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# Einstein relation

About: Einstein relation is a research topic. Over the lifetime, 662 publications have been published within this topic receiving 21177 citations.

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TL;DR: In this paper, a general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of timefluctuation of dynamical variables associated with such irreversible processes.

Abstract: A general type of fluctuation-dissipation theorem is discussed to show that the physical quantities such as complex susceptibility of magnetic or electric polarization and complex conductivity for electric conduction are rigorously expressed in terms of time-fluctuation of dynamical variables associated with such irreversible processes. This is a generalization of statistical mechanics which affords exact formulation as the basis of calculation of such irreversible quantities from atomistic theory. The general formalism of this statistical-mechanical theory is examined in detail. The response, relaxation, and correlation functions are defined in quantummechanical way and their relations are investigated. The formalism is illustrated by simple examples of magnetic and conduction problems. Certain sum rules are discussed for these examples. Finally it is pointed out that this theory may be looked as a generalization of the Einstein relation.

7,090 citations

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TL;DR: In this paper, a general formulation of the quantum theory of steady diffusion is given, where the boundary condition is taken into account by requiring that the solution should lead to a given distribution of average density.

Abstract: A general formulation is given to the quantum theory of steady diffusion. In seeking for a steady solution of Liouville's equation, the boundary condition is taken into account by requiring that the solution should lead to a given distribution of average density. The distribution is to be determin ed by macroscopic law of diffusion and macroscopic boundary condition. The basic equation thus obtained has a form similar to Bloch's kinetic equation and reduces to the latter in the limit of a system of weakly interacting particles. This is shown by generalizing a damping theoretical expansion of Kohn and Luttinger. It is found that the Einstein relation is valid only for the symmetric part of diffusion- and electric conductivity tensors, in agreement with Kasuya's suggestion.

1,209 citations

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TL;DR: In this paper, a framework of energetics was introduced into the stochastic dynamics described by Langevin equation in which fluctuation force obeys the Einstein relation, while the second law and steady state thermodynamics of Oono and Paniconi were obtained as ensemble properties of the process.

Abstract: We introduce a framework of energetics into the stochastic dynamics described by Langevin equation in which fluctuation force obeys the Einstein relation. The energy con servation holds in the individual realization of stochastic process, while the second law and steady state thermodynamics of Oono and Paniconi [Y. Oono and M. Paniconi, this issue] are obtained as ensemble properties of the process.

507 citations

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TL;DR: In this paper, the diffusion coefficient of a cylindrical particle moving in a thin sheet of viscous fluid is derived for the case when the embedding fluid has zero viscosity.

Abstract: The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the movement of molecules in biological membranes. In addition, the Brownian motion is calculated using the Langevin equation, and a logarithmically time-dependent diffusivity is obtained for the case when the embedding fluid has zero viscosity.

332 citations

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TL;DR: In this article, the authors derived the ratio between mobility and diffusion parameters for a Gaussian-like density of states for a wide range of organic materials (polymers or small molecules) and showed that there is an inherent dependence of the transport in trap-free disordered organic materials on the charge density.

Abstract: The ratio between mobility and diffusion parameters is derived for a Gaussian-like density of states. This steady-state analysis is expected to be applicable to a wide range of organic materials (polymers or small molecules) as it relies on the existence of quasiequilibrium only. Our analysis shows that there is an inherent dependence of the transport in trap-free disordered organic materials on the charge density. The implications for the contact phenomena and exciton generation rate in light emitting diodes as well as channel width in field-effect transistors is discussed.

253 citations