相关论文: Localization for One Dimensional, Continuum, Berno…
We consider the multi-particle Anderson model on the lattice with infinite range but sub-exponentially decaying interaction and show the Anderson localization consisting of the spectral exponential and the strong dynamical localization. In…
We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization. This is an extension of the original Kunz-Souillard approach to localization for…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We study one-dimensional, continuum Bernoulli-Anderson models with general single-site potentials and prove positivity of the Lyapunov exponent away from a discrete set of critical energies. The proof is based on F\"urstenberg's Theorem.…
The proof of Anderson localization for the 1D Anderson model with arbitrary (e.g. Bernoulli) disorder, originally given by Carmona-Klein-Martinelli in 1987, is based in part on the multi-scale analysis. Later, in the 90s, it was realized…
We prove localization (near the bottom of the spectrum) for certain non-stationary variants of the Anderson model in three dimensions. More specifically, we prove a Wegner estimate, which implies localization by existing work. Two key…
We present a perturbative approach to disordered systems in one spatial dimension that accesses the full range of phase disorder and clarifies the connection between localization and phase information. We consider a long chain of…
In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…
We study continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…
We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…
We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between…
We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…
This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…
We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay…
In this paper, we use recent breakthroughs in the study of coupled subwavelength resonator systems to reveal new insight into the mechanisms responsible for the fundamental features of Anderson localization. The occurrence strong…
We prove that once one has the ingredients of a ``single-energy multiscale analysis (MSA) result'' on the $\mathbb{Z}^d$ lattice, several spectral and dynamical localization results can be derived, the most prominent being strong dynamical…
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a…