Related papers: Anderson Localization For The Quantum Kicked Rotor…
We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in $\Bbb Z^d$ is {\it stable} under localized time-quasi-periodic perturbations by proving that the…
It was recently shown that wavepackets with skewed momentum distribution exhibit a boomerang-like dynamics in the Anderson model due to Anderson localization: after an initial ballistic motion, they make a U-turn and eventually come back to…
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 show persistence of both Anderson and dynamical localization in Schr\"odinger operators with non-positive (attractive) random decaying potential. We consider an Anderson-type Schr\"odinger operator with a non-positive ergodic random…
In this paper we prove Anderson localization for multi-frequency quasi-periodic extended CMV matrices with analytic Verblunsky coefficients in the regime of positive Lyapunov exponents. By constructing a suitable semialgebraic set and…
We solve the Anderson localization problem on a two-leg ladder by the Fokker-Planck equation approach. The solution is exact in the weak disorder limit at a fixed inter-chain coupling. The study is motivated by progress in investigating the…
We consider a class of ensembles of lattice Schr\"odinger operators with deterministic random potentials, including quasi-periodic potentials with Diophantine frequencies, depending upon an infinite number of parameters in an auxiliary…
We report a careful finite size scaling study of the metal insulator transition in Anderson's model of localisation. We focus on the estimation of the critical exponent $\nu$ that describes the divergence of the localisation length. We…
We study multi-particle interactive quantum disordered systems on a polynomially-growing countable connected graph (Z,E). The novelty is to give localization bounds uniform in finite or infinite volumes (subgraphs) in Z^N as well as for the…
We study the one-dimensional random dimer model, with Hamiltonian $H_\omega=\Delta + V_\omega$, where for all $x\in\Z, V_\omega(2x)=V_\omega(2x+1)$ and where the $V_\omega(2x)$ are i.i.d. Bernoulli random variables taking the values $\pm V,…
Anderson localization is a general phenomenon of wave physics, which stems from the interference between multiple scattering paths1,2. It was originally proposed for electrons in a crystal, but later was also observed for light3-5,…
Anderson localization (AL) phenomena usually exists in systems with random potential. However, disorder-free quantum many-body systems with local conservation can also exhibit AL or even many-body localization transition. In this work, we…
Using a three-frequency one-dimensional kicked rotor experimentally realized with a cold atomic gas, we study the transport properties at the critical point of the metal-insulator Anderson transition. We accurately measure the…
In this paper, we study the quasi-periodic operators $H_{\epsilon,\omega}(x)$: $$(H_{\epsilon,\omega}(x)\vec{\psi})_n=\epsilon\sum_{k\in\mathbb{Z}}W_k\vec{\psi}_{n-k}+V(x+n\omega)\vec{\psi}_n,$$ where…
We consider the discrete Schr\"odinger operator $H=-\Delta+V$ on a cube $M\subset \mathbb{Z}^d$, with periodic or Dirichlet (simple) boundary conditions. We use a hidden landscape function $u$, defined as the solution of an inhomogeneous…
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…
The venerable phenomena of Anderson localization, along with the much more recent many-body localization, both depend crucially on the presence of disorder. The latter enters either in the form of quenched disorder in the parameters of the…
For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047 (2015)] of the Thouless point of view on the…
Anderson localization is related to exponential localization of a particle in the configuration space in the presence of a disorder potential. Anderson localization can be also observed in the momentum space and corresponds to quantum…
We study the multi-particle Anderson model in the continuum and show that under some mild assumptions on the random external potential and the inter-particle interaction, for any finite number of particles, the multi-particle lower edges of…