平衡与非平衡统计的响应理论 力学：因果关系与广义Kramers-Kronig关系

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摘要翻译：
我们考虑了Ruelle提出的一般响应理论，该理论用于描述小扰动对由公理A引起的动力系统非平衡稳态的影响。我们证明了响应函数的因果关系允许为所有非线性阶的相应的磁化率写一组Kramers-Kronig关系。然而，只有一类特殊的可观测敏感性服从Kramers-Kronig关系。给出了任意次谐波响应的具体结果，从而允许进行非常全面的Kramers-Kronig分析，并建立了将系统对短时响应的敏感性的渐近行为联系起来的和规则。这些结果推广了以前关于光学哈密顿系统和简单力学模型的发现，并阐明了考虑因果关系原理对测试自洽性的一般影响：所描述的色散关系构成了任何实验和模型生成的数据集不可避免的基准。为了将平衡系统和非平衡系统的响应理论联系起来，我们重写了Kubo的经典结果，从而得到了与Ruelle提出的响应函数形式相同的响应函数，除了相空间积分中涉及的测度之外。我们简要地讨论了这些结果，考虑到混沌假说，可能与气候研究有关。特别是，虽然涨落-耗散定理不适用于非平衡系统，但由于内部涨落和外部涨落之间的不等价性，Kramers-Kronig关系可能是定义自洽气候变化理论的更稳健的工具。
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英文标题：
《Response Theory for Equilibrium and Non-Equilibrium Statistical
  Mechanics: Causality and Generalized Kramers-Kronig relations》
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作者：
Valerio Lucarini
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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一级分类：Physics        物理学
二级分类：Strongly Correlated Electrons        强关联电子
分类描述：Quantum magnetism, non-Fermi liquids, spin liquids, quantum criticality, charge density waves, metal-insulator transitions
量子磁学，非费米液体，自旋液体，量子临界性，电荷密度波，金属-绝缘体跃迁
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一级分类：Physics        物理学
二级分类：Mathematical Physics        数学物理
分类描述：Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Mathematics        数学
二级分类：Mathematical Physics        数学物理
分类描述：math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域，为这类应用开发数学方法，或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣；主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
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一级分类：Physics        物理学
二级分类：Chaotic Dynamics        混沌动力学
分类描述：Dynamical systems, chaos, quantum chaos, topological dynamics, cycle expansions, turbulence, propagation
动力系统，混沌，量子混沌，拓扑动力学，循环展开，湍流，传播
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一级分类：Physics        物理学
二级分类：Fluid Dynamics        流体动力学
分类描述：Turbulence, instabilities, incompressible/compressible flows, reacting flows. Aero/hydrodynamics, fluid-structure interactions, acoustics. Biological fluid dynamics, micro/nanofluidics, interfacial phenomena. Complex fluids, suspensions and granular flows, porous media flows. Geophysical flows, thermoconvective and stratified flows. Mathematical and computational methods for fluid dynamics, fluid flow models, experimental techniques.
湍流，不稳定性，不可压缩/可压缩流，反应流。气动/流体力学，流体-结构相互作用，声学。生物流体力学，微/纳米流体力学，界面现象。复杂流体，悬浮液和颗粒流，多孔介质流。地球物理流，热对流和层流。流体动力学的数学和计算方法，流体流动模型，实验技术。
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英文摘要：
  We consider the general response theory proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions allows for writing a set of Kramers-Kronig relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of observable susceptibilities obey Kramers-Kronig relations. Specific results are provided for arbitrary order harmonic response, which allows for a very comprehensive Kramers-Kronig analysis and the establishment of sum rules connecting the asymptotic behavior of the susceptibility to the short-time response of the system. These results generalize previous findings on optical Hamiltonian systems and simple mechanical models, and shed light on the general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks for any experimental and model generated dataset. In order to connect the response theory for equilibrium and non equilibrium systems, we rewrite the classical results by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. We briefly discuss how these results, taking into account the chaotic hypothesis, might be relevant for climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, Kramers-Kronig relations might be more robust tools for the definition of a self-consistent theory of climate change.
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PDF链接：
https://arxiv.org/pdf/710.0958

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关键词：kramer 因果关系 RAM NIG KRA 用于 Kronig 影响 涨落 结果