All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 22

Showing per page

A comprehensive proof of localization for continuous Anderson models with singular random potentials

François Germinet, Abel Klein (2013)

Journal of the European Mathematical Society

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 localization at the bottom of the spectrum, which includes Anderson localization (pure point spectrum with exponentially decaying eigenfunctions) with finite multiplicity of eigenvalues, dynamical localization (no spreading of wave packets under the time evolution),...

A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach

Sébastien Breteaux (2014)

Annales de l’institut Fourier

In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.

A lower bound for the principal eigenvalue of the Stokes operator in a random domain

V. V. Yurinsky (2008)

Annales de l'I.H.P. Probabilités et statistiques

This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...

Abel means of operator-valued processes

G. Blower (1995)

Studia Mathematica

Let ( X j ) be a sequence of independent identically distributed random operators on a Banach space. We obtain necessary and sufficient conditions for the Abel means of X n . . . X 2 X 1 to belong to Hardy and Lipschitz spaces a.s. We also obtain necessary and sufficient conditions on the Fourier coefficients of random Taylor series with bounded martingale coefficients to belong to Lipschitz and Bergman spaces.

Asymptotic stability condition for stochastic Markovian systems of differential equations

Efraim Shmerling (2010)

Mathematica Bohemica

Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by d X ( t ) = A ( ξ ( t ) ) X ( t ) d t + H ( ξ ( t ) ) X ( t ) d w ( t ) , where ξ ( t ) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.

Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase

Frédéric Klopp (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...

Localisation for non-monotone Schrödinger operators

Alexander Elgart, Mira Shamis, Sasha Sodin (2014)

Journal of the European Mathematical Society

We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schrödinger operators with non-monotone random potentials, on the d -dimensional lattice. Our results include dynamical localisation, i.e. exponentially decaying bounds on the transition amplitude in the mean. They are derived through the study of fractional moments of the resolvent, which are finite due to resonance-diffusing effects of the disorder. One of the byproducts of the analysis...

Localisation pour des opérateurs de Schrödinger aléatoires dans L 2 ( ℝ d ) : un modèle semi-classique

Frédéric Klopp (1995)

Annales de l'institut Fourier

Dans L 2 ( ℝ d ) , nous démontrons un résultat de localisation exponentielle pour un opérateur de Schrödinger semi-classique à potentiel périodique perturbé par de petites perturbations aléatoires indépendantes identiquement distribuées placées au fond de chaque puits. Pour ce faire, on montre que notre opérateur, restreint à un intervalle d’énergie convenable, est unitairement équivalent à une matrice aléatoire infinie dont on contrôle bien les coefficients. Puis, pour ce type de matrices, on prouve un résultat...

Resonant delocalization for random Schrödinger operators on tree graphs

Michael Aizenman, Simone Warzel (2013)

Journal of the European Mathematical Society

We analyse the spectral phase diagram of Schrödinger operators T + λ V on regular tree graphs, with T the graph adjacency operator and V a random potential given by i i d random variables. The main result is a criterion for the emergence of absolutely continuous ( a c ) spectrum due to fluctuation-enabled resonances between distant sites. Using it we prove that for unbounded random potentials a c spectrum appears at arbitrarily weak disorder ( λ ≪ 1 ) in an energy regime which extends beyond the spectrum of ∼ T . Incorporating...

Spectral statistics for random Schrödinger operators in the localized regime

François Germinet, Frédéric Klopp (2014)

Journal of the European Mathematical Society

We study various statistics related to the eigenvalues and eigenfunctions of random Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy E in the localized phase. Assume the density of states function is not too flat near E . Restrict it to some large cube Λ . Consider now I Λ , a small energy interval centered at E that asymptotically contains infintely many eigenvalues when the volume of the cube Λ grows to infinity. We prove that, with probability one in the large volume...

Currently displaying 1 – 20 of 22

Page 1 Next