Related papers: Exact dynamical decay rate for the almost Mathieu …

We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency.

In [10] Jitomirskaya, Kr\"uger and Liu analysed the dynamical decay in expectation for the super-critical almost-Mathieu operator in function of the coupling parameter , showing that it is equal to the Lyapunov exponent of its transfer…

We introduce self-similar versions of the one-dimensional almost Mathieu operators. Our definition is based on a class of self-similar Laplacians instead of the standard discrete Laplacian, and includes the classical almost Mathieu…

The exponential decay rate of the semigroup $S(t)=e^{t\mathbb{A}}$ generated by the abstract damped wave equation $$\ddot u + 2f(A) \dot u +A u=0 $$ is here addressed, where $A$ is a strictly positive operator. The continuous function $f$,…

We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…

This paper gives a new, simple proof of the known fact that for contact processes on general lattices, in the subcritical regime the expected number of infected sites decays exponentially fast as time tends to infinity. The proof also…

We prove that for Diophantine \om and almost every \th, the almost Mathieu operator, (H_{\omega,\lambda,\theta}\Psi)(n)=\Psi(n+1) + \Psi(n-1) + \lambda\cos 2\pi(\omega n +\theta)\Psi(n), exhibits localization for \lambda > 2 and purely…

We solve the Dry Ten Martini Problem for the unitary almost Mathieu operator with Diophantine frequencies in the non-critical regime.

We consider one-dimensional quasi-periodic Schr\"odinger operators with analytic potentials. In the positive Lyapunov exponent regime, we prove large deviation estimates which lead to optimal H\"older continuity of the Lyapunov exponents…

We study the time evolution of two wave packets prepared at the same initial state, but evolving under slightly different Hamiltonians. For chaotic systems, we determine the circumstances that lead to an exponential decay with time of the…

We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators. For the class of…

We derive sufficient conditions for asymptotic and monotone exponential decay in mean square of solutions of the geometric Brownian motion with delay. The conditions are written in terms of the parameters and are explicit for the case of…

For first order systems, we obtain an efficient bound on the exponential decay of an eigenfunction in terms of the distance between the corresponding eigenvalue and the essential spectrum. As an example, the Dirac operator is considered.

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and…

In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical…

We construct frames of wavepackets produced by parabolic dilation, rotation and translation of (a finite sum of) Gaussians and give asymptotics on the analogue of Daubechies frame criterion. We show that the coefficients in the…

We consider a finite number of orientation preserving $C^2$ interval diffeomorphisms and apply them randomly in such a way that the expected Lyapunov exponents at the boundary points are positive. We prove the exponential decay of…

We study exponential decay of eigenfunctions of self-adjoint higher order elliptic operators on $\R^d$. We show that the possible critical decay rates are determined algebraically. In addition we show absence of super-exponentially decaying…

Chernoff approximations to strongly continuous one-parameter semigroups give solutions to a wide class of differential equations. This paper studies the rate of convergence of the Chernoff approximations. We provide simple natural examples…

A general method for estimating the approximation numbers of composition operators on $\Ht$, using finite-dimensional model subspaces, is studied and applied in the case when the symbol of the operator maps the unit disc to a domain whose…