48 citations · 145 across the 12 of their papers we have counts for
22 papers
Spectral edge behavior for eventually monotone Jacobi and Verblunsky coefficients
Milivoje Lukic
We consider Jacobi matrices with eventually increasing sequences of diagonal and off-diagonal Jacobi parameters. We describe the asymptotic behavior of the subordinate solution at…
bounded variation and absolutely continuous spectrum of Jacobi matrices
Yoram Last, Milivoje Lukic
We disprove a conjecture of Breuer-Last-Simon concerning the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an bounded variation condition w…
Almost Periodicity in Time of Solutions of the Toda Lattice
Ilia Binder, David Damanik, Milivoje Lukic +1
We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous…
Almost Periodicity in Time of Solutions of the KdV Equation
Ilia Binder, David Damanik, Michael Goldstein +1
We study the Cauchy problem for the KdV equation with almost periodic initial data . We consider initial data $V…
Limit-Periodic Continuum Schrödinger Operators with Zero Measure Cantor Spectrum
David Damanik, Jake Fillman, Milivoje Lukic
We consider Schrödinger operators on the real line with limit-periodic potentials and show that, generically, the spectrum is a Cantor set of zero Lebesgue measure and all spectral…
Spectral Homogeneity of Limit-Periodic Schrödinger Operators
Jake Fillman, Milivoje Lukic
We prove that the spectrum of a limit-periodic Schrödinger operator is homogeneous in the sense of Carleson whenever the potential obeys the Pastur--Tkachenko condition. This impli…
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…
On higher-order Szego theorems with a single critical point of arbitrary order
Milivoje Lukic
We prove the following higher-order Szego theorems: if a measure on the unit circle has absolutely continuous part and Verblunsky coefficients with square-summable varia…
Wigner-von Neumann type perturbations of periodic Schrödinger Operators
Milivoje Lukic, Darren C. Ong
We consider decaying oscillatory perturbations of periodic Schrödinger operators on the half line. More precisely, the perturbations we study satisfy a generalized bounded variatio…
Square-summable variation and absolutely continuous spectrum
Milivoje Lukic
Recent results of Denisov and Kaluzhny-Shamis describe the absolutely continuous spectrum of Jacobi matrices with coefficients that obey an l^2 bounded variation condition with ste…
On a conjecture for higher-order Szego theorems
Milivoje Lukic
We disprove a conjecture of Simon for higher-order Szego theorems for orthogonal polynomials on the unit circle and propose a modified version of the conjecture.
Schrodinger operators with slowly decaying Wigner--von Neumann type potentials
Milivoje Lukic
We consider Schrödinger operators with potentials satisfying a generalized bounded variation condition at infinity and an decay condition. This class of potentials includes s…
Derivatives of L^p eigenfunctions of Schrodinger operators
Milivoje Lukic
Assuming the negative part of the potential is uniformly locally , we prove a pointwise estimate on derivatives of eigenfunctions of one-dimensional Schrodinger operator…
Orthogonal Polynomials with Recursion Coefficients of Generalized Bounded Variation
Milivoje Lukic
We consider probability measures on the real line or unit circle with Jacobi or Verblunsky coefficients satisfying an condition and a generalized bounded variation conditi…