Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, it was shown that the timelike asymptotic properties of thermal correlation functions in relativistic quantum field theory can consistently be described in terms of free fields carrying some stochastic degree of freedom which couples to the thermal background.
Abstract: It is shown that the timelike asymptotic properties of thermal correlation functions in relativistic quantum field theory can consistently be described in terms of free fields carrying some stochastic degree of freedom which couples to the thermal background. These ``asymptotic thermal fields'' have specific algebraic properties (commutation relations) and their dynamics can be expressed in terms of asymptotic field equations. The formalism is applied to interacting theories where it yields concrete non-perturbative results for the asymptotic thermal propagators. The results are consistent with the expected features of dissipative propagation of the constitutents of thermal states, outlined in previous work, and they shed new light on the non-perturbative effects of thermal backgrounds.
15 citations
15 citations
15 citations
TL;DR: In this article, a new algorithm for the asymptotic expansion of a solution to an initial value problem for systems of ordinary differential equatioms is presented, which leads to the reduction of numerical effort needed to achieve a given accuracy M compm-ed with the st~mdard uymptotlc expansion method.
Abstract: Atmtract--Pre~mt ed in this paper is a new algorithm for the asymptotic expansion of a solution to an initial value problem for ~ngularly perturbed (stiff) systems of ordinary dlfferemtial eqtmtlons. This algorithm is related to the Chapman-Enskog asymptotic expamdon method mind in the kinetic theory to derive the equatiorm of hydrodynamics, whcxeas the standard algorithm pertains to the Hilbert approach known to give inferior results. In cases of systems of ordinary differential equatioms the new algorithm leads to the reduction of numerical effort needed to achieve a given accuracy M compm-ed with the st~mdard uymptotlc expansion method. The proof of the asymptotic c~vc=lpmce is given. The numerical example demonstrates the feasibility of the new approach.
15 citations
TL;DR: In this paper, the authors prove results on the asymptotic behavior of scalar perturbations both in the approach to the initial singularity of the background model and at late times.
Abstract: In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein–Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behavior of scalar perturbations both in the approach to the initial singularity of the background model and at late times. The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. Expansions for the solutions are obtained in both asymptotic regimes. In both cases, it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. For some nonlinear equations of state, it is found that the late-time asymptotic behavior is qualitatively different from that in the linear case.
15 citations