相关论文: The repulsion between localization centers in the …

We investigate spectral properties of a discrete random displacement model, a Schr\"odinger operator on $\ell^2(\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of…

We study Schr\"odinger operators on quantum graphs where the number of edges between points is determined by orbits of a "shift of finite type". We prove Anderson localization for these systems.

The Typical Medium Theory provides conceptually the simplest order parameter description of Anderson localization by self-consistently calculating the geometrically-averaged (typical) local density of states (LDOS). Here we show how spatial…

Wave localization occurs in all types of vibrating systems, in acoustics, mechanics, optics, or quantum physics. It arises either in systems of irregular geometry (weak localization) or in disordered systems (Anderson localization). We…

We study, both experimentally and numerically, the Anderson localization phenomenon in torsional waves of a disordered elastic rod, which consists of a cylinder with randomly spaced notches. We find that the normal-mode wave amplitudes are…

We establish a close quantitative analogy between the excitation and ionization process of highly excited one electron Rydberg states under microwave driving and charge transport across disordered 1D lattices. Our results open a new arena…

We consider multi-dimensional Schr\"odinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on…

We describe a previously unexplored effect of the continuous spontaneous localization model whereby a correlation develops in the distributions of two nearby non-interacting particles following a period of diffusion. We propose the use of…

In an isolated single-particle quantum system a spatial disorder can induce Anderson localization. Being a result of interference, this phenomenon is expected to be fragile in the face of dissipation. Here we show that dissipation can drive…

The phenomenon of Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different set of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional…

We study low-energy properties of the random displacement model, a random Schr\"odinger operator describing an electron in a randomly deformed lattice. All periodic displacement configurations which minimize the bottom of the spectrum are…

An alternative explanation of the physical nature of Anderson localization phenomenon and one of the most direct ways of its experimental study are discussed.

The statistical properties of overlap sums of groups of four eigenfunctions of the Anderson model for localization as well as combinations of four eigenenergies are computed. Some of the distributions are found to be scaling functions, as…

We consider the random Dirac operators for which we have proved Anderson localization in arXiv:1812.01868. We use the Wegner estimate we have got in that paper to prove Lipschitz regularity of the density of states. Since usual methods for…

We introduce and prove local Wegner estimates for continuous generalized Anderson Hamiltonians, where the single-site random variables are independent but not necessarily identically distributed. In particular, we get Wegner estimates with…

We propose a new random process to construct the eigenvectors of some random operators which make a short and clean connection with the resolvent. In this process the center of localization has to be chosen randomly.

We study the higher-order correlation functions of covariant families of observables associated with random Schr\"odinger operators on the lattice in the strong disorder regime. We prove that if the distribution of the random variables has…

We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes…

We survey the localization theory of random Schr\"odinger operators with singular single-site distributions, focusing on two regimes: (i) H\"older-continuous laws, where quantitative Wegner estimates enable the classical multiscale analysis…

We show that the exact discrete analogue of Schr\"odinger equation can be derived naturally from the Hamiltonian operator of a Schr\"odinger field theory by using the discrete Fourier transform that transforms the operator from momentum…