临界混沌动力系统中的短时Loschirp间隙
Short-Time Loschmidt Gap in Dynamical Systems with Critical Chaos
摘要：
本文研究了一类具有临界混沌的动力系统的Loschlaughecho F（t）。以一个具有奇异位能的受击转子为原型模型，发现经典回波显示出一个间隙（初始下降）1-F_g，其中F_g（α，ε，η）= f_cl（χ_cl equivη^{3-α}/ε），α是位能奇异性的阶数，η是初始相空间密度的扩展，ε是扰动强度。相反，量子回波间隙对α不敏感，由标度律F_g = f_q（χ_q = η^2/ε）描述，该标度律可以通过临界系统的随机矩阵理论建模来捕获。我们跟踪这种量子经典的差异，以强大的衍射效应，占主导地位的动态。
英文摘要：
We study the Loschmidt echo F(t) for a class of dynamical systems showing critical chaos. Using a kicked rotor with singular potential as a prototype model, we found that the classical echo shows a gap (initial drop) 1-F_g where F_g scales as F_g(α, ε, η)= f_cl(χ_cl equivη^{3-α}/ε); αis the order of singularity of the potential, ηis the spread of the initial phase space density and εis the perturbation strength. Instead, the quantum echo gap is insensitive to α, described by a scaling law F_g = f_q(χ_q = η^2/ε) which can be captured by a Random Matrix Theory modeling of critical systems. We trace this quantum-classical discrepancy to strong diffraction effects that dominate the dynamics.
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