周期波导中波的扩散输运
Diffusive transport of waves in a periodic waveguide
摘要：
我们研究了准一维有限周期系统的经典（射线）动力学是扩散波的传播。通过考虑$L$全同混沌腔链的随机矩阵模型，我们证明了即使系统没有无序，其平均电导作为$L$的函数也呈现欧姆行为.这种行为具有平均电导衰减$N/L$，其中$N$是连接腔的引线中的传播模式的数量，对于$1\ll L \lesssim \sqrt{N}.$成立。在这种状态之后，平均电导在由无限链的传播布洛赫模式的平均数量$<N_B>$给出的${\mathcal O}(\sqrt{N})$的值处饱和。我们还研究了弱局域化修正和电导分布，并描述了其行为的系统经历了从扩散到布洛赫弹道的转变。这些预测测试在一个周期性的余弦波导。
英文摘要：
We study the propagation of waves in quasi-one-dimensional finite periodic systems whose classical (ray) dynamics is diffusive. By considering a random matrix model for a chain of $L$ identical chaotic cavities, we show that its average conductance as a function of $L$ displays an ohmic behavior even though the system has no disorder. This behavior, with an average conductance decay $N/L$, where $N$ is the number of propagating modes in the leads that connect the cavities, holds for $1\ll L \lesssim \sqrt{N}.$ After this regime, the average conductance saturates at a value of ${\mathcal O}(\sqrt{N})$ given by the average number of propagating Bloch modes $<N_B>$ of the infinite chain. We also study the weak localization correction and conductance distribution, and characterize its behavior as the system undergoes the transition from diffusive to Bloch-ballistic. These predictions are tested in a periodic cosine waveguide.
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