动力系统中的指数不等式
Exponent Inequalities in Dynamical Systems
摘要：
在这封信中，我们推导出指数不等式的动力学指数$z$的稳态指数$Γ$的一般类随机驱动的动力系统。我们首先推导出一个一般的精确不等式，将响应函数和关联函数联系起来，由此推导出各种指数不等式。然后，我们区分两类动力系统，并获得不同的和互补的不等式有关$z$和$Γ$。这些不等式的后果为一系列广泛的动力学问题，包括临界动力学和Kardar-Parisi-Zhang问题进行了讨论。
英文摘要：
In this letter we derive exponent inequalities relating the dynamic exponent $z$ to the steady state exponent $Γ$ for a general class of stochastically driven dynamical systems. We begin by deriving a general exact inequality, relating the response function and the correlation function, from which the various exponent inequalities emanate. We then distinguish between two classes of dynamical systems and obtain different and complementary inequalities relating $z$ and $Γ$. The consequences of those inequalities for a wide set of dynamical problems, including critical dynamics and Kardar-Parisi-Zhang-like problems are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
