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

Manejo florestal comunitário madeireiro na região Transamazônica.

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Fermi surface in the hidden-order state of URu2_2Si2_2 under intense pulsed magnetic fields up to 81~T

We present measurements of the resistivity $\rho_{x,x}$ of URu2Si2 high-quality single crystals in pulsed high magnetic fields up to 81~T at a temperature of 1.4~K and up to 60~T at temperatures down to 100~mK. For a field \textbf{H} applied along the magnetic easy-axis \textbf{c}, a strong sample-dependence of the low-temperature resistivity in the hidden-order phase is attributed to a high carrier mobility. The interplay between the magnetic and orbital properties is emphasized by the angle-dependence of the phase diagram, where magnetic transition fields and crossover fields related to the Fermi surface properties follow a 1/$\cos\theta$-law, $\theta$ being the angle between \textbf{H} and \textbf{c}. For $\mathbf{H}\parallel\mathbf{c}$, a crossover defined at a kink of $\rho_{x,x}$, as initially reported in [Shishido et al., Phys. Rev. Lett. \textbf{102}, 156403 (2009)], is found to be strongly sample-dependent: its characteristic field $\mu_0H^*$ varies from $\simeq20$~T in our best sample with a residual resistivity ratio RRR of $225$ to $\simeq25$~T in a sample with a RRR of $90$. A second crossover is defined at the maximum of $\rho_{x,x}$ at the sample-independent characteristic field $\mu_0H_{\rho,max}^{LT}\simeq30$~T. Fourier analyzes of SdH oscillations show that $H_{\rho,max}^{LT}$ coincides with a sudden modification of the Fermi surface, while $H^*$ lies in a regime where the Fermi surface is smoothly modified. For $\mathbf{H}\parallel\mathbf{a}$, i) no phase transition is observed at low temperature and the system remains in the hidden-order phase up to 81~T, ii) quantum oscillations surviving up to 7~K are related to a new and almost-spherical orbit - for the first time observed here - at the frequency $F_\lambda\simeq1400$~T and associated with a low effective mass $m^*_\lambda=(1\pm0.5)\cdot m_0$, and iii) no Fermi surface modification occurs up to 81~T.Comment: 11 pages, 8 figure

Upper critical magnetic field in Ba_0.68K_0.32Fe_2As_2 and Ba(Fe_0.93Co_0.07)_2As_2

We report measurements of the temperature dependence of the radio-frequency magnetic penetration depth in Ba_0.68K_0.32Fe_2As_2 and Ba(Fe_0.93Co_0.07)_2As_2 single crystals in pulsed magnetic fields up to 60 T. From our data, we construct an H-T phase diagram for the inter-plane (H || c) and in-plane (H || ab) directions for both compounds. For both field orientations in Ba_0.68K_0.32Fe_2As_2, we find a concave curvature of the Hc2(T) lines with decreasing anisotropy and saturation towards lower temperature. Taking into account Pauli spin paramagnetism we can describe Hc2(T) and its anisotropy. In contrast, we find that Pauli paramagnetic pair breaking is not essential for Ba(Fe_0.93Co_0.07)_2As_2. For this electron-doped compound, the data support a Hc2(T) dependence that can be described by the Werthamer Helfand Hohenberg model for H || ab and a two-gap behavior for H || c.Comment: 7 pages, 8 figure

An Algebraic q-Deformed Form for Shape-Invariant Systems

A quantum deformed theory applicable to all shape-invariant bound-state systems is introduced by defining q-deformed ladder operators. We show these new ladder operators satisfy new q-deformed commutation relations. In this context we construct an alternative q-deformed model that preserve the shape-invariance property presented by primary system. q-deformed generalizations of Morse, Scarf, and Coulomb potentials are given as examples

What Goes in Must Come out: Testing for Biases in Molecular Analysis of Arbuscular Mycorrhizal Fungal Communities

Arbuscular mycorrhizal (AM) fungi are widely distributed microbes that form obligate symbioses with the majority of terrestrial plants, altering nutrient transfers between soils and plants, thereby profoundly affecting plant growth and ecosystem properties. Molecular methods are commonly used in the study of AM fungal communities. However, the biases associated with PCR amplification of these organisms and their ability to be utilized quantitatively has never been fully tested. We used Terminal Restriction Fragment Length Polymorphism (TRFLP) analysis to characterise artificial community templates containing known quantities of defined AM fungal genotypes. This was compared to a parallel in silico analysis that predicted the results of this experiment in the absence of bias. The data suggest that when used quantitatively the TRFLP protocol tested is a powerful, repeatable method for AM fungal community analysis. However, we suggest some limitations to its use for population-level analyses. We found no evidence of PCR bias, supporting the quantitative use of other PCR-based methods for the study of AM fungi such as next generation amplicon sequencing. This finding greatly improves our confidence in methods that quantitatively examine AM fungal communities, providing a greater understanding of the ecology of these important fungi

Mycorrhiza-induced resistance: more than the sum of its parts?

Plants can develop an enhanced defensive capacity in response to infection by arbuscular mycorrhizal fungi (AMF). This ‘mycorrhiza-induced resistance’ (MIR) provides systemic protection against a wide range of attackers and shares characteristics with systemic acquired resistance (SAR) after pathogen infection and induced systemic resistance (ISR) following root colonisation by non-pathogenic rhizobacteria. It is commonly assumed that fungal stimulation of the plant immune system is solely responsible for MIR. In this opinion article, we present a novel model of MIR that integrates different aspects of the induced resistance phenomenon. We propose that MIR is a cumulative effect of direct plant responses to mycorrhizal infection and indirect immune responses to ISR-eliciting rhizobacteria in the mycorrhizosphere

Quenched nematic criticality separating two superconducting domes in an iron-based superconductor under pressure

The nematic electronic state and its associated nematic critical fluctuations have emerged as potential candidates for superconducting pairing in various unconventional superconductors. However, in most materials their coexistence with other magnetically-ordered phases poses significant challenges in establishing their importance. Here, by combining chemical and hydrostatic physical pressure in FeSe$_{0.89}$S$_{0.11}$, we provide a unique access to a clean nematic quantum phase transition in the absence of a long-range magnetic order. We find that in the proximity of the nematic phase transition, there is an unusual non-Fermi liquid behavior in resistivity at high temperatures that evolves into a Fermi liquid behaviour at the lowest temperatures. From quantum oscillations in high magnetic fields, we trace the evolution of the Fermi surface and electronic correlations as a function of applied pressure. We detect experimentally a Lifshitz transition that separates two distinct superconducting regions: one emerging from the nematic electronic phase with a small Fermi surface and strong electronic correlations and the other one with a large Fermi surface and weak correlations that promotes nesting and stabilization of a magnetically-ordered phase at high pressures. The lack of mass divergence suggests that the nematic critical fluctuations are quenched by the strong coupling to the lattice. This establishes that superconductivity is not enhanced at the nematic quantum phase transition in the absence of magnetic order.Comment: 4 figures, 9 page

Evidence for antiferromagnetism coexisting with charge order in the trilayer cuprate HgBa2_2Ca2_2Cu3_3O8+δ_{8+ \delta}

Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO$_2$ planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+ \delta}$ and we report the first quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. The presence of an ordered antiferromagnetic metallic state that extends deep in the superconducting phase is a key ingredient that supports magnetically mediated pairing interaction in cuprates.Comment: 6+5 pages, 4+6 figure