- 作者: 蔡志賢
- 作者服務機構: 國立中山大學應用數學系
- 中文摘要: 隨機矩陣乘積之理論可告訴我們矩陣之範(norm)的增長情形。我們將該理論應用到隨機Schrodinger方程。我們證明當隨機位能具有指數階矩且其分部包含一實數之開區間,則方程式之解呈指數增長。
- 英文摘要: The limit theory of products of random matrices explains the asymptotic behavior of matrix elementsof random products. For each random product, there is an associated Lyapunov exponent which gives ameasure of the exponential growth rate of the matrix norm. We apply the theory of products of randommatrices to the random Schrodinger equations. We, show that if the random potential has an exponentialmoment and contains an interval of R, then the solution increases exponentially.
- 中文關鍵字: random matrix; Lyapunov exponent; random Schrodinger equations
- 英文關鍵字: --