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arXiv 2005.05169cond-mat.stat-mech
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粗粒度二阶响应理论

Coarse-grained Second Order Response Theory

Fenna Müller, Urna Basu, Peter Sollich, Matthias Krüger

摘要:

而线性响应理论,体现了波动耗散定理,可以应用于任何水平的粗粒化,非线性响应理论基本上是微观性质。对于平衡系统的扰动,我们开发了一个精确的理论框架,用于分析粗粒度观测量对时间依赖扰动的非线性(二阶)响应,使用路径积分形式主义。由此产生的表达式涉及的相关性的粗粒度路径权重的观察。这些权重的时间对称部分以复杂的方式取决于路径和扰动协议;此外,Markovianity的缺乏防止粗粒度路径积分的切片。我们表明,这些困难是可以克服的,响应函数可以表示在对应于一个单步扰动的路径权重。因此,这种形式主义导致外推方案,其中测量粗粒度变量的线性响应足以确定其二阶响应。我们用一个精确可解的四态模型和近临界伊辛模型说明了形式主义的有效性。

英文摘要:

While linear response theory, manifested by the fluctuation dissipation theorem, can be applied at any level of coarse graining, nonlinear response theory is fundamentally of microscopic nature. For perturbations of equilibrium systems, we develop an exact theoretical framework for analyzing the nonlinear (second order) response of coarse grained observables to time-dependent perturbations, using a path-integral formalism. The resulting expressions involve correlations of the observable with coarse grained path weights. The time symmetric part of these weights depends on the paths and perturbation protocol in a complex manner; in addition, the absence of Markovianity prevents slicing of the coarse-grained path integral. We show that these difficulties can be overcome and the response function can be expressed in terms of path weights corresponding to a single-step perturbation. This formalism thus leads to an extrapolation scheme where measuring linear responses of coarse-grained variables suffices to determine their second order response. We illustrate the validity of the formalism with an exactly solvable four-state model and the near-critical Ising model.

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