论文标题
来自无序介质的单个铅反射的共鸣：$σ$ - 模型方法
Resonances in a single-lead reflection from a disordered medium: $σ$-model approach
论文作者
论文摘要
使用超对称非线性$σ$ -MODEL的框架，我们开发了对假想零件的密度$ρ（γ）$的通用特征的一般非扰动表征（$ s $ -matrix poles（``width''''）的$ s $ -matrix pules（``resonances''）（``共振''）通过$ m中等的中等范围的$ m中等，以$ m中的wave和$ m中等。 $ρ（γ）$的显式表达式是针对多种时间不变性的系统实例而得出的，尤其是对于准1D和3D媒体而言。在与几个频道（$ M \ sim 1 $）的完美耦合的情况下，最显着的功能是尾巴$ρ（γ）\simγ^{ - 1} $，用于反映指数定位的狭窄共振和$ρ（γ）\ simγ^{ - 2} $ for viciention in n viciention n eacted viciential in nate n viciential nine viciential in nate n eacted nimitions n viciential nime。对于具有$ M \ gg 1 $的多模式准1D线，中间渐近线$ρ（γ）\ simγ^{ - 3/2} $显示出表现出反映足够广泛接触的扩散性质的出现的。
Using the framework of supersymmetric non-linear $σ$-model we develop a general non-perturbative characterisation of universal features of the density $ρ(Γ)$ of the imaginary parts (``width'') for $S$-matrix poles (``resonances'') describing waves incident and reflected from a disordered medium via $M$-channel waveguide/lead. Explicit expressions for $ρ(Γ)$ are derived for several instances of systems with broken time-reversal invariance, in particular for quasi-1D and 3D media. In the case of perfectly coupled lead with a few channels ($M\sim 1$) the most salient features are tails $ρ(Γ)\sim Γ^{-1}$ for narrow resonances reflecting exponential localization and $ρ(Γ)\sim Γ^{-2}$ for broad resonances reflecting states located in the vicinity of the attached wire. For multimode quasi 1D wires with $M\gg 1$, an intermediate asymptotics $ρ(Γ)\sim Γ^{-3/2}$ is shown to emerge reflecting diffusive nature of decay into wide enough contacts.
