Journal ArticleDOI
A cumulant expansion for stochastic linear differential equations. I
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TLDR
In this paper, a systematic expansion for the expectation value of a stochastic process is given, where the expansion parameter is the product of the magnitude of the fluctuations and their auto-correlation time.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 1974-06-01. It has received 308 citations till now. The article focuses on the topics: Stochastic differential equation & Stochastic partial differential equation.read more
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White matter integrity, fiber count, and other fallacies: The do's and don'ts of diffusion MRI
TL;DR: The physics of DW-MRI is reviewed, currently preferred methodology is indicated, and the limits of interpretation of its results are explained, with a list of 'Do's and Don'ts' which define good practice in this expanding area of imaging neuroscience.
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Dynamics of non-Markovian open quantum systems
Inés de Vega,Daniel Alonso +1 more
TL;DR: In this paper, an overview is given of some of the most important techniques available to tackle the dynamics of an OQS beyond the Markov approximation, which requires a large separation of system and environment time scales.
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Stochastic differential equations
TL;DR: In this article, the authors define stochastic differential equations (SDEs) and their occurrence in physics, and present an alternative treatment, applicable only in a special case, but not confined to small ατ c.
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On the relation of protein dynamics and exciton relaxation in pigment–protein complexes: An estimation of the spectral density and a theory for the calculation of optical spectra
Thomas Renger,Rudolph A. Marcus +1 more
TL;DR: In this article, a theory for calculating time and frequency-domain optical spectra of pigment-protein complexes using a density matrix approach is presented. But the authors do not consider the non-Markovian effects in the exciton-vibrational coupling.
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Journal ArticleDOI
Generalized cumulant expansion method
TL;DR: The notion of cumulants and cumulant functions was introduced in this paper, where a moment generating function of a set of stochastic variables defines the cumulus or the semi-invariants and the cumULant function, and the definition of average may be greatly generalized as far as the condition of the average of unity is unity.
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An Operator calculus having applications in quantum electrodynamics
TL;DR: In this article, an ordering subscript is introduced to indicate the order of operation of noncommuting quantities, such that AsBs′ means AB or BA depending on whether s exceeds s′ or vice versa.
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Stochastic liouville equations
TL;DR: In this article, the authors considered a simple example of an oscillator with random frequency modulation and then, concepts of slow and fast modulation are considered, which can be generalized to more general types of stochastic Liouville equations.