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.

arXiv comment26 pages, to appear in Commun. Math. Phys

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Cited by in corpus (21)

• Schrödinger Operators with Dynamically Defined Potentials: A Survey
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Ballistic Transport for Limit-Periodic Jacobi Matrices with Applications to Quantum Many-Body Problems
• On transport properties of isotropic quasiperiodic $XY$ spin chains
• Ballistic Transport in One-Dimensional Quasi-Periodic Continuous Schrödinger Equation
• On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field
• Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schrödinger Equation
• The landscape law for tight binding Hamiltonians
• Singularly continuous spectrum of a self-similar Laplacian on the half-line
• Maximal Speed of Propagation in Open Quantum Systems
• Spectral properties of block Jacobi matrices
• On Lieb-Robinson bounds for a class of continuum fermions
• Exponential tail estimates for quantum lattice dynamics
• Diffusion in the Mean for an Ergodic Schrödinger Equation Perturbed by a Fluctuating Potential
• On the relation between strong ballistic transport and exponential dynamical localization
• Ballistic transport for one-dimensional quasiperiodic Schrödinger operators
• Transport Exponents of Sturmian Hamiltonians
• Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators
• Diffusion in the mean for a periodic Schrödinger equation perturbed by a fluctuating potential
• Ballistic Transport for Periodic Jacobi Operators on ${\mathbb{Z}}^d$
• Stochastic process emerged from lattice fermion systems by repeated measurements and large-time limit