Related papers: Dynamical Upper Bounds for One-Dimensional Quasicr…
We consider discrete one-dimensional Schr\"odinger operators on the whole line and establish a criterion for continuity of spectral measures with respect to $\log$-Hausdorff measures. We apply this result to operators with Sturmian…
We establish quantum dynamical lower bounds for a number of discrete one-dimensional Schr\"odinger operators. These dynamical bounds are derived from power-law upper bounds on the norms of transfer matrices. We develop further the approach…
We prove quantum dynamical upper bounds for operators from the Fibonacci hull. These bounds hold for sufficiently large coupling and they are uniform in the phase. This extends recent work by Killip, Kiselev and Last who obtained these…
We prove quantum dynamical lower bounds for one-dimensional continuum Schr\"odinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states.…
We prove dynamical upper bounds for discrete one-dimensional Schroedinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations. We demonstrate the applicability of our approach by a study of…
Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to…
Motivated by the research on upper bounds on the rate of quantum transport for one-dimensional operators, particularly, the recent works of Jitomirskaya--Liu and Jitomirskaya--Powell and the earlier ones of Damanik--Tcheremchantsev, we…
We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply…
We employ Weyl's method and Vinogradov's method to analyze skew-shift dynamics on semi-algebraic sets. Consequently, we improve the quantum dynamical upper bounds of Jitomirskaya-Powell, Liu, and Shamis-Sodin for long-range operators with…
We establish quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators in situations where, in addition to power-law upper bounds on solutions corresponding to energies in the spectrum, one also has lower bounds…
In this paper we obtain upper quantum dynamical bounds as a corollary of positive Lyapunov exponent for Schr\"odinger operators $H_{f,\theta} u(n)=u(n+1)+u(n-1)+ \phi(f^n\theta)u(n)$, where $\phi : \mathcal{M}\to {\Bbb R}$ is a piecewise…
We establish quantum dynamical upper bounds for quasi-periodic Schr\"odinger operators with Liouville frequencies. Our approach combines semi-algebraic discrepancy estimates for the Kronecker sequence $\{n\alpha\}$ with quantitative Green's…
The Fibonacci Hamiltonian, that is a Schr\"{o}dinger operator associated to a quasiperiodical sturmian potential with respect to the golden mean has been investigated intensively in recent years. Damanik and Tcheremchantsev developed a…
We study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q-moments of the position operator and establish both upper…
We establish localization type dynamical bounds as a corollary of positive Lyapunov exponents for general operators with quasiperiodic potentials defined by piecewise Holder functions.
We develop a general method to bound the spreading of an entire wavepacket under Schr\"odinger dynamics from above. This method derives upper bounds on time-averaged moments of the position operator from lower bounds on norms of transfer…
We present a method for obtaining power-logarithmic bounds on the growth of the moments of the position operator for one-dimensional ergodic Schr\"odinger operators. We use Bourgain's semi-algebraic method to obtain such bounds for…
We prove upper bounds on outside probabilities for generic non-autonomous Schr\"odinger operators on lattices of arbitrary dimension. Our approach is based on a combination of commutator method originated in scattering theory and novel…
Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive…
We obtain (up to logarithmic scaling) the power-law lower bound $M_{p}(T_{k})\gtrsim T_{k}^{(1-\delta)p}$ on a subsequence $T_{k}\rightarrow\infty$, uniformly across $p>0$, for discrete one-dimensional quasiperiodic Schr\"odinger operators…