随机扭曲量子波导的Lifshits尾
Lifshits tails for randomly twisted quantum waveguides
摘要：
本文研究了具有任意安德森型扭转$γ$的三维扭转波导上的Dirichlet Laplacian $H_γ$。引入了$H_γ$算符的积分态密度$N_γ$，并研究了$N_γ$的Lifshits尾，即$N_γ(E)$作为$E \downarrow \inf {\rm supp}\, dN_γ$的渐近行为.特别地，我们研究了在无穷远处的单点扭曲的衰减率的Lifshits指数的依赖性。
英文摘要：
We consider the Dirichlet Laplacian $H_γ$ on a 3D twisted waveguide with random Anderson-type twisting $γ$. We introduce the integrated density of states $N_γ$ for the operator $H_γ$, and investigate the Lifshits tails of $N_γ$, i.e. the asymptotic behavior of $N_γ(E)$ as $E \downarrow \inf {\rm supp}\, dN_γ$. In particular, we study the dependence of the Lifshits exponent on the decay rate of the single-site twisting at infinity.
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