Journal ArticleDOI
Absence of diffusion in the Anderson tight binding model for large disorder or low energy
Jürg Fröhlich,Thomas Spencer +1 more
TLDR
In this article, it was shown that the Green's function of the Anderson tight binding Hamiltonian decays exponentially fast at long distances on Ω v ≥ 0, with probability 1.Abstract:
We prove that the Green's function of the Anderson tight binding Hamiltonian decays exponentially fast at long distances on ℤ
v
, with probability 1. We must assume that either the disorder is large or the energy is sufficiently low. Our proof is based on perturbation theory about an infinite sequence of block Hamiltonians and is related to KAM methods.read more
Citations
More filters
Journal ArticleDOI
Localization at large disorder and at extreme energies: an elementary derivation
TL;DR: In this paper, the authors presented a short proof of localization under the conditions of either strong disorder (λ > λ 0) or extreme energies for a wide class of self adjoint operators with random matrix elements, acting inl 2 spaces.
Journal ArticleDOI
The noncommutative geometry of the quantum Hall effect
TL;DR: An overview of the integer quantum Hall effect is given in this paper, where a mathematical framework using non-ommutative geometry as defined by Connes is prepared. Within this framework, it is proved that the Hall conductivity is quantized and that plateaux occur when the Fermi energy varies in a region of localized states.
Journal ArticleDOI
Transport equations for elastic and other waves in random media
TL;DR: In this paper, the authors derived and analyzed transport equations for the energy density of waves of any kind in a random medium, taking account of nonuniformities of the background medium, scattering by random inhomogeneities, polarization effects, coupling of different types of waves, etc.
Journal ArticleDOI
On Many-Body Localization for Quantum Spin Chains
TL;DR: In this article, the authors prove that many-body localization follows from a physically reasonable assumption that limits the amount of level attraction in the system, and use a sequence of local unitary transformations to diagonalize the Hamiltonian and connect the exact many body eigenfunctions to the original basis vectors.
Journal ArticleDOI
Regularity properties and pathologies of position-space renormalization-group transformations: Scope and limitations of Gibbsian theory
TL;DR: In this article, the conceptual foundations of the renormalization-group (RG) formalism are considered and rigorous theorems on the regularity properties and possible pathologies of the RG map are presented.
References
More filters
Journal ArticleDOI
Absence of Diffusion in Certain Random Lattices
TL;DR: In this article, a simple model for spin diffusion or conduction in the "impurity band" is presented, which involves transport in a lattice which is in some sense random, and in them diffusion is expected to take place via quantum jumps between localized sites.
Journal ArticleDOI
The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas
Jürg Fröhlich,Thomas Spencer +1 more
TL;DR: In this paper, the existence of a Kosterlitz-Thouless transition in the rotator, the Villain, the solid-on-solid, and the ℤ n −1 model in two dimensions was proved.
Journal ArticleDOI
Sur le spectre des opérateurs aux différences finies aléatoires
Hervé Kunz,Bernard Souillard +1 more
TL;DR: In this article, a class of random finite difference Schrodinger operators with a random potential was studied and the exact location of the spectrum was obtained with probability one, in various situations, and criterions for a given part in the spectrum to be pure point or purely continuous.
Journal ArticleDOI
Bounds on the density of states in disordered systems
TL;DR: It is proven that the averaged density of states does neither vanish nor diverge inside the band for a class of tight-binding models governed by short-range one-particle Hamiltonians with site-diagonal and/or off- diagonal disorder and continuous distribution of the matrix elements.