Related papers: Upper Bounds in Quantum Dynamics
We consider transport exponents associated with the dynamics of a wavepacket in a discrete one-dimensional quantum system and develop a general method for proving upper bounds for these exponents in terms of the norms of transfer matrices…
We develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers. Here we derive upper bounds for non-time averaged outside probabilities…
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…
A method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random (possibly correlated) Jacobi matrix. As an application, one obtains sharp upper bounds…
We consider discrete Schr\"odinger operators with Sturmian potentials and study the transport exponents associated with them. Under suitable assumptions on the frequency, we establish upper and lower bounds for the upper transport…
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…
We derive a general upper bound on the spreading rate of wavepackets in the framework of Schr\"odinger time evolution. Our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically…
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 present a simple method, not based on the transfer matrices, to prove vanishing of dynamical transport exponents. The method is applied to long range quasiperiodic operators.
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 consider the iteration of a unitary operator on a separable Hilbert space and study the spreading rates of the associated discrete-time dynamical system relative to a given orthonormal basis. We prove lower bounds for the transport…
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…
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 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…
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…
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 prove the existence of ballistic transport for the Schr\"odinger operator with limit-periodic or quasi-periodic potential in dimension two. This is done under certain regularity assumptions on the potential which have been used in prior…
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 conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting…
In this paper, we consider the transport properties of the class of limit-periodic continuum Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator $H$, and…