Theory and application of Fermi pseudo-potential in one dimension

The theory of interaction at one point is developed for the one-dimensional Schrodinger equation. In analog with the three-dimensional case, the resulting interaction is referred to as the Fermi pseudo-potential. The dominant feature of this one-dimensional problem comes from the fact that the real line becomes disconnected when one point is removed. The general interaction at one point is found to be the sum of three terms, the well-known delta-function potential and two Fermi pseudo-potentials, one odd under space reflection and the other even. The odd one gives the proper interpretation for the delta'(x) potential, while the even one is unexpected and more interesting. Among the many applications of these Fermi pseudo-potentials, the simplest one is described. It consists of a superposition of the delta-function potential and the even pseudo-potential applied to two-channel scattering. This simplest application leads to a model of the quantum memory, an essential component of any quantum computer.Comment: RevTeX4, 32 pages, no figure

Bound States in n Dimensions (Especially n = 1 and n = 2)

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the "right" coupling constant behaviour for large coupling.Comment: Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems

Testable upper bound on ρ = Ref/ Im f

At LHC energies we reach a point where ln(s/m2) > 10. In this paper we give upper bounds on ρ = Ref/ Im f that have no unknown constants and are thus experimentally testable

Universality of Low-Energy Scattering in 2+1 Dimensions: The Non Symmetric Case

For a very large class of potentials, $V(\vec{x})$, $\vec{x}\in R^2$, we prove the universality of the low energy scattering amplitude, $f(\vec{k}', \vec{k})$. The result is $f=\sqrt{\frac{\pi}{2}}\{1/log k)+O(1/(log k)^2)$. The only exceptions occur if $V$ happens to have a zero energy bound state. Our new result includes as a special subclass the case of rotationally symmetric potentials, $V(|\vec{x}|)$.Comment: 65 pages, Latex, significant changes, new sections and appendice

Mitochondrial apoptosis induced by Chamaemelum nobile extract in breast cancer cells

Chamaemelum nobile (Asteraceae) commonly known as ‹Roman chamomile› is a medicinal plant used for numerous diseases in traditional medicine, although its anticancer activity is unknown. The present study was carried out to investigate the anticancer as well as apoptotic activity of ethyl acetate fraction of C. nobile on different cancerous cell lines. The cells were treated with varying concentrations (0.001-0.25 mg/mL) of this fraction for 24, 48 and 72 h. Apoptosis induced in MCF-7 cells following treatment with ethyl acetate fraction was measured using Annexin V/PI, flowcytometry and western blotting analysis. The results showed that C. nobile ethyl acetate fraction revealed relatively high antiproliferative activity on MCF-7 cells; however, it caused minimal growth inhibitory response in normal cells. The involvement of apoptosis as a major cause of the fraction-induced cell death was confirmed by annexin-V/PI assay. In addition, ethyl acetate fraction triggered the mitochondrial apoptotic pathway by decreasing the Bcl-2 as well as increasing of Bax protein expressions and subsequently increasing Bax/Bcl-2 ratio. Furthermore, decreased proliferation of MCF-7 cells in the presence of the fraction was associated with G2/M phase cell cycle arrest. These findings confirm that ethyl acetate fraction of C.nobile may contain a diversity of phytochemicals which suppress the proliferation of MCF-7 cells by inducing apoptosis. © 2016 by School of Pharmacy Shaheed Beheshti University of Medical Sciences and Health Services

Total Widths And Slopes From Complex Regge Trajectories

Maximally complex Regge trajectories are introduced for which both Re $\alpha(s)$ and Im $\alpha(s)$ grow as $s^{1-\epsilon}$ ($\epsilon$ small and positive). Our expression reduces to the standard real linear form as the imaginary part (proportional to $\epsilon$) goes to zero. A scaling formula for the total widths emerges: $\Gamma_{TOT}/M\to$ constant for large M, in very good agreement with data for mesons and baryons. The unitarity corrections also enhance the space-like slopes from their time-like values, thereby resolving an old problem with the $\rho$ trajectory in $\pi N$ charge exchange. Finally, the unitarily enhanced intercept, $\alpha_{\rho}\approx 0.525$, \nolinebreak is in good accord with the Donnachie-Landshoff total cross section analysis.Comment: 9 pages, 3 Figure