Spectral shift function for operators with crossed magnetic and electric fields

We obtain a representation formula for the derivative of the spectral shift function $\xi(\lambda; B, \epsilon)$ related to the operators $H_0(B,\epsilon) = (D_x - By)^2 + D_y^2 + \epsilon x$ and $H(B, \epsilon) = H_0(B, \epsilon) + V(x,y), \: B > 0, \epsilon > 0$. We establish a limiting absorption principle for $H(B, \epsilon)$ and an estimate ${\mathcal O}(\epsilon^{n-2})$ for $\xi'(\lambda; B, \epsilon)$, provided $\lambda \notin \sigma(Q)$, where $Q = (D_x - By)^2 + D_y^2 + V(x,y).

Localized spectral asymptotics for boundary value problems and correlation effects in the free Fermi gas in general domains

We rigorously derive explicit formulae for the pair correlation function of the ground state of the free Fermi gas in the thermodynamic limit for general geometries of the macroscopic regions occupied by the particles and arbitrary dimension. As a consequence we also establish the asymptotic validity of the local density approximation for the corresponding exchange energy. At constant density these formulae are universal and do not depend on the geometry of the underlying macroscopic domain. In order to identify the correlation effects in the thermodynamic limit, we prove a local Weyl law for the spectral asymptotics of the Laplacian for certain quantum observables which are themselves dependent on a small parameter under very general boundary conditions

Semiclassical structure of chaotic resonance eigenfunctions

We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as $\hbar\to 0$ on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates $\{\psi(\hbar)\}_{\hbar\to 0}$ is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker map, for which the probability density in position space is observed to have self-similarity properties.Comment: 4 pages, 4 figures; some minor corrections, some changes in presentatio

Classical limit of the quantum Zeno effect

The evolution of a quantum system subjected to infinitely many measurements in a finite time interval is confined in a proper subspace of the Hilbert space. This phenomenon is called "quantum Zeno effect": a particle under intensive observation does not evolve. This effect is at variance with the classical evolution, which obviously is not affected by any observations. By a semiclassical analysis we will show that the quantum Zeno effect vanishes at all orders, when the Planck constant tends to zero, and thus it is a purely quantum phenomenon without classical analog, at the same level of tunneling.Comment: 10 pages, 2 figure

Bio-Waste Aloe vera Leaves as an efficient adsorbent for Titan Yellow from Wastewater: Structuring of a novel adsorbent using Plackett-Burman factorial design

Titan yellow (TY), a triazene azo dye, was removed from contaminated wastewater samples using a green adsorbent recycled from Aloe vera leaves (AV) waste. Two adsorbents were developed-air-dried Aloe vera (ADAV) and thermally treated Aloe vera (TTAV). Adsorption efficacy of both adsorbents was assessed in terms of percent removal (%R) of TY and adsorption capacity (qe). ADAV had a better performance compared to TTAV. Plackett-Burman design (PBD) was exploited to establish the experimental pattern of the study. Four variables were studied: pH, adsorbent dose (AD), dye concentration (DC), and stirring time (ST). Analysis of variance (ANOVA) at 95.0 confidence interval (CI), control, and quality charts helped establish regression model(s). Characterization of both adsorbents was performed using FT-IR/Raman spectroscopy together with TGA/dTGA and SEM/energy dispersive X-ray spectroscopy (EDX) analyses. Textural properties were determined using nitrogen adsorption isotherms at 77 K. Results showed that the surface areas of ADAV and TTAV300 were 3.940 and 7.076 m2/g, respectively. Raman analysis showed that the TTAV had clear Dand G-bands. Equilibrium studies revealed that data were well fitted to Freundlich isotherm with a maximum adsorption capacity of 55.25 mg/g using Langmuir equation, and the adsorption was physisorption. Adsorption followed a pseudo-second order that occurred in two steps-diffusion and then adsorption. - 2019 by the authors.The project members would like to extend their special thanks to the Central Lab Unit (CLU) at the Qatar University. This work was made possible by Qatar University Internal Student Grant [QUST-2-CAS-2019-18] from Qatar University. The statements made herein are solely the responsibility of the authors. The publication of this article was funded by the Qatar National LibraryScopu

Fractal Weyl law for quantum fractal eigenstates

The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate.Comment: 4 pages, 5 figs, minor modifications, research at http://www.quantware.ups-tlse.fr

Poly(ethylene) glycols and mechanochemistry for the preparation of bioactive 3,5-disubstituted hydantoins

International audienceMechanochemistry was effective for the preparation of 3,5-disubstituted hydantoins from a-amino methyl esters, using either 1,1 0-carbonyldiimidazole (CDI) or alkyl isocyanates. The preparation of the antimicrobial additives, 3-allyl-5,5 0-dimethyl hydantoin (ADMH) and 1-chloro-3-ethyl-5,5 0-dimethyl hydantoin (CEDMH) were performed by grinding. A chlorination reaction, never described before by mechanochemistry was achieved by Ca(ClO) 2 , while the preparation of the bioactive anticonvulsant marketed drug ethotoin was achieved by a novel approach based on poly(ethylene) glycol (PEGs) assisted grinding

Probabilistic Weyl laws for quantized tori

For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical experiments the same Weyl law also holds for ``false'' eigenvalues created by pseudospectral effects.Comment: 33 pages, 3 figures, v2 corrected listed titl

Quantum electrodynamics of relativistic bound states with cutoffs

We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.Comment: To appear in "Journal of Hyperbolic Differential Equation