相关论文: Non-Lyapunov annealed decay for 1d Anderson eigenf…

A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $\delta $ peak potentials is used to study numerically the influence of a spatial disorder on the conductance fluctuations and distribution at different regimes.…

Recent work has shown that statistical arguments, seemingly well-justified in higher dimensions, can also be used to derive reasonable, albeit less accurate, estimates of the largest Lyapunov exponent ${\chi}$ in lower-dimensional…

We quantify the coupling asymptotics for the Lyapunov-exponent of a one-frequency quasi-periodic Schr\"odinger operator with analytic potential sampling function. The result refines the well-known lower bound of the Lyapunov-exponent by…

We study two phases of a heterotic standard model, obtained from a Calabi-Yau compactification of the E8xE8 heterotic string, in the context of the associated four-dimensional effective theories. In the first phase we have a standard model…

The invariant imbedding evolution equations for the amplitude reflection and transmission coefficients of a disordered 1D chain are shown to follow from the continuum limit, for weak disorder, of recursion relations between reflection…

In this paper we study the pinning model with correlated Gaussian disorder. The presence of correlations makes the annealed model more involved than the usual homogeneous model, which is fully solvable. We prove however that if the disorder…

The problem of Anderson localization, as well as the single particle localization-delocalizaton transition of the Aubry-Andr\'e model, is studied employing operator Krylov space methods. It is shown that even when the dynamics is generated…

We study when Fourier transforms of Gibbs measures of sufficiently nonlinear expanding Markov maps decay at infinity at a polynomial rate. Assuming finite Lyapunov exponent, we reduce this to a nonlinearity assumption, which we verify for…

We consider one-step cocycles of $2 \times 2$ matrices, and we are interested in their Lyapunov-optimizing measures, i.e., invariant probability measures that maximize or minimize a Lyapunov exponent. If the cocycle is dominated, that is,…

A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here…

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…

We exhibit a large class of Lyapunov functionals for nonlinear drift-diffusion equations with non-homogeneous Dirichlet boundary conditions. These are generalizations of large deviation functionals for underlying stochastic many-particle…

The present paper provides an overview of results obtained in four recent papers by the authors. These papers address the problem of intermittency for the Parabolic Anderson Model in a \emph{time-dependent random medium}, describing the…

For a quadratic Markov branching process (QMBP), we show that the decay parameter is equal to the first eigenvalue of a Sturm-Liouville operator associated with the PDE that the generating function of the transition probability satisfies.…

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

The Anderson model for independent electrons in a disordered potential is transformed analytically and exactly to a basis of random extended states leading to a variant of augmented space. In addition to the widely-accepted phase diagrams…

We study the critical dynamics of matter waves at the 3D Anderson mobility edge in cold-atom disorder quench experiments. General scaling arguments are supported by precision numerics for the spectral function, diffusion coefficient, and…

Localization of wave functions in disordered systems can be characterized by the Lyapunov exponent, which is zero in the extended phase and nonzero in the localized phase. Previous studies have shown that this exponent is an analytic…

A. Bornh\"oft, R. Hanke-Rauschenbach, and K. Sundmacher, [Nonlinear Dyn., 73 (2013), pp. 535-549] introduced a qualitative simplification to the ADM1 model for anaerobic digestion. We obtain global results for this model by first analyzing…

In this paper, we study the large-time behavior of solutions to a class of partially dissipative linear hyperbolic systems with applications in velocity-jump processes in several dimensions. Given integers $n,d\ge 1$, let $\mathbf…