Analytical treatment of stabilization

We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the theoretical context when the dynamics is described by the Stark Hamiltonian. The main outcome of these studies is that the governing parameters for this phenomenon are the total classical momentum transfer and the total classical displacement. Whenever these two quantities vanish, asymptotically weak stabilization does exist. For all other situations we did not find any evidence for stabilization. We found no evidence that strong stabilization might occur. Our results agree qualitatively with the existing experimental findings

Parametric Competition in non-autonomous Hamiltonian Systems

In this work we use the formalism of chord functions (\emph{i.e.} characteristic functions) to analytically solve quadratic non-autonomous Hamiltonians coupled to a reservoir composed by an infinity set of oscillators, with Gaussian initial state. We analytically obtain a solution for the characteristic function under dissipation, and therefore for the determinant of the covariance matrix and the von Neumann entropy, where the latter is the physical quantity of interest. We study in details two examples that are known to show dynamical squeezing and instability effects: the inverted harmonic oscillator and an oscillator with time dependent frequency. We show that it will appear in both cases a clear competition between instability and dissipation. If the dissipation is small when compared to the instability, the squeezing generation is dominant and one can see an increasing in the von Neumann entropy. When the dissipation is large enough, the dynamical squeezing generation in one of the quadratures is retained, thence the growth in the von Neumann entropy is contained

Existence criteria for stabilization from the scaling behaviour of ionization probabilities

We provide a systematic derivation of the scaling behaviour of various quantities and establish in particular the scale invariance of the ionization probability. We discuss the gauge invariance of the scaling properties and the manner in which they can be exploited as consistency check in explicit analytical expressions, in perturbation theory, in the Kramers-Henneberger and Floquet approximation, in upper and lower bound estimates and fully numerical solutions of the time dependent Schroedinger equation. The scaling invariance leads to a differential equation which has to be satisfied by the ionization probability and which yields an alternative criterium for the existence of atomic bound state stabilization.Comment: 12 pages of Latex, one figur

Relationships between nutrient composition of flowers and fruit quality in orange trees grown in calcareous soil

To determine if flower nutrient composition can be used to predict fruit quality, a field experiment was conducted over three seasons (1996-1999) in a commercial orange orchard (Citrus sinensis (L.) Osbeck cv. 'Valencia Late', budded on Troyer citrange rootstock) established on a calcareous soil in southern Portugal. Flowers were collected from 20 trees during full bloom in April and their nutrient composition determined, and fruits were harvested the following March and their quality evaluated. Patterns of covariation in flower nutrient concentrations and in fruit quality variables were evaluated by principal component analysis. Regression models relating fruit quality variables to flower nutrient composition were developed by stepwise selection procedures. The predictive power of the regression models was evaluated with an independent data set. Nutrient composition of flowers at full bloom could be used to predict the fruit quality variables fresh fruit mass and maturation index in the following year. Magnesium, Ca and Zn concentrations measured in flowers were related to fruit fresh mass estimations and N, P, Mg and Fe concentrations were related to fruit maturation index. We also established reference values for the nutrient composition of flowers based on measurements made in trees that produced large (> 76 mm in diameter) fruit.info:eu-repo/semantics/publishedVersio

Low redshift constraints on energy-momentum-powered gravity models

There has been recent interest in the cosmological consequences of energy-momentum-powered gravity models, in which the matter side of Einstein's equations is modified by the addition of a term proportional to some power, $n$, of the energy-momentum tensor, in addition to the canonical linear term. In this work we treat these models as phenomenological extensions of the standard $\Lambda$CDM, containing both matter and a cosmological constant. We also quantitatively constrain the additional model parameters using low redshift background cosmology data that are specifically from Type Ia supernovas and Hubble parameter measurements. We start by studying specific cases of these models with fixed values of $n,$ which lead to an analytic expression for the Friedmann equation; we discuss both their current constraints and how the models may be further constrained by future observations of Type Ia supernovas for WFIRST complemented by measurements of the redshift drift by the ELT. We then consider and constrain a more extended parameter space, allowing $n$ to be a free parameter and considering scenarios with and without a cosmological constant. These models do not solve the cosmological constant problem per se. Nonetheless these models can phenomenologically lead to a recent accelerating universe without a cosmological constant at the cost of having a preferred matter density of around $\Omega_M\sim0.4$ instead of the usual $\Omega_M\sim0.3$. Finally we also briefly constrain scenarios without a cosmological constant, where the single component has a constant equation of state which needs not be that of matter; we provide an illustrative comparison of this model with a more standard dynamical dark energy model with a constant equation of state.Comment: 13+2 pages, 12+1 figures; A&A (in press

Control of state and state entanglement with a single auxiliary subsystem

We present a strategy to control the evolution of a quantum system. The novel aspect of this protocol is the use of a \emph{single auxiliary subsystem}. Two applications are given, one which allows for state preservation and another which controls the degree of entanglement of a given initial state

Non-Hermitian Hamiltonians with real eigenvalues coupled to electric fields: from the time-independent to the time dependent quantum mechanical formulation

We provide a reviewlike introduction into the quantum mechanical formalism related to non-Hermitian Hamiltonian systems with real eigenvalues. Starting with the time-independent framework we explain how to determine an appropriate domain of a non-Hermitian Hamiltonian and pay particular attention to the role played by PT-symmetry and pseudo-Hermiticity. We discuss the time-evolution of such systems having in particular the question in mind of how to couple consistently an electric field to pseudo-Hermitian Hamiltonians. We illustrate the general formalism with three explicit examples: i) the generalized Swanson Hamiltonians, which constitute non-Hermitian extensions of anharmonic oscillators, ii) the spiked harmonic oscillator, which exhibits explicit supersymmetry and iii) the -x^4-potential, which serves as a toy model for the quantum field theoretical phi^4-theory.Comment: 14 pages, 3 figures, to appear in Laser Physics, minor typos correcte