空间非齐次一维三态量子游荡的一致平稳测度

Uniform Stationary Measure of Space-Inhomogeneous One-Dimensional Three-State Quantum Walks

摘要: 本文研究了空间非齐次三态量子游荡在直线和环上的一致平稳测度。首先，利用直线上的转移矩阵处理了演化矩阵的特征值问题并给出了相应的特征向量，得到该量子游荡在直线上具有一致平稳测度。另外还给出了空间非齐次三态量子游荡在直线上演化矩阵的周期性表示；在此基础上，将游荡的位置空间限制到环上，证明了环上一致平稳测度的存在性并给出了表示。

Abstract: In this paper, we consider the uniform stationary measure of space-inhomogeneous three state quantum walks on the line and cycles. Firstly, the eigenvalue problem is solved by transfer matrix and the corresponding uniform stationary measure is given on the line. In addition, we give the periodic representation of the evolution matrix under the model on the line. Then, we show the uniform stationary measure of the cycles by restricting the position space to the cycles.