445 research outputs found
A Christoffel-Darboux formula for multiple orthogonal polynomials
Bleher and Kuijlaars recently showed that the eigenvalue correlations from
matrix ensembles with external source can be expressed by means of a kernel
built out of special multiple orthogonal polynomials. We derive a
Christoffel-Darboux formula for this kernel for general multiple orthogonal
polynomials. In addition, we show that the formula can be written in terms of
the solution of the Riemann-Hilbert problem for multiple orthogonal
polynomials, which will be useful for asymptotic analysis.Comment: 11 pages, no figure
Robust quantum control by shaped pulse
Considering the problem of the control of a two-state quantum system by an
external field, we establish a general and versatile method that allows the
derivation of smooth pulses, suitable for ultrafast applications, that feature
the properties of high-fidelity, robustness, and low area. Such shaped pulses
can be viewed as a single-shot generalization of the composite pulse technique
with a time-dependent phase
Capacity of a bosonic memory channel with Gauss-Markov noise
We address the classical capacity of a quantum bosonic memory channel with
additive noise, subject to an input energy constraint. The memory is modeled by
correlated noise emerging from a Gauss-Markov process. Under reasonable
assumptions, we show that the optimal modulation results from a "quantum
water-filling" solution above a certain input energy threshold, similar to the
optimal modulation for parallel classical Gaussian channels. We also derive
analytically the optimal multimode input state above this threshold, which
enables us to compute the capacity of this memory channel in the limit of an
infinite number of modes. The method can also be applied to a more general
noise environment which is constructed by a stationary Gauss process. The
extension of our results to the case of broadband bosonic channels with colored
Gaussian noise should also be straightforward.Comment: 11 pages, 4 figures, final corrections mad
Optimized time-dependent perturbation theory for pulse-driven quantum dynamics in atomic or molecular systems
We present a time-dependent perturbative approach adapted to the treatment of
intense pulsed interactions. We show there is a freedom in choosing secular
terms and use it to optimize the accuracy of the approximation. We apply this
formulation to a unitary superconvergent technique and improve the accuracy by
several orders of magnitude with respect to the Magnus expansion.Comment: 4 pages, 2 figure
Laser control for the optimal evolution of pure quantum states
Starting from an initial pure quantum state, we present a strategy for
reaching a target state corresponding to the extremum (maximum or minimum) of a
given observable. We show that a sequence of pulses of moderate intensity,
applied at times when the average of the observable reaches its local or global
extremum, constitutes a strategy transferable to different control issues.
Among them, post-pulse molecular alignment and orientation are presented as
examples. The robustness of such strategies with respect to experimentally
relevant parameters is also examined.Comment: 16 pages, 9 figure
Reaching optimally oriented molecular states by laser kicks
We present a strategy for post-pulse orientation aiming both at efficiency
and maximal duration within a rotational period. We first identify the
optimally oriented states which fulfill both requirements. We show that a
sequence of half-cycle pulses of moderate intensity can be devised for reaching
these target states.Comment: 4 pages, 3 figure
Unitary time-dependent superconvergent technique for pulse-driven quantum dynamics
We present a superconvergent Kolmogorov-Arnold-Moser type of perturbation theory for time-dependent Hamiltonians. It is strictly unitary upon truncation at an arbitrary order and not restricted to periodic or quasiperiodic Hamiltonians. Moreover, for pulse-driven systems we construct explicitly the KAM transformations involved in the iterative procedure. The technique is illustrated on a two-level model perturbed by a pulsed interaction for which we obtain convergence all the way from the sudden regime to the opposite adiabatic regime
Sociodemographic Determinants for Oral Health Risk Profiles
The present study aimed to explore the association between caries risk profiles and different sociodemographic factors .
The study sample (n = 104) was randomly selected within an urban population in Flanders, Belgium. Caries risk was assessed by anamnesis, clinical examination, salivary tests, and a questionnaire. Age, gender, and socio-economic status were extracted from social insurance data files. Social indicators were âoccupational status,â âbeing entitled to the increased allowance for health care interventionsâ and having access to the âMaximum Billâ (MAF), initiatives undertaken to protect deprived families. In the bivariate analysis there were significant differences in risk profiles between occupational groups (P < .001), between entitled and non-entitled individuals to the increased allowance (P = .02), and between access or no-access to the MAF (P < .01). The multiple logistic model showed a significantly higher chance of being in the low risk group for individuals with no-access to the MAF compared to those with access (OR:14.33â95% C.I. 2.14â95.84)
Time-dependent unitary perturbation theory for intense laser driven molecular orientation
We apply a time-dependent perturbation theory based on unitary
transformations combined with averaging techniques, on molecular orientation
dynamics by ultrashort pulses. We test the validity and the accuracy of this
approach on LiCl described within a rigid-rotor model and find that it is more
accurate than other approximations. Furthermore, it is shown that a noticeable
orientation can be achieved for experimentally standard short laser pulses of
zero time average. In this case, we determine the dynamically relevant
parameters by using the perturbative propagator, that is derived from this
scheme, and we investigate the temperature effects on the molecular orientation
dynamics.Comment: 16 pages, 6 figure
Non-intersecting squared Bessel paths and multiple orthogonal polynomials for modified Bessel weights
We study a model of non-intersecting squared Bessel processes in the
confluent case: all paths start at time at the same positive value , remain positive, and are conditioned to end at time at . In
the limit , after appropriate rescaling, the paths fill out a
region in the -plane that we describe explicitly. In particular, the paths
initially stay away from the hard edge at , but at a certain critical
time the smallest paths hit the hard edge and from then on are stuck to
it. For we obtain the usual scaling limits from random matrix
theory, namely the sine, Airy, and Bessel kernels. A key fact is that the
positions of the paths at any time constitute a multiple orthogonal
polynomial ensemble, corresponding to a system of two modified Bessel-type
weights. As a consequence, there is a matrix valued
Riemann-Hilbert problem characterizing this model, that we analyze in the large
limit using the Deift-Zhou steepest descent method. There are some novel
ingredients in the Riemann-Hilbert analysis that are of independent interest.Comment: 59 pages, 11 figure
- âŠ