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.

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...

An excitation and emission wavelength dependent non-exponential fluorescence decay behaviour of room temperature ionic liquids (RTILs) has been noted. Average fluorescence lifetimes have been found to vary by a factor of three or more. Red emitting dyes dissolved in RTILs are found to follow hitherto unobserved single exponential fluorescence decay behaviour.

I’ve no doubt that for ODEs, the questions and techniques for exponential decay of solutions go back a long way, maybe even to the nineteenth century. For one body systems with decaying potential, I think they are at least in Titchmarsh’s book. For ODEs with explicit polynomially growing potentials there are precise asymptotics going back to the at least the middle of the twentieth century. My ...

Time-resolved fluorescence of 4',6-diamidino-2-phenylindole (DAPI) complexes show that for a homogeneous polymer (polyd(AT) or polyd(A).polyd(T)) at high P/D (phosphate/dye) ratio, a single exponential component adequately describes the fluorescence decay. For the AT polymers at low P/D ratio or for native DNA, the decay cannot be described by a single-exponential term. A continuous distributio...

We study the abelian sandpile model on a random binary tree. Using a transfer matrix approach introduced by Dhar & Majumdar, we prove exponential decay of correlations, and in a small supercritical region exponential decay of avalanche sizes. This shows a phase transition phenomenon between exponential decay and power law decay of avalanche sizes. Our main technical tools are: (1) A recursion f...

We study the spatial decay of electron coherence due to electron-electron interaction in a finite-length disorder-free quantum wire. Based on the Luttinger liquid theory, we demonstrate that the coherence length characterizing the exponential decay of the coherence can vary from region to region, and that the coherence can even revive after the decay. This counterintuitive behavior, which is in...