Miyazaki

2016

The Journal of Chemical Physics

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In studying large molecular systems, insights can better be extracted by selecting a limited number of physical quantities for analysis rather than treating every atomic coordinate in detail. Some information may, however, be lost by projecting the total system onto a small number of coordinates. For such problems, the generalized Langevin equation (GLE) is shown to provide a useful framework to examine the interaction between the observed variables and their environment. Starting with the GLE obtained from the time series of the observed quantity, we perform a transformation to introduce a set of variables that describe dynamical modes existing in the environment. The introduced variables are shown to effectively recover the essential information of the total system that appeared to be lost by the projection.

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Theoretical Foundations

Grigolini¹

1985

Advances in Chemical Physics

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Non-Markoffian excitation-relaxation processes

Cited by 40 publications

References 50 publications

On the environmental modes for the generalized Langevin equation

On the environmental modes for the generalized Langevin equation

Recovering hidden dynamical modes from the generalized Langevin equation

Theoretical Foundations

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