48 citations · 145 across the 12 of their papers we have counts for
9 papers · 1 filter
A Multi-Scale Analysis Scheme on Abelian Groups with an Application to Operators Dual to Hill's Equation
David Damanik, Michael Goldstein, Milivoje Lukic
We present an abstract multiscale analysis scheme for matrix functions , where is an Abelian group equipped with a dist…
Generalized Prüfer variables for perturbations of Jacobi and CMV matrices
Milivoje Lukic, Darren C. Ong
Prüfer variables are a standard tool in spectral theory, developed originally for perturbations of the free Schrödinger operator. They were generalized by Kiselev, Remling, and Sim…
Characterizations of Uniform Hyperbolicity and Spectra of CMV Matrices
David Damanik, Jake Fillman, Milivoje Lukic +1
We provide an elementary proof of the equivalence of various notions of uniform hyperbolicity for a class of cocycles and establish a Johnson-type theor…
The Isospectral Torus of Quasi-Periodic Schrödinger Operators via Periodic Approximations
David Damanik, Michael Goldstein, Milivoje Lukic
We study the quasi-periodic Schrödinger operator in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^ν}c(m)\exp (2πi mω…
New Anomalous Lieb-Robinson Bounds in Quasi-Periodic XY Chains
David Damanik, Marius Lemm, Milivoje Lukic +1
We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson bound for an isotropic XY chain in a quasi-periodic transversal magnetic field…
The Spectrum of a Schrödinger Operator With Small Quasi-Periodic Potential is Homogeneous
David Damanik, Michael Goldstein, Milivoje Lukic
We consider the quasi-periodic Schrödinger operator in , where the potential is given by $$ V(x) = \sum_{m \in \mathbb{Z}^ν\set…
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
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 li…
On Anomalous Lieb-Robinson Bounds for the Fibonacci XY Chain
David Damanik, Marius Lemm, Milivoje Lukic +1
We rigorously prove a new kind of anomalous (or sub-ballistic) Lieb-Robinson bound for the isotropic XY chain with Fibonacci external magnetic field at arbitrary coupling. It is an…
Uniform Hyperbolicity for Szegő Cocycles and Applications to Random CMV Matrices and the Ising Model
David Damanik, Jake Fillman, Milivoje Lukic +1
We consider products of the matrices associated with the Szegő recursion from the theory of orthogonal polynomials on the unit circle and show that under suitable assumptions, thei…