论文标题
$ S $矩阵能量相关性和混沌系统的时间延迟的半经典方法
Semiclassical approach to $S$ matrix energy correlations and time delay in chaotic systems
论文作者
论文摘要
$ m $二维散射矩阵$ s（e）$，它连接到混沌系统中的传出波始终是统一的，但显示出对能量的复杂依赖。这部分是用$ s（E+ε）S^\ Dagger（e-ε）$的键构建的相关器编码的，平均$ e $，以及时间延迟操作员的统计属性，$ q（e）= - i \ i \ hbar s^\ hbar s^\ Dagger ds/de $。使用半经典方法，用于具有破碎的时间逆转对称性的系统，我们得出了能量相关器的两种表达式：一个作为$ 1/m $的功率系列，其系数是$ε$的合理函数，另一个是$ε$的电源系列，其系数为$ m $ $ m $。从后者中，我们提取了$ \ rm {tr}（q^n）$的明确公式，该公式对所有$ n $都是有效的，并且与随机矩阵理论预测一致。
The $M$-dimensional scattering matrix $S(E)$ which connects incoming to outgoing waves in a chaotic systyem is always unitary, but shows complicated dependence on the energy. This is partly encoded in correlators constructed from traces of powers of $S(E+ε)S^\dagger(E-ε)$, averaged over $E$, and by the statistical properties of the time delay operator, $Q(E)=-i\hbar S^\dagger dS/dE$. Using a semiclassical approach for systems with broken time reversal symmetry, we derive two kind of expressions for the energy correlators: one as a power series in $1/M$ whose coefficients are rational functions of $ε$, and another as a power series in $ε$ whose coefficients are rational functions of $M$. From the latter we extract an explicit formula for $\rm{Tr}(Q^n)$ which is valid for all $n$ and is in agreement with random matrix theory predictions.
