Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems
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DOI：
10.1007/s00220-015-2346-4
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发表时间：
2014-07
影响因子：
2.4
通讯作者：
D. Damanik;Milivoje Lukic;W. Yessen
中科院分区：
文献类型：
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作者：
D. Damanik;Milivoje Lukic;W. Yessen
本文研究了基于Jacobi矩阵或块Jacobi矩阵的量子动力学，其对角线项和非对角线项由周期或极限周期序列调制。特别地，我们研究了传输指数。在周期情况下，我们证明了弹道输运，而在极限周期情况下，我们讨论了各种现象，如准弹道输运和弱动力局域化。我们还介绍了一些量子多体问题的应用。特别地，我们建立了具有周期参数的各向异性XY链的Lieb-Robinson速度的严格正下界。
We investigate quantum dynamics with the underlying Hamiltonian being a Jacobi or a block Jacobi matrix with the diagonal and the off-diagonal terms modulated by a periodic or a limit-periodic sequence. In particular, we investigate the transport exponents. In the periodic case we demonstrate ballistic transport, while in the limit-periodic case we discuss various phenomena, such as quasi-ballistic transport and weak dynamical localization. We also present applications to some quantum many body problems. In particular, we establish for the anisotropic XY chain onwith periodic parameters an explicit strictly positive lower bound for the Lieb–Robinson velocity.