Process tomography via sequential measurements on a single quantum system

We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.Comment: 7 pages, 2 figure

Nonlinear State-Space Models for Microeconometric Panel Data

In applied microeconometric panel data analyses, time-constant random effects and first-order Markov chains are the most prevalent structures to account for intertemporal correlations in limited dependent variable models. An example from health economics shows that the addition of a simple autoregressive error terms leads to a more plausible and parsimonious model which also captures the dynamic features better. The computational problems encountered in the estimation of such models - and a broader class formulated in the framework of nonlinear state space models - hampers their widespread use. This paper discusses the application of different nonlinear filtering approaches developed in the time-series literature to these models and suggests that a straightforward algorithm based on sequential Gaussian quadrature can be expected to perform well in this setting. This conjecture is impressively confirmed by an extensive analysis of the example application

Nonparametric estimation of the fragmentation kernel based on a PDE stationary distribution approximation

We consider a stochastic individual-based model in continuous time to describe a size-structured population for cell divisions. This model is motivated by the detection of cellular aging in biology. We address here the problem of nonparametric estimation of the kernel ruling the divisions based on the eigenvalue problem related to the asymptotic behavior in large population. This inverse problem involves a multiplicative deconvolution operator. Using Fourier technics we derive a nonparametric estimator whose consistency is studied. The main difficulty comes from the non-standard equations connecting the Fourier transforms of the kernel and the parameters of the model. A numerical study is carried out and we pay special attention to the derivation of bandwidths by using resampling

Measurability of kinetic temperature from metal absorption-line spectra formed in chaotic media

We present a new method for recovering the kinetic temperature of the intervening diffuse gas to an accuracy of 10%. The method is based on the comparison of unsaturated absorption-line profiles of two species with different atomic weights. The species are assumed to have the same temperature and bulk motion within the absorbing region. The computational technique involves the Fourier transform of the absorption profiles and the consequent Entropy-Regularized chi^2-Minimization [ERM] to estimate the model parameters. The procedure is tested using synthetic spectra of CII, SiII and FeII ions. The comparison with the standard Voigt fitting analysis is performed and it is shown that the Voigt deconvolution of the complex absorption-line profiles may result in estimated temperatures which are not physical. We also successfully analyze Keck telescope spectra of CII1334 and SiII1260 lines observed at the redshift z = 3.572 toward the quasar Q1937--1009 by Tytler {\it et al.}.Comment: 25 pages, 6 Postscript figures, aaspp4.sty file, submit. Ap