相关论文: Ergodic Schrodinger operators on the Bethe lattice…

We consider Schr\"odinger operators in $\ell^2(\Z)$ whose potentials are defined via continuous sampling along the orbits of a homeomorphism on a compact metric space. We show that for each non-atomic ergodic measure $\mu$, there is a dense…

In this paper we establish an abstract, dynamical Thouless-type formula for affine families of $\mathrm{GL} (2,\mathbb{R})$ cocycles. This result extends the classical formula relating, via the Hilbert transform, the maximal Lyapunov…

We consider Schr\"odinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a…

In this article we prove an upper bound for the Lyapunov exponent $\gamma(E)$ and a two-sided bound for the integrated density of states $N(E)$ at an arbitrary energy $E>0$ of random Schr\"odinger operators in one dimension. These…

We consider discrete Schr"odinger operators on the line with potentials generated by a minimal homeomorphism on a compact metric space and a continuous sampling function. We introduce the concepts of topological and metric repetition…

The object of the present study is the integrated density of states of a quantum particle in multi-dimensional Euclidean space which is characterized by a Schr\"odinger operator with a constant magnetic field and a random potential which…

We consider ergodic random magnetic Schr\"odinger operators on the metric graph $\mathbb{Z}^d$ with random potentials and random boundary conditions taking values in a finite set. We show that normalized finite volume eigenvalue counting…

We study a matrix-valued Schr\"odinger operator with random point interactions. We prove the absence of absolutely continuous spectrum for this operator by proving that away from a discrete set its Lyapunov exponents do not vanish. For this…

We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit…

Let $ (\Theta,T,\mu) $ be an ergodic topological dynamical system. The fibered rotation number for cocycles in $ \Theta\times \mathrm{SL}(2,\mathbb{R}) $, acting on $ \Theta\times \mathbb{R}\mathbb{P}^1 $ is well-defined and has wide…

We consider discrete one-dimensional Schr\"odinger operators whose potentials are generated by sampling along the orbits of a general hyperbolic transformation. Specifically, we show that if the sampling function is a non-constant H\"older…

In this paper, we study the multidimensional lattice Schr\"odinger operators with $C^2$-cosine like quasi-periodic (QP) potential. We establish quantitative Green's function estimates, the arithmetic version of Anderson (and dynamical)…

We develop the basic theory of ergodic Schr\"odinger operators, which is well known for ergodic probability measures, in the case of a base dynamics on an infinite measure space. This includes the almost sure constancy of the spectrum and…

We give three formulas for meromorphic eigenfunctions (scattering states) of Sutherland's integrable N-body Schroedinger operators and their generalizations. The first is an explicit computation of the Etingof-Kirillov traces of…

We propose an alternative, statistical, derivation of the Thermodynamic Bethe Ansatz based on the tree expansion of the Gaudin determinant. We illustrate the method on the simplest example of a theory with diagonal scattering and no bound…

We prove that any ergodic nonatomic probability-preserving action of an irreducible lattice in a semisimple group, at least one factor being connected and higher-rank, is essentially free. This generalizes the result of Stuck and Zimmer…

For large but finite systems the static properties of the infinite ranged Sherrington-Kirkpatrick model are numerically investigated in the entire the glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in…

Oseledets' celebrated Multiplicative Ergodic Theorem (MET) is concerned with the exponential growth rates of vectors under the action of a linear cocycle on R^d. When the linear actions are invertible, the MET guarantees an…

We study ergodic random Schr"odinger operators on a covering manifold, where the randomness enters both via the potential and the metric. We prove measurability of the random operators, almost sure constancy of their spectral properties,…

We establish smoothness of the density of states for 1D lattice Schrodinger operators with potential taking values $\pm\lambda$, for $\lambda$ in a class of small algebraic numbers and energy $E\in)-2, 2($ suitably restricted away from…