Dynamical screening of the Coulomb interaction for two confined electrons in a magnetic field

We show that a difference in time scales of vertical and lateral dynamics permits one to analyze the problem of interacting electrons confined in an axially symmetric three-dimensional potential with a lateral oscillator confinement by means of the effective two-dimensional Hamiltonian with a screened Coulomb interaction. Using an adiabatic approximation based on action-angle variables, we present solutions for the effective charge of the Coulomb interaction (screening) for a vertical confinement potential simulated by parabolic, square, and triangular wells. While for the parabolic potential the solution for the effective charge is given in a closed anlytical form, for the other cases similar solutions can be easily calculated numerically.Comment: 10 pages, 6 figure

A geometrical crossover in excited states of two-electron quantum dots in a magnetic field

We use the entanglement measure to study the evolution of quantum correlations in two-electron axially-symmetric parabolic quantum dots under a perpendicular magnetic field. We found that the entanglement indicates on the shape transition in the density distribution of two electrons in the lowest state with zero angular momentum projection at the specific value of the applied magnetic field.Facultad de Ciencias Exacta

A geometrical crossover in excited states of two-electron quantum dots in a magnetic field

We use the entanglement measure to study the evolution of quantum correlations in two-electron axially-symmetric parabolic quantum dots under a perpendicular magnetic field. We found that the entanglement indicates on the shape transition in the density distribution of two electrons in the lowest state with zero angular momentum projection at the specific value of the applied magnetic field.Facultad de Ciencias Exacta

Research correlation vegetation index of corn with speed of movement sensor and elevation of field

This paper presents field scouting of corn in order to determine the content of nitrogen in the green parts of the plants. The aim was to measure the vegetative index using two optical sensors by OptRx AGL Technology. The sensors are positioned at a distance of 3.5 m, individually observing five rows of corn. The speed of movement of the tractor and also elevation of field are varied. The measured vegetative index of the plants is correlated, in first, with the speed of the sensor on the platform. The measured vegetative index of the plants is correlated after that with elevation also. Both of that case are shown that the Normalised Difference Red Edge (NDRE) as represent of vegetative index is not correlated with speed and elevation. This Results represented with Pearson Correlation Coefficient and Spearman's Correlation Coefficient are statistical signatifical. This conclusions are valid only for short rang of speed and elevation research. Average speed was 6,39 km/hr and rang of elevation was 1.6 m (106.8-108.4 m)

On analytical solutions of f(R) modified gravity theories in FLRW cosmologies

A novel analytical method for f(R) modified theories without matter in Friedmann-Lemaitre-Robertson-Walker spacetimes is introduced. The equation of motion for the scale factor in terms of cosmic time is reduced to the equation for the evolution of the Ricci scalar R with the Hubble parameter H. The solution of equation of motion for actions of the form of power law in Ricci scalar R, is presented with a detailed elaboration of the action quadratic in R. The reverse use of the introduced method is exemplified in finding functional forms f(R) which lead to specified scale factor functions. The analytical solutions are corroborated by numerical calculations with excellent agreement. Possible further applications to the phases of inflationary expansion and late-time acceleration as well as f(R) theories with radiation are outlined.Comment: 16 pages, 6 figures. v2: minor changes, references added. v3: minor changes, more references added. v4: version to appear in IJMPD. v5: DOI and journal reference adde

A geometrical crossover in excited states of two-electron quantum dots in a magnetic field

We use the entanglement measure to study the evolution of quantum correlations in two-electron axially-symmetric parabolic quantum dots under a perpendicular magnetic field. We found that the entanglement indicates on the shape transition in the density distribution of two electrons in the lowest state with zero angular momentum projection at the specific value of the applied magnetic field.Facultad de Ciencias Exacta

Khronon inflation

We study the possibility that the approximate time shift symmetry during inflation is promoted to the full invariance under time reparametrization t \to \tilde t(t), or equivalently under field redefinition of the inflaton \phi \to \tilde\phi(\phi). The symmetry allows only two operators at leading order in derivatives, so that all n-point functions of scalar perturbations are fixed in terms of the power spectrum normalization and the speed of sound. During inflation the decaying mode only decays as 1/a and this opens up the possibility to violate some of the consistency relations in the squeezed limit, although this violation is suppressed by the (small) breaking of the field reparametrization symmetry. In particular one can get terms in the 3-point function that are only suppressed by 1/k_L in the squeezed limit k_L \to 0 compared to the local shape.Comment: 15 pages, 1 figure, v2. changes regarding the violation of the consistency relation. JCAP published versio

Threshold Laws for the Break-up of Atomic Particles into Several Charged Fragments

The processes with three or more charged particles in the final state exhibit particular threshold behavior, as inferred by the famous Wannier law for (2e + ion) system. We formulate a general solution which determines the threshold behavior of the cross section for multiple fragmentation. Applications to several systems of particular importance with three, four and five leptons (electrons and positrons) in the field of charged core; and two pairs of identical particles with opposite charges are presented. New threshold exponents for these systems are predicted, while some previously suggested threshold laws are revised.Comment: 40 pages, Revtex, scheduled for the July issue of Phys.Rev.A (1998

Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies

We study a one-dimensional system composed of three charged bosons confined in an external harmonic potential. More precisely, we investigate the ground-state correlation properties of the system, paying particular attention to the strong-interaction limit. We explain for the first time the nature of the degeneracies appearing in this limit in the spectrum of the reduced density matrix. An explicit representation of the asymptotic natural orbitals and their occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal

Symmetry breaking and the random-phase approximation in small quantum dots

The random-phase approximation has been used to compute the properties of parabolic two-dimensional quantum dots beyond the mean-field approximation. Special emphasis is put on the ground state correlation energy, the symmetry restoration and the role of the spurious modes within the random-phase approximation. A systematics with the Coulombic interaction strength is presented for the 2-electron dot, while for the 6- and 12-electron dots selected cases are discussed. The validity of the random-phase approximation is assessed by comparison with available exact results.Comment: 9 pages, 4 embedded + 6 gif Figs. Published versio