Bethe晶格上耦合非均匀无序输运通道的局域化
Localization in coupled heterogeneously disordered transport channels on the Bethe lattice
摘要：
本文研究了具有不同性质的输运通道耦合在一起的系统中的安德森局域化。这个问题自然出现在混合粒子的系统中，例如激子-极化激元，其中哪个传输通道主导耦合系统并不明显。在这里，我们解决的问题，是否强和弱无序通道之间的耦合将导致本地化（绝缘）或离域（金属）的行为。补充了早期的一维研究[H. Y. Xie，V.E. Kravtsov和M. Müller，Phys. Rev. B \textbf{86} 014205（2012）]，这里在具有参数不同的参数的双层Bethe晶格上解决了该问题。与一维解析解的比较表明，维数起着至关重要的作用。在D=1中，定位通常由较脏的通道主导，其设置后向散射率。相比之下，在贝特晶格上，离域通道几乎总是离域的，即使当耦合到强烈本地化的通道。我们推测，这种现象也适用于有限维$D>2$。相互作用的多体系统的可能影响进行了讨论。
英文摘要：
We study the Anderson localization in systems, in which transport channels with rather different properties are coupled together. This problem arises naturally in systems of hybrid particles, such as exciton-polaritons, where it is not obvious which transport channel dominates the coupled system. Here we address the question of whether the coupling between a strongly and a weakly disordered channel will result in localized (insulating) or delocalized (metallic) behavior. Complementing an earlier study in 1D [H. Y. Xie, V. E. Kravtsov, and M. Müller, Phys. Rev. B \textbf{86} 014205 (2012)], the problem is solved here on a bilayer Bethe lattice with parametrically different parameters. The comparison with the analytical solution in 1D shows that dimensionality plays a crucial role. In D=1 localization is in general dominated by the dirtier channel, which sets the backscattering rate. In contrast, on the Bethe lattice a delocalized channel remains almost always delocalized, even when coupled to strongly localized channels. We conjecture that this phenomenology holds true for finite dimensions $D>2$ as well. Possible implications for interacting many-body systems are discussed.
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