A unified approach to Darboux transformations

We analyze a certain class of integral equations related to Marchenko equations and Gel'fand-Levitan equations associated with various systems of ordinary differential operators. When the integral operator is perturbed by a finite-rank perturbation, we explicitly evaluate the change in the solution. We show how this result provides a unified approach to Darboux transformations associated with various systems of ordinary differential operators. We illustrate our theory by deriving the Darboux transformation for the Zakharov-Shabat system and show how the potential and wave function change when a discrete eigenvalue is added to the spectrum.Comment: final version that will appear in Inverse Problem

Exploring perinatal asphyxia by metabolomics

Brain damage related to perinatal asphyxia is the second cause of neuro-disability worldwide. Its incidence was estimated in 2010 as 8.5 cases per 1000 live births worldwide, with no further recent improvement even in more industrialized countries. If so, hypoxic-ischemic encephalopathy is still an issue of global health concern. It is thought that a consistent number of cases may be avoided, and its sequelae may be preventable by a prompt and efficient physical and therapeutic treatment. The lack of early, reliable, and specific biomarkers has up to now hampered a more effective use of hypothermia, which represents the only validated therapy for this condition. The urge to unravel the biological modifications underlying perinatal asphyxia and hypoxic-ischemic encephalopathy needs new diagnostic and therapeutic tools. Metabolomics for its own features is a powerful approach that may help for the identification of specific metabolic profiles related to the pathological mechanism and foreseeable outcome. The metabolomic profiles of animal and human infants exposed to perinatal asphyxia or developing hypoxic-ischemic encephalopathy have so far been investigated by means of 1H nuclear magnetic resonance spectroscopy and mass spectrometry coupled with gas or liquid chromatography, leading to the identification of promising metabolomic signatures. In this work, an extensive review of the relevant literature was performed

Calibration-Free and High-Sensitivity Microwave Detectors Based on InAs/InP Nanowire Double Quantum Dots

At the cutting-edge of microwave detection technology, novel approaches which exploit the interaction between microwaves and quantum devices are rising. In this study, microwaves are efficiently detected exploiting the unique transport features of InAs/InP nanowire double quantum dot-based devices, suitably configured to allow the precise and calibration-free measurement of the local field. Prototypical nanoscale detectors are operated both at zero and finite source-drain bias, addressing and rationalizing the microwave impact on the charge stability diagram. The detector performance is addressed by measuring its responsivity, quantum efficiency and noise equivalent power that, upon impedance matching optimization, are estimated to reach values up to approximate to 2000 A W-1, 0.04 and root HZ, respectively. The interaction mechanism between the microwave field and the quantum confined energy levels of the double quantum dots is unveiled and it is shown that these semiconductor nanostructures allow the direct assessment of the local intensity of the microwave field without the need for any calibration tool. Thus, the reported nanoscale devices based on III-V nanowire heterostructures represent a novel class of calibration-free and highly sensitive probes of microwave radiation, with nanometer-scale spatial resolution, that may foster the development of novel high-performance microwave circuitries

Exact Solutions to the Sine-Gordon Equation

A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are exponentially asymptotic to integer multiples of $2\pi$ as $x\to\pm\infty.$ The solution formulas are expressed explicitly in terms of a real triplet of constant matrices. The method presented is generalizable to other integrable evolution equations where the inverse scattering transform is applied via the use of a Marchenko integral equation. By expressing the kernel of that Marchenko equation as a matrix exponential in terms of the matrix triplet and by exploiting the separability of that kernel, an exact solution formula to the Marchenko equation is derived, yielding various equivalent exact solution formulas for the sine-Gordon equation.Comment: 43 page

ZnSe Nanoparticles for Thermoelectrics: Impact of Cu-Doping

The present study investigates the impact of copper doping on the thermoelectric properties of zinc selenide (ZnSe) nanoparticles synthesized by the hydrothermal method. Nanoparticle samples with varying copper concentrations were prepared and their thermoelectric performances were evaluated by measuring the electrical transport properties, the Seebeck coefficient, and extracting the power factor. The results demonstrate that the thermoelectric properties of Cu-doped ZnSe nanoparticles are significantly enhanced by doping, mainly as an effect of an improved electrical conductivity, providing a promising avenue for energy applications of these nanomaterials. To gain further insights into the fundamental mechanisms underlying the observed improvements in thermoelectric performance of the samples, the morphological, structural, and vibrational properties were characterized using a combination of scanning electron microscopy, X-ray diffraction, and Raman spectroscopy

Microwave-Assisted Tunneling in Hard-Wall InAs/InP Nanowire Quantum Dots

With downscaling of electronic circuits, components based on semiconductor quantum dots are assuming increasing relevance for future technologies. Their response under external stimuli intrinsically depend on their quantum properties. Here we investigate single-electron tunneling in hard-wall InAs/InP nanowires in the presence of an off-resonant microwave drive. Our heterostructured nanowires include InAs quantum dots (QDs) and exhibit different tunnel-current regimes. In particular, for source-drain bias up to few mV Coulomb diamonds spread with increasing contrast as a function of microwave power and present multiple current polarity reversals. This behavior can be modelled in terms of voltage fluctuations induced by the microwave field and presents features that depend on the interplay of the discrete energy levels that contribute to the tunneling process

Exact solutions to the focusing nonlinear Schrodinger equation

A method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line. An explicit formula and its equivalents are presented to express such exact solutions in a compact form in terms of matrix exponentials. Such exact solutions can alternatively be written explicitly as algebraic combinations of exponential, trigonometric, and polynomial functions of the spatial and temporal coordinates.Comment: 60 pages, 18 figure