Introduction of a Quantum of Time (chronon), and its Consequences for Quantum Mechanics

We discuss the consequences of the introduction of a quantum of time $\tau_0$ in the formalism of non-relativistic quantum mechanics, by referring ourselves in particular to the theory of the chronon as proposed by P.Caldirola. Such an interesting "finite difference" theory, forwards ---at the classical level--- a solution for the motion of a particle endowed with a non-negligible charge in an external electromagnetic field, overcoming all the known difficulties met by Abraham-Lorentz's and Dirac's approaches (and even allowing a clear answer to the question whether a free falling charged particle does or does not emit radiation), and ---at the quantum level--- yields a remarkable mass spectrum for leptons. After having briefly reviewed Caldirola's approach, our first aim is to work out, discuss, and compare one another the new representations of Quantum Mechanics (QM) resulting from it, in the Schrödinger, Heisenberg and density-operator (Liouville-von Neumann) pictures, respectively. Moreover, for each representation, three ( retarded, symmetric and advanced) formulations are possible, which refer either to times $t$ and $t-\tau_0$, or to times $t-\tau_0/2$ and $t+\tau_0/2$, or to times $t$ and $t+\tau_0$, respectively. It is interesting to notice that, when the chronon tends to zero, the ordinary QM is obtained as the limiting case of the "symmetric" formulation only; while the "retarded" one does naturally appear to describe QM with friction, i.e., to describe dissipative quantum systems (like a particle moving in an absorbing medium). In this sense, discretized QM is much richer than the ordinary one. We also obtain the (advanced) finite-difference Schrödinger equation within the Feynman path integral approach, and study some of its relevant solutions. W

Monitoramento do ciclo de videiras pelo Índice de Vegetação por Diferença Normalizada obtido de imagens Landsat 8 no município de Veranópolis-RS, Brasil.

O objetivo deste trabalho foi monitorar o ciclo de videiras (Vitis vinifera) em diferentes sistemas de condução na Serra Gaúcha-RS por meio do Índice de Vegetação por Diferença Normalizada (NDVI) obtido de imagens Landsat8/OLI

Oscilloscope measurement of the synchronous phase shift in an electron storage ring

We present a new technique to measure the synchronous phase shift in an electron storage ring. A digital sampling oscilloscope is used to observe the cavity and beam signals simultaneously, and the amplitude and relative phase are obtained from a Fourier transform of the time-domain data. This procedure gives 6 mdeg resolution and is largely insensitive to input signal amplitude variations. The measurement system was used to study the dependence of the synchronous phase shift on beam current, gap voltage, and beam energy in the Brazilian Synchrotron Light Source electron storage ring

BEC-BCS crossover in a cold and magnetized two color NJL model

The BEC-BCS crossover for a NJL model with diquark interactions is studied in the presence of an external magnetic field. Particular attention is paid to different regularization schemes used in the literature. A thorough comparison of results is performed for the case of a cold and magnetized two-color NJL model. According to our results, the critical chemical potential for the BEC transition exhibits a clear inverse magnetic catalysis effect for magnetic fields in the range $1 \lesssim eB/m_\pi^2 \lesssim 20$. As for the BEC-BCS crossover, the corresponding critical chemical potential is very weakly sensitive to magnetic fields up to $eB \sim 9\ m_\pi^2$, showing a much smaller inverse magnetic catalysis as compared to the BEC transition, and displays a strong magnetic catalysis from this point on.Comment: 15 pages, 8 figures; v2 PRD versio

(Giant) Vortex - (anti) vortex interaction in bulk superconductors: The Ginzburg-Landau theory

The vortex-vortex interaction potential in bulk superconductors is calculated within the Ginzburg-Landau (GL) theory and is obtained from a numerical solution of a set of two coupled non-linear GL differential equations for the vector potential and the superconducting order parameter, where the merger of vortices into a giant vortex is allowed. Further, the interaction potentials between a vortex and a giant vortex and between a vortex and an antivortex are obtained for both type-I and type-II superconductors. Our numerical results agree asymptotically with the analytical expressions for large inter-vortex separations which are available in the literature. We propose new empirical expressions valid over the full interaction range, which are fitted to our numerical data for different values of the GL parameter