Asymptotic normality for the counting process of weak records and \delta-records in discrete models

Let $\{X_n,n\ge1\}$ be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call $X_n$ a $\delta$-record if $X_n>\max\{X_1,...,X_{n-1}\}+\delta$, where $\delta$ is an integer constant. We use martingale arguments to show that the counting process of $\delta$-records among the first $n$ observations, suitably centered and scaled, is asymptotically normally distributed for $\delta\ne0$. In particular, taking $\delta=-1$ we obtain a central limit theorem for the number of weak records.Comment: Published at http://dx.doi.org/10.3150/07-BEJ6027 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

A quantum trajectory description of decoherence

A complete theoretical treatment in many problems relevant to physics, chemistry, and biology requires considering the action of the environment over the system of interest. Usually the environment involves a relatively large number of degrees of freedom, this making the problem numerically intractable from a purely quantum-mechanical point of view. To overcome this drawback, a new class of quantum trajectories is proposed. These trajectories, based on the same grounds as Bohmian ones, are solely associated to the system reduced density matrix, since the evolution of the environment degrees of freedom is not considered explicitly. Within this approach, environment effects come into play through a time-dependent damping factor that appears in the system equations of motion. Apart from their evident computational advantage, this type of trajectories also results very insightful to understand the system decoherence. In particular, here we show the usefulness of these trajectories analyzing decoherence effects in interference phenomena, taking as a working model the well-known double-slit experiment.Comment: 8 pages, 3 figure

Time resolved pattern evolution in a large aperture laser

We have measured quasi-instantaneous transverse patterns in a broad aperture laser. Non-ordered patterns yielding to boundary determined regular structures in progressive time-integrated recording are observed. The linear analysis and numerical integration of the full Maxwell-Bloch equations allow us to interpret the features of the experiment. We show that this system being far from threshold cannot be fully understood with a perturbative model.Comment: 7 pages, 5 GIF figures . To be published in Phys. Rev. Let