ZARISKI CLOSURE OF SUBGROUPS OF THE SYMPLECTIC GROUP AND LYAPUNOV EXPONENTS OF THE SCHRODINGER OPERATOR ON THE STRIP
ZARISKI CLOSURE OF SUBGROUPS OF THE SYMPLECTIC GROUP AND LYAPUNOV EXPONENTS OF THE SCHRODINGER OPERATOR ON THE STRIP
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DOI：
10.1007/bf02099606
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发表时间：
1995-12-01
影响因子：
2.4
通讯作者：
GOLDSHEID, IY
中科院分区：
文献类型：
--
作者：
GOLDSHEID, IY
本文考虑具有随机位势的Schrodinger方程-y（n+1）+（Q（n）- EI）y（n）- y（n-1）= 0，其中Q（n）是一列独立同分布的真实的值随机对称m × m-矩阵，y（n）是R（m）的一个元素，-无穷证明了如果包含矩阵分布的支撑的矩阵的最小Jordan代数与所有（实值）对称矩阵的Jordan代数一致，则对于除了（可能）有限个值之外的所有E，我们的Schrodinger方程的所有Lyapunov指数都是不同的（因此相应的Schrodinger算子的谱是纯点的）.
We consider the Schrodinger equation with a random potential-y(n+1) + (Q(n) - EI)y(n) - y(n-1) = 0,where Q(n), is a sequence of independent identically distributed random symmetric m x m-matrices with real valued elements, y(n), is an element of R(m), -infinity < n < infinity, E is the real parameter, and I is the identity matrix. We show that if the smallest Jordan algebra of matrices containing the support of the distribution of matrices Q(n), coincides with Jordan algebra of all (real-valued) symmetric matrices then for all but (maybe) a finite number of values of E all the Lyapunov exponents of our Schrodinger equation are different (and thus the spectrum of the corresponding Schrodinger operator is pure point).