Related papers: Delocalization and Heisenberg's uncertainty relati…
Heisenberg's intuition was that there should be a tradeoff between measuring a particle's position with greater precision and disturbing its momentum. Recent formulations of this idea have focused on the question of how well two…
Heisenberg's uncertainty principle is formulated for a set of generalized measurements within the framework of majorization theory, resulting in a partial uncertainty order on probability vectors that is stronger than those based on…
We study overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of…
This work establishes the Anderson localization in both the spectral exponential and the strong dynamical localization for the multi-particle Anderson tight-binding model with correlated but strongly mixing random external potential. The…
In quantum mechanics, the Heisenberg uncertainty relation presents an ultimate limit to the precision by which one can predict the outcome of position and momentum measurements on a particle. Heisenberg explicitly stated this relation for…
We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can…
We consider the evolution of an initially localized wave packet after a sudden change in the Hamiltonian, i.e.\ a quench. When both bound and scattering eigenstates exist in the post-quench Hamiltonian, one might expect partial…
Anderson localization is a fundamental phenomenon in disordered quantum systems, where transport is suppressed by wave interference from extensive randomness. Moving beyond traditional multi-impurity scenarios, we investigate…
We re-derive the Schr\"{o}dinger-Robertson uncertainty principle for the position and momentum of a quantum particle. Our derivation does not directly employ commutation relations, but works by reduction to an eigenvalue problem related to…
The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by…
We report on recent studies of the spin-half Heisenberg and the Hubbard model on the sawtooth chain. For both models we construct a class of exact eigenstates which are localized due to the frustrating geometry of the lattice for a certain…
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schr\"odinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization…
The salient feature of both classical and quantum gravity is its universal and attractive character. However, less is known about the behaviour and build-up of quantum correlations when quantum systems interact via graviton exchange. In…
We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-Andr\'e-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^\sigma}$) when the quasiperiodicity parameter is chosen to be a member of…
The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these…
We derive a field-theoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic non-random hopping elements in any…
In the present paper we consider the quintic defocusing nonlinear Schr\"odinger equation in presence of a disordered random potential and we analyze the effects of the quintic nonlinearity on the Anderson localization of the solution. The…
We present a thorough numerical study of the Richardson model with quenched disorder (a fully-connected XX-model with longitudinal random fields). We study the onset of delocalization in typical states (many-body delocalization) and the…
As part of condensed-matter physics, the field of Anderson localization concerns the study of conductance of electrons in a random medium. We summarize and explain the results obtained in "A new numerical approach to Anderson…
The phenomenon of localization is usually accompanied with the presence of quenched disorder. To what extent disorder is necessary for localization is a well-known open problem. In this paper, we prove the instability of localization in…