Related papers: On the relation between strong ballistic transport…
In this paper, we show that one-dimensional discrete multi-frequency quasiperiodic Schr\"odinger operators with smooth potentials demonstrate ballistic motion on the set of energies on which the corresponding Schr\"odinger cocycles are…
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…
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 study the transport properties of Schr\"{o}dinger operators on $\mathbb{Z}^2$ with potentials that are periodic in one direction and compactly supported in the other. Such systems are known to produce surface states that are weakly…
For the solution $u(t)$ to the discrete Schr\"odinger equation $${\rm i}\frac{d}{dt}u_n(t)=-(u_{n+1}(t)+u_{n-1}(t))+V(\theta + n\alpha)u_n(t), \quad n\in\Z,$$ with $\alpha\in\R\setminus\Q$ and $V\in C^\omega(\T,\R)$, we consider the growth…
A new method is developed for the study of transport properties of 1D models with random potentials. It is based on an exact transformation that reduces discrete Schr\"odinger equation in the tight-binding model to a two-dimensional…
Bloch-Boltzmann transport theory fails to describe the carrier diffusion in current crystalline organic semiconductors, where the presence of large-amplitude thermal molecular motions causes substantial dynamical disorder. The charge…
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…
We investigate the dynamics of non-interacting particles in a one-dimensional tight-binding chain in the presence of an electric field with random amplitude drawn from a Gaussian distribution, and explicitly focus on the nature of quantum…
This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum…
We study Jacobi matrices that are uniformly approximated by periodic operators. We show that if the rate of approximation is sufficiently rapid, then the associated quantum dynamics are ballistic in a rather strong sense; namely, the…
We consider a particular class of lattice Schr\"odinger operators with deterministic potentials depending upon an infinite number of parameters in an auxiliary measurable space. We prove exponential dynamical localization for generic…
We consider continuous one-dimensional multifrequency Schr\"odinger operators, with analytic potential, and prove Anderson localization in the regime of positive Lyapunov exponent for almost all phases and almost all Diophantine…
We consider overdamped Brownian dynamics in a periodic potential with temporally oscillating amplitude. We analyze the transport which shows effective diffusion enhanced by the oscillations and derive approximate expressions for the…
We develop a sharp palindromic argument for general 1D operators, that proves absence of semi-uniform localization in the regime of exponential symmetry-based resonances. This provides the first examples of operators with dynamical…
We prove the existence of ballistic transport for a Schr\"odinger operator with a generic quasi-periodic potential in any dimension $d>1$.
A fourth-order Schr\"{o}dinger equation for the description of charge transport in semiconductors in the ballistic regime is proposed with the inclusion of non-parabolic effects in the dispersion relation in order to go beyond the simple…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
We establish Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies, the proof is based on a novel dynamical rigidity argument.
We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency.