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

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.

26 pages, to appear in Commun. Math. Phys

References in corpus (2)

• Many body localization in Heisenberg XXZ magnet in a random field
• Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs

Cited by in corpus (1)

• Transport Exponents of Sturmian Hamiltonians