Quantum Diffusion and Delocalization for Band Matrices with General Distribution
Quantum Diffusion and Delocalization for Band Matrices with General Distribution
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DOI：
10.1007/s00023-011-0104-5
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发表时间：
2011-11-01
影响因子：
1.5
通讯作者：
Knowles, Antti
中科院分区：
文献类型：
--
作者：
Erdos, Laszlo;Knowles, Antti
我们考虑d>；=1维厄米特对称随机带矩阵H。矩阵元素H-xy以x为指标，y是Z(D)的Lambda子集的一个元素，它们是独立的，它们的方差对某个概率密度f满足sigma(2)(Xy)xy：=E|H-xy|(2)=W-df((x-y)/W)。我们假设每个矩阵元素H-xy的定律是对称的，并且呈现亚指数衰减。证明了受哈密顿量H约束的量子粒子的时间演化在时间尺度t0上是扩散的，其中M：=1/(Maxx，y sigma(2)(Xy))。
We consider Hermitian and symmetric random band matrices H in d >= 1 dimensions. The matrix elements H-xy, indexed by x, y is an element of Lambda subset of Z(d), are independent and their variances satisfy sigma(2)(xy)xy := E|H-xy|(2) = W-d f((x-y)/W) for some probability density f. We assume that the law of each matrix element H-xy is symmetric and exhibits subexponential decay. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales t 0, where M := 1/(maxx,y sigma(2)(xy)).