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Kelvin–Stokes theorem
About: Kelvin–Stokes theorem is a research topic. Over the lifetime, 1127 publications have been published within this topic receiving 20642 citations.
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TL;DR: In this article, the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium, which may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion.
Abstract: The linear response theory has given a general proof of the fluctuation-dissipation theorem which states that the linear response of a given system to an external perturbation is expressed in terms of fluctuation properties of the system in thermal equilibrium. This theorem may be represented by a stochastic equation describing the fluctuation, which is a generalization of the familiar Langevin equation in the classical theory of Brownian motion. In this generalized equation the friction force becomes retarded or frequency-dependent and the random force is no more white. They are related to each other by a generalized Nyquist theorem which is in fact another expression of the fluctuation-dissipation theorem. This point of view can be applied to a wide class of irreversible process including collective modes in many-particle systems as has already been shown by Mori. As an illustrative example, the density response problem is briefly discussed.
4,096 citations
842 citations
Book•
01 Jan 1933
TL;DR: The General Tauberian Theorem (GHT) as mentioned in this paper is a special Tauberians theorem which is based on the Plancherel's Theorem and the Special Tauberia Theorem.
Abstract: 1. Plancherel's Theorem 2. The General Tauberian Theorem 3. Special Tauberian Theorums 4. Generalized Harmonic Analysis.
746 citations
702 citations
TL;DR: In this paper, a general Hermitian scalar field, assumed to be an operator−valued tempered distribution, is considered and a theorem which relates certain complex Lorentz transformations to the TCP transformation is stated and proved.
Abstract: A general Hermitian scalar field, assumed to be an operator−valued tempered distribution, is considered. A theorem which relates certain complex Lorentz transformations to the TCP transformation is stated and proved. With reference to this theorem, duality conditions are considered, and it is shown that such conditions hold under various physically reasonable assumptions about the field. A theorem analogous to Borchers’ theorem on relatively local fields is stated and proved. Local internal symmetries are discussed, and it is shown that any such symmetry commutes with the Poincare
618 citations