论文标题
在离散schrödinger操作员的周期性近似值的带宽上
On the Bandwidths of Periodic Approximations to Discrete Schrödinger Operators
论文作者
论文摘要
我们研究了ergodicSchrödinger操作员的光谱特性如何反映在其周期性近似的渐近性质中，因为该周期趋于无穷大。我们解决的第一个属性是对数尺度上带宽的渐近学，它量化了有限体积限制对边界条件的敏感性。我们证明，带宽始终可以根据Lyapunov指数从下面的界定。在I.I.D电势满足的其他假设下，我们还证明了匹配的上限。最后，我们提供了一个额外的假设，该假设在I.I.D情况下也得到了满足，在该情况下，相应的特征向量对定位中心呈指数定位，而不是浮点数。
We study how the spectral properties of ergodic Schrödinger operators are reflected in the asymptotic properties of its periodic approximation as the period tends to infinity. The first property we address is the asymptotics of the bandwidths on the logarithmic scale, which quantifies the sensitivity of the finite volume restriction to the boundary conditions. We show that the bandwidths can always be bounded from below in terms of the Lyapunov exponent. Under an additional assumption satisfied by i.i.d potentials, we also prove a matching upper bound. Finally, we provide an additional assumption which is also satisfied in the i.i.d case, under which the corresponding eigenvectors are exponentially localised with a localisation centre independent of the Floquet number.
