Related papers: Upper bounds on transport exponents for long range…
We show that a class of Poincar\'e-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly…
The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…
We prove a criterion for absence of eigenvalues for one-dimensional Schr\"odinger operators. This criterion can be regarded as an $L^1$-version of Gordon's theorem and it has a broader range of application. Absence of eigenvalues is then…
We obtain approximate solutions defining the mobility edge separating localized and extended states for several classes of generic one-dimensional quasiperiodic models. We validate our analytical ansatz with exact numerical calculations.…
We prove that the size of the spectral gaps of weakly coupled quasi-periodic Schr\"odinger operators with Liouville frequencies decays exponentially. As an application, we obtain the homogeneity of the spectrum.
This article concerns a class of beam equations with damping on rectangular tori. When the generators satisfy certain relationship, by excluding some value of two model parameters, we prove that such models admit small amplitude…
The prospects of extracting transport coefficients from euclidean lattice simulations are discussed. Some general comments on the reconstruction of spectral functions using the Maximal Entropy Method are given as well.
In molecular dynamics, transport coefficients measure the sensitivity of the invariant probability measure of the stochastic dynamics at hand with respect to some perturbation. They are typically computed using either the linear response of…
An intriguing regime of universal charge transport at high entropy density has been proposed for periodically driven interacting one-dimensional systems with Bloch bands separated by a large single-particle band gap. For weak interactions,…
We develop a theory of operator renewal sequences in the context of infinite ergodic theory. For large classes of dynamical systems preserving an infinite measure, we determine the asymptotic behaviour of iterates $L^n$ of the transfer…
We prove the spaceability of the set of hypercyclic vectors for {\em shifts-like operators}. Shift-like operators appear naturally as composition operators on $L^p(X)$, when the underlying space $X$ is dissipative. In the process of proving…
We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains $\Omega \subset \mathbb R^n$ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
Monotone operators and (firmly) nonexpansive mappings are fundamental objects in modern analysis and computational optimization. Five years ago, it was shown that if finitely many firmly nonexpansive mappings have or "almost have" fixed…
Exponential operator decompositions are an important tool in many fields of physics, for example, in quantum control, quantum computation, or condensed matter physics. In this work, we present a method for obtaining such decompositions,…
We characterize disjoint hypercyclic sequences of wedge operators. Also, we give some sufficient conditions for a sequence of the dual wedge operators to be disjoint topologically transitive. Finally, we give some concrete examples and…
In networks of mobile autonomous agents, e.g. for data acquisition, we may wish to maximize data transfer or to reliably transfer a minimum amount of data, subject to quality of service or energy constraints. These requirements can be…
Transport equations can be derived from quantum field theory assuming a loss of information about the details of the initial state and a gradient expansion. While the latter can be systematically improved, the assumption about a memory loss…
We explicitly determine the high-energy asymptotics for Weyl-Titchmarsh matrices associated with general Dirac-type operators on half-lines and on $\bbR$. We also prove new local uniqueness results for Dirac-type operators in terms of…
This paper investigates the existence of almost periodic traveling fronts for Fisher-KPP lattice equations in one-dimensional almost periodic media. By the Lyapunov exponent of the linearized operator near the unstable steady state, we give…