Electron pairing: from metastable electron pair to bipolaron

Starting from the shell structure in atoms and the significant correlation within electron pairs, we distinguish the exchange-correlation effects between two electrons of opposite spins occupying the same orbital from the average correlation among many electrons in a crystal. In the periodic potential of the crystal with lattice constant larger than the effective Bohr radius of the valence electrons, these correlated electron pairs can form a metastable energy band above the corresponding single-electron band separated by an energy gap. In order to determine if these metastable electron pairs can be stabilized, we calculate the many-electron exchange-correlation renormalization and the polaron correction to the two-band system with single electrons and electron pairs. We find that the electron-phonon interaction is essential to counterbalance the Coulomb repulsion and to stabilize the electron pairs. The interplay of the electron-electron and electron-phonon interactions, manifested in the exchange-correlation energies, polaron effects, and screening, is responsible for the formation of electron pairs (bipolarons) that are located on the Fermi surface of the single-electron band.Comment: 17 pages, 6 figures, Journal of Physics Communications 201

Emigration and development in the European periphery: Portugal’s case

In the literature on the relationship between migration and development, it is common to assess the impacts of migration on countries of origin and on destination countries separately (see Goldin, Cameron and Blarajan, 2011: 162‑210). Strictly speaking, this differentiation tends to correspond to another one, made in practice but rarely specified, which involves the overlap between country of origin and developing country, on the one hand, and between country of destination and developed country, on the other. Transposing many of the conclusions of this literature to analyse the impacts of emigration in a country of origin classified as of high human development, like Portugal, is often difficult, requiring a careful selection of what is or is not applicable and analytical readiness to identify and explain particular dynamics of this type of countries: developed countries of emigration.info:eu-repo/semantics/publishedVersio

Melting temperature of screened Wigner crystal on helium films by molecular dynamics

Using molecular dynamics (MD) simulation, we have calculated the melting temperature of two-dimensional electron systems on $240$\AA-$500$\AA helium films supported by substrates of dielectric constants $\epsilon_{s}=2.2-11.9$ at areal densities $n$ varying from $3\times 10^{9}$ cm$^{-2}$ to $1.3\times 10^{10}$ cm$^{-2}$. Our results are in good agreement with the available theoretical and experimental results.Comment: 4 pages and 4 figure

Supersymmetric and Shape-Invariant Generalization for Nonresonant and Intensity-Dependent Jaynes-Cummings Systems

A class of shape-invariant bound-state problems which represent transition in a two-level system introduced earlier are generalized to include arbitrary energy splittings between the two levels as well as intensity-dependent interactions. We show that the couple-channel Hamiltonians obtained correspond to the generalizations of the nonresonant and intensity-dependent nonresonant Jaynes-Cummings Hamiltonians, widely used in quantized theories of laser. In this general context, we determine the eigenstates, eigenvalues, the time evolution matrix and the population inversion matrix factor.Comment: A combined version of quant-ph/0005045 and quant-ph/0005046. 24 pages, LATE

Formation energy and interaction of point defects in two-dimensional colloidal crystals

The manipulation of individual colloidal particles using optical tweezers has allowed vacancies to be created in two-dimensional (2d) colloidal crystals, with unprecedented possibility of real-time monitoring the dynamics of such defects (Nature {\bf 413}, 147 (2001)). In this Letter, we employ molecular dynamics (MD) simulations to calculate the formation energy of single defects and the binding energy between pairs of defects in a 2d colloidal crystal. In the light of our results, experimental observations of vacancies could be explained and then compared to simulation results for the interstitial defects. We see a remarkable similarity between our results for a 2d colloidal crystal and the 2d Wigner crystal (Phys. Rev. Lett. {\bf 86}, 492 (2001)). The results show that the formation energy to create a single interstitial is $12$ lower than that of the vacancy. Because the pair binding energies of the defects are strongly attractive for short distances, the ground state should correspond to bound pairs with the interstitial bound pairs being the most probable.Comment: 5 pages, 2 figure

