SUSY transformation of the Green function and a trace formula

An integral relation is established between the Green functions corresponding to two Hamiltonians which are supersymmetric (SUSY) partners and in general may possess both discrete and continuous spectra. It is shown that when the continuous spectrum is present the trace of the difference of the Green functions for SUSY partners is a finite quantity which may or may not be equal to zero despite the divergence of the traces of each Green function. Our findings are illustrated by using the free particle example considered both on the whole real line and on a half line

Recovery of a quarkonium system from experimental data

For confining potentials of the form q(r)=r+p(r), where p(r) decays rapidly and is smooth for r>0, it is proved that q(r) can be uniquely recovered from the data {E_j,s_j}, where E_j are the bound states energies and s_j are the values of u'_j(0), and u_j(r) are the normalized eigenfunctions of the problem -u_j" +q(r)u_j=E_ju_j, r>0, u_j(0)=0, ||u_j||=1, where the norm is L^2(0, \infty) norm. An algorithm is given for recovery of p(r) from few experimental data

Topological model of soap froth evolution with deterministic T2-processes

We introduce a topological model for the evolution of 2d soap froth. The topological rearrangements (T2 processes) are deterministic (unlike the standard stochastic model): the final topology depends on the areas of the neighboring cells. The new model gives agreement with experiments in the transient regime, where the previous models failed qualitatively, and also improves agreement in the scaling state.Comment: latex, 12 pages, 2 figure

Diffusion of a granular pulse in a rotating drum

The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to elucidate the effect of the confining end-plate of the drum. We then show that the diffusion is neither subdiffusive nor superdiffusive but normal. This is demonstrated by rescaling the concentration profiles obtained at various stages and by studying the time evolution of the mean squared deviation. Finally we study the self-diffusion of both large and small grains and we show that it is normal and that the diffusion coefficient is independent of the grain size

Signatures of the order parameter of a superconducting adatom layer in quasiparticle interference patterns

Experiments have observed superconductivity in atomically-thin metallic layers deposited on semiconducting substrates. As in any superconductor, it is important to determine the structure of the superconducting pairing function in order to reveal the mechanism responsible for superconductivity. To that end, we study the possible superconducting states of two-dimensional triangular lattices. We calculate the quasiparticle interference (QPI) patterns which would result from various nearest-neighbor pairing order parameters, and show how the QPI can be used to distinguish between those order parameters. The QPI patterns are the momentum-space representations of real-space local density-of-states fluctuations: the QPI signal at momentum $q$ reveals the strength of scattering processes at that momentum transfer. We show how characteristic differences between scattering from charge disorder (i.e. impurities) and from order-parameter disorder (i.e. vortices) can be used to identify the angular momentum of the superconducting pairs.Comment: 12 pages, 8 figure

Example of two different potentials which have practically the same fixed-energy phase shifts

It is shown that the Newton-Sabatier procedure for inverting the fixed-energy phase shifts for a potential is not an inversion method but a parameter-fitting procedure. Theoretically there is no guarantee that this procedure is applicable to the given set of the phase shifts, if it is applicable, there is no guaran- tee that the potential it produces generates the phase shifts from which it was reconstructed. Moreover, no generic potential, specifically, no potential which is not analytic in a neighborhood of the positive real semiaxis can be reconstructed by the Newton-Sabatier procedure. A numerical method is given for finding spherically symmetric compactly supported potentials which produce practically the same set of fixed-energy phase shifts for all values of angular momentum. Concrete example of such potentials is given

Effects of Noise in a Cortical Neural Model

Recently Segev et al. (Phys. Rev. E 64,2001, Phys.Rev.Let. 88, 2002) made long-term observations of spontaneous activity of in-vitro cortical networks, which differ from predictions of current models in many features. In this paper we generalize the EI cortical model introduced in a previous paper (S.Scarpetta et al. Neural Comput. 14, 2002), including intrinsic white noise and analyzing effects of noise on the spontaneous activity of the nonlinear system, in order to account for the experimental results of Segev et al.. Analytically we can distinguish different regimes of activity, depending from the model parameters. Using analytical results as a guide line, we perform simulations of the nonlinear stochastic model in two different regimes, B and C. The Power Spectrum Density (PSD) of the activity and the Inter-Event-Interval (IEI) distributions are computed, and compared with experimental results. In regime B the network shows stochastic resonance phenomena and noise induces aperiodic collective synchronous oscillations that mimic experimental observations at 0.5 mM Ca concentration. In regime C the model shows spontaneous synchronous periodic activity that mimic activity observed at 1 mM Ca concentration and the PSD shows two peaks at the 1st and 2nd harmonics in agreement with experiments at 1 mM Ca. Moreover (due to intrinsic noise and nonlinear activation function effects) the PSD shows a broad band peak at low frequency. This feature, observed experimentally, does not find explanation in the previous models. Besides we identify parametric changes (namely increase of noise or decreasing of excitatory connections) that reproduces the fading of periodicity found experimentally at long times, and we identify a way to discriminate between those two possible effects measuring experimentally the low frequency PSD.Comment: 25 pages, 10 figures, to appear in Phys. Rev.

SLOB, a SLOWPOKE Channel Binding Protein, Regulates Insulin Pathway Signaling and Metabolism in Drosophila

There is ample evidence that ion channel modulation by accessory proteins within a macromolecular complex can regulate channel activity and thereby impact neuronal excitability. However, the downstream consequences of ion channel modulation remain largely undetermined. The Drosophila melanogaster large conductance calcium-activated potassium channel SLOWPOKE (SLO) undergoes modulation via its binding partner SLO-binding protein (SLOB). Regulation of SLO by SLOB influences the voltage dependence of SLO activation and modulates synaptic transmission. SLO and SLOB are expressed especially prominently in median neurosecretory cells (mNSCs) in the pars intercerebralis (PI) region of the brain; these cells also express and secrete Drosophila insulin like peptides (dILPs). Previously, we found that flies lacking SLOB exhibit increased resistance to starvation, and we reasoned that SLOB may regulate aspects of insulin signaling and metabolism. Here we investigate the role of SLOB in metabolism and find that slob null flies exhibit changes in energy storage and insulin pathway signaling. In addition, slob null flies have decreased levels of dilp3 and increased levels of takeout, a gene known to be involved in feeding and metabolism. Targeted expression of SLOB to mNSCs rescues these alterations in gene expression, as well as the metabolic phenotypes. Analysis of fly lines mutant for both slob and slo indicate that the effect of SLOB on metabolism and gene expression is via SLO. We propose that modulation of SLO by SLOB regulates neurotransmission in mNSCs, influencing downstream insulin pathway signaling and metabolism