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arXiv · 1407.5067

Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems

David Damanik·Milivoje Lukic·William Yessen
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Abstract

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 on $\mathbb{Z}$ with periodic parameters an explicit strictly positive lower bound for the Lieb-Robinson velocity.

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David Damanik, Milivoje Lukic, William Yessen. 2015-01-15. Quantum Dynamics of Periodic and Limit-Periodic Jacobi and Block Jacobi Matrices with Applications to Some Quantum Many Body Problems. https://doi.org/10.1007/s00220-015-2346-4

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