Evolution of physical processes in models of population dynamics

Neste texto apresentamos e discutimos um breve panorama cronológico para a dinâmica de populações, observando o ponto de vista dos autores, bem como a evolução dos principais modelos matemáticos e sua importância histórica. Com foco na predição temporal e espacial da variação do número de indivíduos de uma população, analisamos como modelar matematicamente os processos físicos como crescimento, interação, difusão e fluxo de um coletivo de indivíduos. Partimos do bem conhecido modelo de Fibonacci e discutimos como modelos que o sucederam, a saber, o modelo Malthusiano, Lotka-Volterra e Fisher-Kolmogorov, foram capazes de ampliar o entendimento do comportamento de uma população. Apresentamos, nesta linha temporal sinuosa, como as interações entre uma mesma espécie e entre espécies podem ser explicadas e modeladas. Mostramos como funciona o processo de extinção de uma espécie predadora, o fenômeno de difusão de um coletivo devido as mais diversas exigências espaciais, as migrações e invasões de territórios por meio de uma dinâmica convectiva nos modelos de dinâmica de uma população e também como a não-localidade nas interações e no crescimento ampliam enormemente nosso entendimento sobre os padrões na natureza.In this paper we present and discuss a brief overview chronological for the population dynamics, observing the point of view of the authors, as well as the evolution of the main mathematical models and its historical importance. Focusing on temporal and spatial prediction of the variation in the number of individuals in a population, we analyze how to mathematically model the physical processes such as growth, interaction, dissemination and flow of a collective of individuals. We start from the well-known model of Fibonacci and discussed how models who succeeded him, namely the Malthusian model, Lotka-Volterra and Fisher-Kolmogorov were able to expand the understanding of the behavior of a population. Here, in this winding timeline as the interactions between species and between species can be explained and modeled. We show how the process of extinguishing a predatory species works, the diffusion phenomenon of a collective because the most diverse space requirements, migration and invasions of territories by means of convective momentum in dynamic models of a population as well as non-locality in interactions and growth greatly expand our understanding of the patterns in nature

Classical artificial two-dimensional atoms: the Thomson model

The ring configurations for classical two-dimensional atoms are calculated within the Thomson model and compared with the results from `exact' numerical simulations. The influence of the functional form of the confinement potential and the repulsive interaction potential between the particles on the configurations is investigated. We also give exact results on those eigenmodes of the system whose frequency does not depend on the number of particles in the system.Comment: 9 pages, RevTeX, 4 figure

Generalized Ladder Operators for Shape-invariant Potentials

A general form for ladder operators is used to construct a method to solve bound-state Schr\"odinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for the radial harmonic oscillator and Coulomb potentials.Comment: in Revte

Self-organization and pattern formation in physical and biological systems

Neste trabalho apresentamos uma breve discussão sobre a descrição matemática do fenômeno formação de padrão em sistemas biológicos, observando os modelos matemáticos de dinâmica de populações. Listamos vários exemplos de sistemas físicos, químicos e biológicos que exibem este fenômeno enfatizando, em cada um, os parâmetros principais envolvidos em seu entendimento. Mostramos que, no caso das populações, o fenômeno padrão pode ser modelado ao modificarmos a equação de Fisher-Kolmogorov, considerando uma interação não-local para o termo de competição. Apresentamos um estudo analítico e numérico da equação de Fisher-Kolmogorov com difusão e analisamos o papel dos termos de crescimento, difusão e competição na formação dos padrões.In this work we present a brief discussion of the mathematical description of pattern formation phenomena in biological systems through the mathematical models of population dynamics. We present some examples of physical, chemical and biological systems which exhibit this phenomena. For each system we show the main parameters that describe the patterns. We show that in the case of population, patterns can be described when we modify the Fisher-Kolmogorov equation, considering a non-local interaction for the competition term. We present an analytical and numerical study of the Fisher-Kolmogorov equation with diffusion and we analyze the role of growth, diffusion and competition term in the pattern formation

Algebraic Nature of Shape-Invariant and Self-Similar Potentials

Self-similar potentials generalize the concept of shape-invariance which was originally introduced to explore exactly-solvable potentials in quantum mechanics. In this article it is shown that previously introduced algebraic approach to the latter can be generalized to the former. The infinite Lie algebras introduced in this context are shown to be closely related to the q-algebras. The associated coherent states are investigated.Comment: 8 page