The present paper generalizes the analysis [18, 2] of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general pair potential (Hamiltonian function). The novelty, as compared to [18, 2], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other ext...

We give a proof of dynamical localization in the form of exponential decay of spatial correlations in the time evolution for the one-dimensional continuum Anderson model via the fractional moments method. This follows via exponential decay of fractional moments of the Green function, which is shown to hold at arbitrary energy and for any single-site distribution with bounded, compactly supporte...

The framework to describe natural phenomena at their basics being quantum mechanics, there exist a large number of common global phenomena occurring in different branches of natural sciences. One such global phenomenon is spontaneous quantum decay. However, its long time behaviour is experimentally poorly known. Here we show, that by combining two genuine quantum mechanical results, it is possi...

We consider the Bresse system with frictional dissipative terms acting in all the equations. We show the exponential decay of the solution by using a method developed by Z. Liu and S. Zheng and their collaborators in past years. The numerical computations were made by using the finite difference method to prove the theoretical results. In particular, the finite difference method in our case is ...

We have calculated, quantitatively, the time decay of donor-acceptor pair luminescence in compensated semiconductors, incorporating the effect of the potential fluctuations which exist in such materials. We show that the often-reported stretched-exponential decay law can here be derived rigorously, but only to a very close approximation, and, moreover, only provided that there is an alternate, ...

We consider both soft potentials with angular cutoff and Landau collision kernels in the Boltzmann theory inside a periodic box. We prove that any smooth perturbation near a given Maxwellian approaches zero at the rate of e−λt p for some λ > 0 and 0 < p < 1. Our method is based on an unified energy estimate with appropriate exponential velocity weight. Our results extend the classical result Ca...

This is the second part of a series of papers where we develop rigorous decay estimates for breather solutions of an averaged version of the non-linear Schrödinger equation. In this part we study the diffraction managed discrete nonlinear Schrödinger equation, an equation which describes coupled waveguide arrays with periodic diffraction management geometries. We show that, for vanishing averag...

We study the asymptotic behavior of the Euler-Bernoulli beam which is clamped at one end and free at the other end. We apply a boundary control with memory at the free end of the beam and prove that the “exponential decay” of the memory kernel is a necessary and sufficient condition for the exponential decay of the energy.

We study generalizations of Agmon-type estimates on eigenfunctions for Schrödinger operators. In the first part, we prove an exponential decay estimate on eigenfunctions for a class of pseudodifferential operators. In the second part, we study the semiclassical limit of ~-pseudodifferential operators, and exponential decay estimates on eigenfunctions and Briet-Combes-Duclos-type resolvent estim...

The study of stabilization of the linear dissipative wave equation in a bounded domain with Dirichlet boundary condition is now an old problem. The exponential decay rate of the energy was established by Bardos, Lebeau and Rauch [ BLR] under a geometrical hypothesis linked with the geodesics. Furthermore such condition called geometric control condition is almost necessary to get a uniform expo...